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GATE CS - 1991www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com SECTION - A 1. Fill in the blanks: (i) For the digital in figure, the expression for the output f is _________ a b x f y (ii) In interleaved memory organization, consecutive words are stored in consecutive memory modules in ________ interleaving, whereas consecutive words are stored within the module in ________ interleaving. (iii) Consider the number given by the decimal expression: 163 * 9 + 162 * 7 + 16 * 5 + 3 The number of 1’s in the unsigned binary representation of the number is ________. (iv) Using the 8087 arithmetic coprocessor with the 8087 CPU requires that the 8087 CPU is operated ________. (v) When two 4-bit binary number A = a3 a2 a1 a0 and B = b3 b2 b1b0 are multiplied, the digit c1 of the product C is given by _________ (vi) Consider the following PASCAL program segment: if i mode 2 = 0 then while i > = 0 do begin i:=i div 2; if i mod 2 < > 0 do then i:=i – 1 else i:=i – 2 end An appropriate loop-invariant for the while-loop is ______ (vii) The minimum number of comparisons required to sort 5 elements is _____ Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (viii) The weighted external path length of the binary tree in figure is _____ 15 10 9 2 7 5 4 (ix) If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ______ 7 3 1 5 6 4 8 2 (x) Consider the following recursive definition of fib: fib (n) : = if n = 0 then 1 else if n = 1 than 1 else fib (n – 1) + fib ( n – 2) The number of times fib is called (including the first call) for an evaluation of fib (7) is ___________ (xi) The arithmetic expression : ( a + b ) * c − d / e * *f is to be evaluated on a twoaddress machine, where each operands, the number of registers required to evaluate this expression is ______. The number of memory access of operand is __________. (xii) A given set of processes can be implemented by using only parbegin/parend statement, if the precedence graph of these processes is ________ (xiii) The number of integer-triples (i.j.k) with 1 ≤ i.j.k ≤ 300 such that i + j + k is divisible by 3 is ________ (xiv) If the longest chain in a partial order is of length n then the partial order can be written as a ______ of n antichains. (xv) The maximum number of possible edges in an undirected graph with a vertices and k components is ________. Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 2. Match the pairs in the following questions by writing the corresponding letters only. (i) (A) IEEE 488 (P) specifies the interface for connecting a single device (B) IEEE 796 (Q) specifies the bus standard for connecting a computer to other devices including CPU’s (C) IEEE 696 (R) specifies the standard for an instrumentation bus (D) RS232-C (S) specifies the bus standard for the “backplane” bus called multibus. (ii) For the 8086 microprocessor: (A) RQ/GT (P) Used by processor for holding the bus for consecutive instruction cycles. (B) LOCK (Q) Used for extending the memory or I/O cycle times (C) HOLD (R) Used for getting hold of processor bus in minimum bus mode (D) READY (S) Used for requesting processor bus in minimum bus mode. (iii) (A) Buddy system (P) Run-time type specification (B) Interpretation (Q) Segmentation (C) Pointer type (R) Memory allocation (D) Virtual memory (S) Garbage collection (iv) (A) The number distinct binary trees with n nodes (P) n! 2 (B) The number of binary strings of length of 2n with an equal number of 0’s and 1’s 3n (Q) n (C) The number of even permutations of n objects 2n (R) n (D) The number of binary strings of length 6m which are palindromes with 2n 0’s. (S) 1 2n n + 1 n Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 3. Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: (i) The advantages of CMOS technology over a MOS is: (a) lower power dissipation (b) greater speed (c) smaller chip size (d) fewer masks for fabrication (e) none of the above (ii) Advantage of synchronous sequential circuits over asynchronous ones is: (a) faster operation (b) ease of avoiding problems due to hazards (c) lower hardware requirement (d) better noise immunity (e) none of the above (iii) The total size of address space is a virtual memory systems is limited by (a) the length of MAR (b) the available secondary storage (c) the available main memory (d) all of the above (e) none of the above (iv) The TRAP interrupt mechanism of the 8085 microprocessor: (a) executes an instruction supplied by an external device through the INTA signal (b) executes an instruction from memory location 20H (c) executes a NOP (d) none of the above (v) The ALE line of an 8085 microprocessor is used to: (a) latch the output of an I/O instruction into an external latch (b) deactivate the chip-select signal from memory devices (c) latch the 8 bits of address lines AD7-AD0 into an external latch (d) find the interrupt enable status of the TRAP interrupt (e) None of the above Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (vi) Kruskal’s algorithm for finding a minimum spanning tree of a weighted graph G with vertices and m edges has the time complexity of: ( ) (a) O n2 (b) O ( mn ) (c) O ( m + n ) (d) O ( m log n ) ( ) (e) O m2 (vii) The following sequence of operations is performed on a stack: PUSH (10), PUSH (20), POP, PUSH (10), PUSH (20), POP, POP, POP, PUSH (20), POP The sequence of values popped out is: (a) 20, 10, 20, 10, 20 (b) 20, 20, 10, 10, 20 (c) 10, 20, 20, 10, 20 (d) 20, 20, 10, 20, 10 (viii) Consider the following Pascal function: function X (M:integer) : integer; var i:integer; begin i = 0; while i*i<M do i; =i+1 X;=i end The function call X(N), if N is positive, will return (a) (b) ( N) ( N) +1 (c) N (d) N + 1 (e) None of the above (ix) A “link editor” is a program that: (a) matches the parameters of the macro-definition with locations of the parameters of the macro call Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (b) matches external names of one program with their location in other programs (c) matches the parameters of subroutine definition with the location of parameters of subroutine call. (d) acts as link between text editor and the user (e) acts as a link between compiler and user program. (x) Indicate all the true statements from the following: (a) Recursive descent parsing cannot be used for grammar with left recursion. (b) The intermediate form the representing expressions which is best suited for code optimization is the post fix form. (c) A programming language not supporting either recursion or pointer type does not need the support of dynamic memory allocation. (d) Although C does not support call by name parameter passing, the effect can be correctly simulated in C. (e) No feature of Pascal violates strong typing in Pascal. (xi) Indicate all the false statements from the statements given below: (a) The amount of virtual memory available is limited by the availability of secondary storage. (b) Any implementation of a critical section requires the use of an indivisible machine-instruction, such as test-and-set. (c) The LRU page replacement policy may cause hashing for some type of programs. (d) The best fit techniques for memory allocation ensures the memory will never be fragmented. (xii) If F1 , F2 and F3 are propositional F1 ∧ F2 → F3 and F1 ∧ F1 →~ F2 are both formulae tautologies, such then which that of the following is true: (a) Both F1 and F2 are tautologies (b) The conjunction F1 ∧ F2 is not satisfiable (c) Neither is tautologous (d) Neither is satisfiable (e) None of the above (xiii) Let r = 1 (1 + 0 ) *, s = 11 * 0 and t = 1 * 0 be three regular expressions. Which one of the following is true? (a) L ( s ) ⊆ L ( r ) and L ( s ) ⊆ L ( t ) (b) L ( r ) ⊆ L ( s ) and L ( s ) ⊆ L ( t ) Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (c) L ( s ) ⊆ L ( t ) and L ( s ) ⊆ L ( r ) (d) L ( t ) ⊆ L ( s ) and L ( s ) ⊆ L ( r ) (e) None of the above (xiv)Which one of the following is the strongest correct statement about a finite language over some finite alphabet ∑ ? (a) It could be undecidable (b) It is Turing-machine recognizable (c) It is a context-sensitive language (d) It is a regular language (e) None of the above 4. Give short answers to the following questions: (i) Convert the following Pascal statement to a single assignment statement: if x > 5 they y:=true else y:=false; (ii) Convert the Pascal statement repeat S until B; into an equivalent Pascal statement that uses the while construct. (iii) Obtain the optimal binary search tree with equal probabilities for the identifier set ( a1 , a2 , a3 ) = (if, stop,while ) (iv) If a finite axiom system A for a theory is complete and consistent, then is every subsystem of A complete and consistent? Explain briefly. SECTION – B 5. (a) Analyse the circuit in figure and complete the following table: a b 0 0 1 1 0 1 0 1 Qn a Q b Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (b) Find the minimum sum of products form of the logic function. f ( A, B, C , D ) = ∑ m (0, 2, 8,10,15) + ∑ d (3,11,12,14) Where m and d denote the min-terms and don’t cares respectively. (c) Find the maximum clock frequency at which the counter in figure, can be operated. Assume that the propagation delay through each flip-flop and AND gate is 10 ns. Also assume that the setup time for the JK inputs of the flipflops is negligible. 1 J0 K0 J1 Q0 Q1 J2 Q2 CK K1 CK K2 CK Clock 6. (a) Using D flip-flop and gates, design a parallel-in/serial-out shift register that shifts data from left to right with the following input lines: (i) Clock CLK (ii) Three parallel data inputs A, B, c (iii) Serial input S (iv) Control input load / SHIFT . (b) Design a 1024 bit serial-in/serial-out unidirectional shift register using a 1K × 1 bit RAM with data input Din , data output Dout and control input READ/ WRITE . You may assume that availability of standard SSI and MSI components such as gates, registers and counters. 7. It is required to design a hardwired controller to handle the fetch cycle of a single address of an indexed instruction should be derived in the fetch cycle itself. Assume that the lower order 8 bits of an instruction constitute the operand field. (a) Give the register transfer sequence for realizing the above instruction fetch cycle. (b) Draw the logic schematic of the hardwired controller including the date path. 8. (a) Consider an 8085 based system operating with the following specification: Crystal frequency : 6 MHz ROM map : 0000 through 07FF Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1991 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com RAM map : 1000 through 17 FF: ROM requires one wait state. RAM requires no wait state. Determine the instruction cycle time for each of the following instructions: (i) ORI A, 22 (ii) DCR M Assume the following initial conditions of the CPU registers (in hex) for each of the instructions: A = 55, B = AA, C = F7, D = 10, H = 10, L = FF, PC = 0200, SP = 17FO. (b) Developing an output port interface (draw a block schematic) for an 8085 based system with a demultiplexed address bus which incorporates a handshake protocol as per the timing diagram given in figure. The interface should include a status input port at I/O address 40H which reads the INTERRUPT and BUFFFULL signals through the most significant bit and the least significant bit, respectively. The output data port is at the same I/O address 40H and is activated by a write operation. Assume the availability of SSI and MSI level components only. Write a short program segment which performs a 200 H byte programmed I/O data transfer to the device from memory address 3400 H, PORT-DATE OUTPUT WR OF PORT 40 H INTERRUPT BUFFULL STROBE INPUT FROM DEVICE 9. (a) Consider the following pseudo-code (all data items are of type integer): Procedure P (a, b, c); a:=2; c:=a+b; end {P} begin x:=1 y:=5; Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. begin a:=1.com Join discussion of this test paper at http://forum. Q.GATE CS . end {Q}. P. ‘b=’.x*y.gateforum. visit www. P(x. if (i) static scope rules and (ii) dynamic scope rules are used Var. 10. Write (‘x=’. and more. convert the grammar into one which does not generate expressions with redundant parentheses.b) end. b:=10 end {P}. Procedure P. var a. Do this with minimum number of changes to the given production rules and adding at most one more production rule. a. give an unambiguous grammar that gives/precedence over (b) Does the grammar allow expressions with redundant parentheses as in (id/id) or in id-(id/id)? If so. Write (‘a =’.com Think GATE Think GATE Forum .gatementor. b : inteer.com z:=100.2007 conducted by GATE Forum in over 25 cities all over India. if the parameters are passed to the procedure P by (i) value. b:=2.z). For more details.x.z) end: Determine its output. Join All India Mock GATE Classroom Test Series . b : integer.z=’. procedure Q. Percentile. interaction with IISc alumni in our online discussion forums. All India Rank. a. Consider the following grammar for arithmetic expression using binary operators – and/which are not associative: E → E −T T T → T F F F → ( E ) id (E is the start symbol) (a) Is this grammar unambiguous? If so.1991 www. indicate the output. what is the relative precedence between – and/if not. (ii) reference and (iii) name. (b) For the following pseudo-code. a:=5. com Join discussion of this test paper at http://forum. a database consists of the following relations: SUPPLIER (SCODE.2007 conducted by GATE Forum in over 25 cities all over India. QJY) Join All India Mock GATE Classroom Test Series . PDESC. (a) Does the scheme ensure mutual exclusion in the critical section? Briefly explain.com Think GATE Think GATE Forum .gateforum.1991 www. For more details. flag [i]:=true end end critical section if turn = i then turn:=j. interaction with IISc alumni in our online discussion forums. All India Rank. Percentile. flag [i] : true end. 12. k : if flag [k] then begin flag [i]:=false. repeat flag [i]:=true. Consider the following scheme for implementing a critical section in a situation with three processes Pj and Pk . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Suppose.gatementor. explain and suggest modifications to the code to solve this problem. PRNAME. CITY) PART (PCODE. flag [i]:=false non-critical section until false.com 11. CITY) PROJECTS (PRCODE. (b) Is there a situation in which a waiting process can never enter the critical section? If so.GATE CS . PNAME. while flag [j] or flag [k] do case turn of j : if flag [j] then begin flag [i]:=false. and more. SNAME. PCODE. visit www.gateforum. while turn ≠ i do skip. while turn ≠ i do skip. PRCODE. CITY) SPRR (SCODE. Pi . x ) ) ∧ ( Ax ) ( Ay ) ( Az ) ( R ( x. 14. Give a brief analysis for the time-complexity of your algorithm).GATE CS . interaction with IISc alumni in our online discussion forums. (ii) Get PRCODE values for projects supplied by at least one supplier not in the same city. but do not print triples in which the two CITY values are the same. (ii) Print all triples (CITY. z ) → R ( x.gatementor.1991 www. Give an optimal algorithm is pseudo-code for sorting a sequence of n numbers which has only k distinct numbers (k is not known a Priori. Percentile. such that a supplier in the first city supplies the specified part to a project in the second city. visit www. y ) →~ R ( y. PCODE. (a) Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a*b. y ) ∧ R ( y . and more. (c) Outline a procedure in pseudo-code to delete an arbitrary node from such a binary tree with n nodes that preserves the structure. Consider the binary tree in Figure: 1 18 5 20 7 25 13 27 11 9 15 17 (a) What structure is represented by the binary tree? (b) Give the different steps for deleting the node with key 5 so that the structure is preserved.gateforum.com (a) Write SQL programs corresponding to the following queries: (i) Print PCODE value for parts supplied to any project in DELHI by a supplier in DELHI.gateforum. All India Rank. For more details. 13.com Think GATE Think GATE Forum . (b) Consider the following first order formula: ( Ax ) ( Ey ) R ( x. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. z ) ) ∧ ( Ax ) ~ R ( x. x ) Join All India Mock GATE Classroom Test Series . (b) Write algebraic solutions to the following: (i) Get SCODE values for suppliers who supply to both projects PR1 and PR2.com Join discussion of this test paper at http://forum.2007 conducted by GATE Forum in over 25 cities all over India. What is the worst-case time-complexity of your procedure? 15. y ) ∧ ( Ax ) ( Ay ) ( R ( x. CITY). 1991 www. (a) Show that Turing machines. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (b) Let L be the language of all binary strings in which the third symbol from the right is a1. and the property that every prefix and w has atleast as many 0’s as 1’s.gatementor. recognize preasely the class or regular languages. 17.com Think GATE Think GATE Forum .2007 conducted by GATE Forum in over 25 cities all over India. (b) Show that all vertices in an undirected finite graph cannot have distinct degrees. Percentile. For more details.gateforum. which have a read only input tape and constant size work tape.com (A-universal quantifier and E-existential quantifier) Does it have finite models? Is it satisfiable? Is so.GATE CS . give a countable model for it. if the graph has at least two vertices. 16. (a) Find the number of binary strings w of length 2n with an equal number os 1’s and 0’s. All India Rank. and more.com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums. Give a non-deterministic finite automaton that recognizes L. How many states does the minimized equivalent deterministic finite automaton have? Justify your answer briefly? Join All India Mock GATE Classroom Test Series . visit www.gateforum. the size of address field is 4-bits. Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: (i) The operation which is commutative but not associative is: (a) AND (b) OR (c) EX-OR (d) NAND (ii) All digital circuits can be realized using only (a) Ex-OR gates (b) Multiplexers (c) Half adders (d) OR gates Join All India Mock GATE Classroom Test Series . (vi) In an 11-bit computer instruction format.com Join discussion of this test paper at http://forum.2007 conducted by GATE Forum in over 25 cities all over India.com SECTION – A 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. It accomplishes reliable data transfer because for every data item sent by the transmitter __________.gateforum. For more details. The extra parity bits required would be ________ and the 3-bit error detection is possible because the code has a minimum distance of ________ (iii) Many microprocessors have a specified lower limit on clock frequency (apart from the maximum clock frequency limit) because ______ (iv) Many of the advanced microprocessors prefetch instructions and store it in an instruction buffer to speed up processing.com Think GATE Think GATE Forum .1992 www. interaction with IISc alumni in our online discussion forums. Percentile. Fill in the blanks: (i) The Boolean function in sum of products form where K-map is given below (figure) is:___________ C 0 B 1 0 1 0 1 A A (ii) Consider a 3-bit error detection and 1-bit error correction hamming code for 4-bit date.GATE CS . The computer uses expanding OP code technique and has 5 two-address instructions and 32 two-address instructions and the number of zero-address instructions it can support is _________ (vii) Macro expansion is done in pass one instead of pass two in a pass macro assembler because _________ (viii) The purpose of instruction location counter in an assembler is _______ (ix) Complexity of Kruskal’s algorithm for finding the minimum spanning tree of an undirected graph containing n vertices and m edges if the edges are sorted is __________ (x) Maximum number of edges in a planar graph with n vertices is ________ 2.gatementor. All India Rank.gateforum. visit www. This speed up is achieved because _________ (v) A simple and reliable data transfer can be accomplished by using the ‘handshake protocol’. and more. 6 vertices (b) 6 edges. For more details.com Join discussion of this test paper at http://forum.com Think GATE Think GATE Forum .gateforum. construct (b) while …… construct (c) case …… construct (d) call …… construct (v) Start and stop bits do not contain an ‘information’ but are used in serial communication for (a) Error detection (b) Error correction (c) Synchronization (d) Slowing down the communications (vi) Which of the following problems is not NP-hard? (a) Hamiltonian circuit problem (b) The 0/1 Knapsack problem (c) Finding bi-connected components of a graph (d) The graph colouring problem (vii) A 2-3 tree is tree such that (a) all internal nodes have either 2 or 3 children (b) all paths from root to the leaves have the same length The number of internal nodes of a 2-3 tree having 9 leaves could be (a) 4 (b) 5 (c) 6 (d) 7 (viii) A non-planar graph with minimum number of vertices has (a) 9 edges. 5 vertices (d) 9 edges. then ….gatementor. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. This instruction can be useful in implementing. Percentile. This is not a very commonly used instruction as it changes the flow of control in rather ‘unstructured’ fashion. else ….com (iii) Bit-slice processors (a) Can be cascaded to get any desired word length processor (b) speed of operation is independent of the word length configured (c) don’t contain anything equivalent of program counter in a ‘normal’ microprocessor (d) contain only the data path of a ‘normal’ CPU (iv) PCHL is an instruction in 8085 which transfers the contents of the register pair HL to PC.gateforum. 4 vertices (c) 10 edges.2007 conducted by GATE Forum in over 25 cities all over India. All India Rank. visit www.GATE CS ..1992 www.. 5 vertices (ix) Following algorithm(s) can be used to sort n integers in the range 1 K n3 in 0 (n) time (a) Heapsort (b) Quicksort (c) Mergesort (d) Radixsort Join All India Mock GATE Classroom Test Series . and more. (a) if ……. interaction with IISc alumni in our online discussion forums. Which of the following statements is/are true? (a) FOLLOW(A) and FOLLOW (A) may be different.com Think GATE Think GATE Forum . (xv) Which of the following predicate calculus statements is/are valid: (a) ( ∀x ) P ( x ) ∨ ( ∀x ) Q ( x ) → ( ∀x ) {P ( x ) ∨ Q ( x )} (b) ( ∃x ) P ( x ) ∧ ( ∃x ) Q ( x ) → ( ∃x ) {P ( x ) ∧ Q ( x )} (c) ( ∀x ) {P ( x ) ∨ Q ( x )} → ( ∀x ) P ( x ) ∨ ( ∀x ) Q ( x ) (d) ( ∃x ) {P ( x ) ∨ Q ( x )} →~ ( ∀x ) P ( x ) ∨ ( ∃x ) Q ( x ) Join All India Mock GATE Classroom Test Series .1992 www. and more. For more details.2007 conducted by GATE Forum in over 25 cities all over India.com (x) At a particular time of computation the value of a counting semaphore is 7.gatementor. We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word “sentential” by “left sentential” and “right most sentential” respectively in the definition of FOLLOW(A). (b) FOLLOW(A) and FOLLOW (A) are always the same. interaction with IISc alumni in our online discussion forums. (c) All the three sets are identical. Then 20 P operations and 15 V operations were completed on this semaphore.gateforum. All India Rank. (d) None of the above (xiii) For a context-free grammar. Each process may need 3 tape drives. The resulting value of the semaphore is: (a) 42 (b) 2 (c) 7 (d) 12 (xi) A computer system has 6 tape drives. visit www.gateforum. (b) The secondary memory device in a virtual memory system (c) A line printer used to print the output of a number of jobs. with n process completing for them.com Join discussion of this test paper at http://forum. Percentile. FOLLOW(A) is the set of terminals that can appear immediately to the right of non-terminal A in some “sentential” form. (b) The shift entries are identical in both the tables. (d) All the three sets are different. (d) The error entries in the tables may be different.GATE CS . (xiv) Consider the SLR(1) and LALR (1) parsing tables for a context free grammar. Which of the following statements is/are true? (a) The go to part of both tables may be different. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (c) The reduce entries in the tables may be different. The maximum value of n for which the system is guaranteed to be deadlock free is: (a) 2 (b) 3 (c) 4 (d) 1 (xii) Which of the following is an example of a spooled device? (a) The terminal used to the input data for a program being executed. gatementor. X .ENDM .gateforum.com Join discussion of this test paper at http://forum.IF NE.ENDC .ENDC .MACRO M2.ENDC . All India Rank. (a) M1 is non-deterministic finite automaton (b) M1 is a non-deterministic PDA (c) M1 is a non-deterministic Turing machine (d) For no machine M1 use the above statement true 3. X M1 X+1 M2X . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. visit www.1992 www.X .com (xvi) Which of the following is/are tautology (a) a ∨ b → b ∧ c (b) a ∧ b → b ∨ c (c) a ∨ b → ( b → c ) (d) a → b → ( b → c ) (xvii) Which of the following regular expression identifies are true? (a) r (*) = r * (c) (b) ( r + s ) * = r * +s * ( r * s *) = ( r + s ) * (d) r * s* = r * + s * (xviii) If G is a context-free grammar and w is a string of length l in L(G).IF NE.IF EQ.com Think GATE Think GATE Forum . For more details. if G is Chomsky normal form? (a) 2l (b) 2l + 1 (c) 2l .2007 conducted by GATE Forum in over 25 cities all over India. Write short answers to the following: (i) Which of the following macros can put a macro assembler into an infinite loop? .GATE CS .gateforum.ENDC .. how long is a derivation of w in G.WORD X + 1 .IF EQ. and more.1 (d) l (xix) Context-free languages are (a) closed under union (b) closed under complementation (c) closed under intersection (d) closed under Kleene closure (xx) In which of the cases stated below is the following statement true? “For every non-deterministic machine M1 there exists an equivalent deterministic machine M2 recognizing the same language“.ENDM Give an example of a call that does so. (ii) Mention the pass number for each of the following activities that occur in a two pass assembler Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums.X . X . Percentile.MACRI M1. X WORD X . gateforum. interaction with IISc alumni in our online discussion forums. using an interrupt mask register. Determine the average time of the main memory. give an input for which Quicksort takes maximum time. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. are 500 n sec and 50 n sec. (b) A priority encoder accepts three input signals (A. Percentile. B and C) and produce a two-bit output ( X1 .gateforum. A microprocessor is capable of addressing 1 megabyte of memory with a 20-bit address bus.2007 conducted by GATE Forum in over 25 cities all over India.com (a) object code generation (b) literals added literal table (c) listing printed (d) address resolution of local symbols (iii) How many edges are there in a forest with p components having n vertices in all? (iv) Assume that the last element of the set is used as partition element in Quicksort. visit www.com Join discussion of this test paper at http://forum.n] are to be sorted. All India Rank. The hit ratio for the read access only is 0. 256 K bytes of EPROM. Assume A has the highest priority followed by B and C has the lowest priority. For more details. If n distinct elements from the set [1…. in which Priority of A > Priority of B > Priority of C. Join All India Mock GATE Classroom Test Series . B and C are corrected to the bus of a computer. Three interrupt request lines INTR1. The system to be designed requires 256 K bytes of RAM. Explain what is the condition for overflow in two’s complement arithmetic.GATE CS .gatementor. input/output transfers for all three devices use interrupt control. A carry from the most significant but does not always correspond to an overflow. 6.1992 www. It is estimated that 80% of the main memory request are for read the rest for write. Draw a schematic of the priority logic.com Think GATE Think GATE Forum . in a computer system. 16 I/O devices (memory mapped I/O) and 1 K byte of EERAM (electrically erasable RAM). respectively. (c) Design a 3-bit counter using D-flip flops such that not more than one flip-flop changes state between any two consecutive states. If none of the inputs are active the output should be 00.9 and a write-through policy (where both main and cache memories are updated simultaneously) is used. design the priority encoder using 4:1 multiplexers as the main components.. (a) The access times of the main memory and the Cache memory. X 0 ) corresponding to the highest priority active input signal. (b) Three devices A. 5. INTR2 and INTR3 are available with priority of INTR1 > priority of INTR2 > priority of INTR3. (v) Which page replacement policy sometimes leads to more page faults when size of memory is increased? SECTION – B 4. (a) Consider addition in two’s complement arithmetic. design the extra logic required for interfacing EERAM. Assume that the variables have been suitably declared. Describe the algorithm in a PASCAL – like language.gateforum. Let T be a Depth First Tree of a undirected graph G. An array P indexed by vertices of G is given. following operations on the set S are to be performed in constant time (independent of cardinality of S).1992 www. Time taken by your method must be proportional to the length of the cycle. Suggest a data structure for representing a subnet S of integers from 1 to n. 8.gateforum. Consider the function F(n) for which the pseudo code is given below: Function F(n) begin F1 1 if(n=1) then F 3 else For i = 1 to n do begin C0 For j = 1 to F(n – 1) do begin C C + 1 end F1 = F1 * C end F = F1 end [n is a positive integer greater than zero] (a) Derive a recurrence relation for F(n) (b) Solve the recurrence relation for a closed form solutions of F(n). 7. Percentile. in T.GATE CS .gatementor.2007 conducted by GATE Forum in over 25 cities all over India. and more.com Join discussion of this test paper at http://forum. All India Rank.5 mHz and provides time equivalent to two clock cycles for memory read and write. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums.e.com (a) Design a memory map (to reduce decoding logic) and show the decoding logic if the components available are: Type Size Speed RAM 6K×8 140 n sec EPROM 256 K × 8 150 n sec EERAM 256 × 8 500 n sec-read 3µsec-write (b) The micro processor is operating at 12. Parent of the root is the root itself.v) of G not in T (i. For more details.com Think GATE Think GATE Forum . Join All India Mock GATE Classroom Test Series . 9.. P[V] is the parent of vertex V. visit www. Assuming control signals similar to 8085. Give a method for finding and printing the cycle formed if the edge (u. e ∈ G − T ) is now added to T. Procedure B. 3. …… end a. Procedure A.com Join discussion of this test paper at http://forum.GATE CS . Be sure to indicate which of the two procedures named A you are referring to.gateforum. Give routines for these operations in an English like language. call-by-name. Program Test. 10. (b) Show the activation records and the display structure just after the procedures called at lines marked x and y have started their execution. All India Rank. end A. or-by-value result) is the following sequence of actions truing to implement for a procedure call P (A[i]) where P (i:integer) is a procedure and A is an integer array? 1. return one element of the set S (any arbitrary element will do) (iii) ADD (X): Add integer x to set S (iv) DELETE(X): Delete integer x from S. For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. end B. begin y:A. Set A[i] to z. interaction with IISc alumni in our online discussion forums. Is the implementation correct? Explain and correct it if necessary. and more. Create a new local variable.gateforum.com Think GATE Think GATE Forum . You may assume that the data structure has been suitably initialized. 2. Procedure A. Execute the body of P using z for A[i] 4. begin x:A. Give pictorial examples of your data structure. Join All India Mock GATE Classroom Test Series . call-by-reference. begin B. You are supposed to make only small changes. say z. end Test. visit www.1992 www.com (i) MEMBER (X): (ii) FIND-ONE(S): Check whether X is the set S or not If S is not empty. Clearly state your assumptions regarding initialization. Percentile. Assign to z the value of A[i].2007 conducted by GATE Forum in over 25 cities all over India. (a) What type of parameter passing mechanism (call-by-value. All India Rank. S7 Parend.1992 www. (a) Write syntax directed definitions (semantic rules) for the following grammar to add the type of each identifier to its entry in the symbol table during semantic analysis. and more.gateforum. begin S6:S8 End parend end. For more details. (a) Draw the precedence graph for the concurrent program given below: S1 parbegin begin S2:S4 end.com Join discussion of this test paper at http://forum. Assume the usual rules of precedence of the operators. d. and e was referend at time t = -2. interaction with IISc alumni in our online discussion forums. parbegin S5. T int T real L L.gatementor.gateforum. e}. id L id (b) Write 3-address intermediate code (quadruples) for the following boolean expression in the sequence as it would be generated by a compiler.GATE CS . S9 (b) Let the page reference and the working set window be c c d b c e c e a d and 4. D TL. Percentile. begin S3. The initial working set at time t = 0 contains the pages {a. where a was referenced at time t = 0. determine the total number of page faults and the average number of page frames used by computing the working set at each reference. Rewriting the grammar is not permitted and semantic rules are to be added to the ends of productions only. d was referenced at time t = -1. Partial evaluation of Boolean expressions is not permitted.com 11.2007 conducted by GATE Forum in over 25 cities all over India. (a + b) > (c + d) or a > c and b < d 12. visit www.com Think GATE Think GATE Forum . Join All India Mock GATE Classroom Test Series . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. respectively. such that a2 = e (b) Consider the set of integers {1.GATE CS .gatementor. For more details. (a) If G is a group of even order. Which of the following three statements are true? Prove your answer. then show that there exists an element a ≠ e.com Join discussion of this test paper at http://forum. SNACKS) LIKES (CUSTOMER. the second tells which snacks each hotel serves and the last indicates which snacks are liked by each customer. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (b) Suppose we have a database consisting of the following three relations: FREQUENTS (CUSTOMER.2007 conducted by GATE Forum in over 25 cities all over India. visit www.1992 www.2. 16. Express the following query in relational algebra: print the hotels that serve a snack that customer Rama likes. and more. HOTEL) SERVES (HOTEL. a is a constant and P.3.gateforum. All India Rank. (b) Let S be the set of all integers and let n > 1 be a fixed integer.gateforum. (iii) Regular languages are closed under infinite union. interaction with IISc alumni in our online discussion forums. SNACKS) The first indicates the hotels each customer visits. (ii) The language {O′′ n is a prime} is not regular. a R biff a-b is a multiple of n.com Think GATE Think GATE Forum . 6. 24} together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor).com 13. R are monadic predicates. the identity in g. Which of the following algebraic structures does this represent? 15. (i) The union of two recursive languages is recursive. A → = B ) or resolution to show that the following set is inconsistent: (1) Q ( x ) → P ( x ) V ~ R ( a ) (2) R ( a ) ~ Q ( a ) (3) Q ( a ) (4) ~ P ( y ) Where x and y are universally quantified variables. Show that R is an equivalence relation and finds its equivalence classes for n = 5. Define for a. (i) group (ii) ring (iii) field (iv) lattice (a) Uses Modus ponens ( A. (a) How is redundancy reduced in the following models? (i) Hierarchical (ii) Network (iii) Relational Write a one line answer in each case. 14. 8. Percentile. Join All India Mock GATE Classroom Test Series . b ∈ S. Q. 4.12. GATE CS . 0. 0 ) (c) (0.com SECTION .A 1. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up. we get the sum of the series.1 The eigen vector(s) of the matrix 0 0 α 0 0 0 .gateforum.3 (b) non-linear (c) homogeneous (d) of degree two Simpson’s rule for integration gives exact result when f ( x ) is a polynomial of degree (a) 1 1. 0. In questions 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.5 (b) 2 (c) 3 (d) 4 Which of the following is (are) valid FORTRAN 77 statement(s)? (a) DO 13 I = 1 (b) A = DIM ***7 (c) READ = 15.6 π2 4 1 1 1 + 2 + 2 + K is 2 3 5 7 (b) π2 6 (c) π2 8 (d) π2 12 Which of the following improper integrals is (are) convergent? Join All India Mock GATE Classroom Test Series .2 (0. α ) (b) (α .1) (d) ( 0. 0 ) The differential equation d 2 y dy + + sin y = 0 is: dx 2 dx (a) linear 1. All India Rank. Write the code letter(s) a. Percentile. and more.1993 www. 1.com Think GATE Think GATE Forum . d corresponding to the correct alternative(s) in the answer book. − p < x < f (x) = is x.gatementor. For more details. α .1 to 1. 0. interaction with IISc alumni in our online discussion forums.gateforum. 0 < x < p p + 4 1 1 ∑ π n (cos nπ − 1) cos nx − n cos nπ sin nx 2 But putting x = π. c. α ≠ 0 is ( are ) 0 0 0 (a) 1.2007 conducted by GATE Forum in over 25 cities all over India. visit www.com Join discussion of this test paper at http://forum. 1+ (a) 1.4 1. b. one or more of the alternatives are correct.7 below.0 (d) GO TO 3 = 10 Fourier series of the periodic function (period 2π) defined by 0. -1) is ________ Given the differential equation. y ) = x 2 y − 3xy + 2y + x has (a) no local extremum (b) one local minimum but no local maximum (c) one local maximum but no local minimum (d) one local minimum and one local maximum 2. For more details. 1.0 * X 3 1 = −2 * *2 + + is _____ X *3 4 2.1993 www. y ′ = x − y with the initial condition y ( 0 ) = 0 . In the answer book write the question number and the answer only.0.1 is ________ 2.10 below.1 to 2. ur The angular velocity ω at the point (1. and more.3 2.gateforum.4 is _______ (3m) ! x 3m 3 ( m !) is: ______________ ur If the linear velocity V is given by ur V = x 2 yi + xyz $j − yz 2 k . ( ) x e x − 1 + 2 ( cos x − 1) 2.1) calculated numerically upto the third place of decimal by the second order Runga-Kutta method with step size h = 0. Percentile. Also. each blank ( _____) is to be suitably filled in.com Think GATE Think GATE Forum .1 lim 2.GATE CS .com (a) 1. All India Rank. Do not copy the question. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum.2007 conducted by GATE Forum in over 25 cities all over India.7 ∫ 1 0 sin x dx 1 − cos x (b) ∫ ∞ 0 cos x dx 1+ x (c) ∫ ∞ 0 x dx 1 + x2 (d) ∫ 1 0 1 − cos x dx x5 2 The function f ( x.2 The radius of convergence of the power series x (1 − cos x ) x →0 ∞ ∑ 2. In questions 2.com Join discussion of this test paper at http://forum.gatementor. The value of y ( 0.6 The value of the double integral 1 1 x 0 ∫ ∫ 0 I in the FORTRAN 77 statement x dxdy is ______ 1 + y2 Join All India Mock GATE Classroom Test Series . the value of 5. interaction with IISc alumni in our online discussion forums. visit www. no explanations for the answers are to be given.5 For X = 4. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus..GATE CS . calculated by the use of Cayley-Hamilton 0 0 i i 0 0 0 −i theorem or otherwise. i.com 2.9 The differential equation y n + y = 0 is subjected to the boundary conditions.V. sin t if (2n − 1) π ≤ t ≤ 2nπ ( n = 1. the value of integral ur 1 $ is _______ ∫ ∫ s. y (0) = 0 y (λ ) = 0 In order that the equation has non-trivial solution(s).gateforum.ndS 2. interaction with IISc alumni in our online discussion forums.2007 conducted by GATE Forum in over 25 cities all over India.com Think GATE Think GATE Forum .gateforum. and more. K) f (t ) = otherwise 0 is ___________ f(t) π 2π 3π 4π 5π 6π 7π 8π t 0 Join All India Mock GATE Classroom Test Series .8 1 0 0 1 0 −1 0 −1 If A = the matrix A4 . visit www. All India Rank. the general value of λ is __________ 2. 3. Percentile.7 2. is _________ ur Given V = x cos2 yi$ + x 2e z $j + z sin2 yk and S the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes.e. 2.1993 www.10 The Laplace transform of the periodic function f ( t ) described by the curve below.com Join discussion of this test paper at http://forum. For more details.gatementor. Credit will be given if only all the correct alternatives have been indicated.3.b = 1 (c) a + b = 0 (b) a + b = 1 (d) a. There may be more than one correct alternative the multiple-choice questions. For the initial state of 000.GATE CS . should have a stable state. the restriction on the inputs is given by (a) a. and more.1993 www.b = 1 (e) a + b = 1 6. 6.y) A y 6. Question 6 has 8 parts. and 8 has 7 parts. For more details.com SECTION II – A INSTRUCTIONS: There are THREE questions in this Section. All India Rank. x f(x.2007 conducted by GATE Forum in over 25 cities all over India. 7 has 10 parts. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. Each part of a question carries 2 marks. Identify the logic function performed by the circuit shown in figure. (a) exclusive OR (b) exclusive NOR (c) NAND (d) NOR (e) None of the above If the state machine described in figure. interaction with IISc alumni in our online discussion forums. visit www.1.gateforum.2.com Join discussion of this test paper at http://forum.com Think GATE Think GATE Forum .gateforum. the function performed by the arrangement of the J-K flip-flops in figure is: J K Q Q J K Q2 J Q Q K Q Clock (a) Shift Register (b) Mod-3 Counter (c) Mod-6 Counter (d) Mod-2 Counter (e) None of the above Join All India Mock GATE Classroom Test Series . 6. Percentile. Assume that each character code consists of 8 bits.gateforum.gateforum. interaction with IISc alumni in our online discussion forums.com 6. with one head.2007 conducted by GATE Forum in over 25 cities all over India.101)2 = x )10 (b) 1118 )10 = y ) H 6.500 bits The average latency of this device is P msec and the data transfer rate is Q bits/sec. what is the percentage of the total time that the CPU devotes for the main program execution. visit www.1993 www. 6. Arrival of interrupt input 10µ sec Main program execution Main program execution 10µ sec Saving of CPU state 80µ sec 10µ sec Restoration of CPU state Interrupt Service Execution Given that an interrupt input arrives every 1 msec.com Think GATE Think GATE Forum .4. A certain moving arm disk storage. The size of the ROM (number of words × number of bits) that is required to accommodate the Truth table is M words × N bits.7. and more.5. and with two stop bits. For more details. (a) 110. Convert the following numbers in the given bases into their equivalents in the desired bases.com Join discussion of this test paper at http://forum. The details of an interrupt cycle are shown in figure. A ROM is used to store the Truth table for a binary multiple unit that will multiply two 4-bit numbers. Percentile.gatementor.6. has the following specifications. All India Rank. Join All India Mock GATE Classroom Test Series .8. Number of tracks/recording surface = 200 Disk rotation speed = 2400 rpm Track storage capacity = 62. 6. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Write the values of M and N. Write the value of P and Q.GATE CS . is (a) 109 (b) 216 (c) 218 (d) 219 (e) 240 6. The number of characters that can be transmitted per second through an asynchronous serial line at 2400 baud rate. because n is the actual parameter corresponding to x in procedure Q. Q (d) P. Q(n*1. For more details. write (m).com Join discussion of this test paper at http://forum. begin m : = 1. because n is the actual parameter corresponding to y in procedure Q. var m : integer. output by the program PARAM is: (a) 1.GATE CS . (b) 0.3.1 to 7. end. because n is the actual parameter to y in procedure Q. because m is a local variable in P (b) 0. interaction with IISc alumni in our online discussion forums.gateforum.2. begin x:=y+1. x:=y+1 end.gatementor. refer to the PASCAL program shown below. x.1993 www.m). y : integer). procedure P (var. output by the program PARAM is: (a) 0. All India Rank.2007 conducted by GATE Forum in over 25 cities all over India. What is the scope of m declared in the main program? (a) PARAM. (e) none of the above 7. because m is the actual parameter that corresponds to the formal parameter in p (c) 0. vary : integer). output). (c) 1. begin m:=0. The value of m. Q (b) PARAM. visit www. because both x and y are just references to m which gets modified in procedure P (e) none of the above 7.com 7. n:=0. Program PARAM (input. because n is the actual parameter corresponding to x in procedure Q. var m. P(m. Note: For sub-questions 7. because both x and y are just reference to m. n : integer.n). Percentile. write (n) end 7. (d) 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.1. and y has the value 0 (d) 1. and more. P. Q (e) none of the above Join All India Mock GATE Classroom Test Series .3. P (c) PARAM.gateforum.com Think GATE Think GATE Forum . The value of n. procedure Q (x:integer. b:=a-b. begin new (ptr).2007 conducted by GATE Forum in over 25 cities all over India. (e) None of the above. Percentile. a:=a-b end. . which of the following are true? program main (output). For more details.6. ptr:=nil. (a) The program leads to compile time error (b) The program leads to run time error (c) The program outputs 5.gatementor. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS .com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums.com Join discussion of this test paper at http://forum. begin a:=a+b. What does the following code do? var a. n : link end.com 7.2 (d) The program produces error relating to nil pointer dereferencing (e) None of the above 7.1993 www. type link = ^data. data = record d : real. b : integer.4.gateforum. A simple two-pass assembler does the following in the first pass: (a) It allocates space for the literals.d:=5. (b) It computes the total length of the program (c) It builds the symbol table for the symbols and their values. (d) It generates code for all the load and store register instructions.ptr^. write ln(ptr) end. and more. (a) exchanges a and b (b) doubles a and stores in b (c) doubles b and stores in a (d) leaves a and b unchanged (e) none of the above 7. var ptr : link. visit www. For the program segment given below. Join All India Mock GATE Classroom Test Series .gateforum. All India Rank.2.5. 4 and 6 respectively.com 7. r. which have peak demands of 3. For what value of m deadlock will not occur? (a) 7 (b) 9 (c) 10 (d) 13 (e) 15 7.gateforum.gatementor. B and C.2007 conducted by GATE Forum in over 25 cities all over India. Consider a simple connected graph G with n vertices and n-edges (n>2). Join All India Mock GATE Classroom Test Series . Percentile.gateforum. interaction with IISc alumni in our online discussion forums. which of the following statements are true? (a) G has no cycles. q.10. (e) None of the above. A part of the system software.1993 www. These resources are shared by 3 processes A.7. (d) The graph obtained by removing any two edges from G is not connected. The root directory of a disk should be placed (a) at a fixed address in main memory (b) at a fixed location on the disk (c) anywhere on the disk (d) at a fixed location on the system disk 7. (a) 4 (b) 10 (c) 11 (d) 12 (e) None of the above 8.1. which under all circumstances must reside in the main memory. t. Assume that the following jobs are to be executed on a single processor system Job Id CPU Burst time p 4 q 1 r 8 s 1 t 2 The jobs are assumed to have arrived at time 0+ and in the order p. For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum. (e) anywhere on the system disk Consider a system having m resources of the same type.9. is: (a) text editor (b) assembler (c) linker (d) loader (e) none of the above 7. (b) The graph obtained by removing any edge from G is not connected. s. (c) G has at least one cycle.GATE CS . and more. All India Rank. Then. calculate the departure time (completion time) for job p if scheduling is round robin with time slice 1. visit www.8. 8. gatementor. on reals is (a) a partial ordering since it is asymmetric and reflexive (b) a partial ordering since it is antisymmetric and reflexive (c) not a partial ordering because it is not asymmetric and not reflexive (d) not a partial ordering because it is not antisymmetric and reflexive (e) none of the above 8.gateforum.2007 conducted by GATE Forum in over 25 cities all over India.6. is: (a) mn (e) 8.com Think GATE Think GATE Forum . Let S be an infinite set and S1 K .com 8. where O ( n ) stands for order n is: 1≤ k ≤ n ( ) (a) O ( n ) ( (e) O 1.GATE CS .5. The proposition P ∧ (~ p ∨ q ) is: (a) a tautology (b) logically equivalent to p ∧ q (c) logically equivalent to p ∨ q (d) a contradiction (e) none of the above 8.4. Let A and B be sets with cardinalities m and n respectively. m (b) n Pm (c) m Cn (d) nCm Pn ∑ O ( n) .1993 www. Let A be a finite set of size n. visit www.2. Sn be sets such that S1 ∪ S2 ∪ K ∪ Sn = S.com Join discussion of this test paper at http://forum.gateforum. <. The number of oneone mappings (injections) from A to B.3. All India Rank. and more. The number of elements in the power set of A × A is: (a) 22 n 2 (b) 2n (c) 2 (2 ) n ( ) (d) 22 n (e) None of the above 8.7. The less-than relation. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (a) at least one of the set Si is a finite set (b) not more than one of the set Si can be finite (c) at least one of the sets Si is an infinite set (d) not more than oen of the sets Si can be infinite (e) None of the above 8. when m < n.5n2 (b) O n2 ( ) (c) O n3 ( (d) O 3n2 ) ) Join All India Mock GATE Classroom Test Series . Percentile. For more details. interaction with IISc alumni in our online discussion forums. Then. com Think GATE Think GATE Forum . Percentile. Show that any binary Boolean function can be implemented using half adders only.B INSTRUCTIONS: There are TEN questions in this section. a page transfer occurs from Mi +1 to Mi and the average time required for such a page swap is Ti . In particular. the contents of RegR are incremented by 1’. In the three-level memory hierarchy shown in the following table. what are the contents of PC after the execution of this instruction? 11.00998 0. 9. 10. after fetching the operand. For more details.1993 www. Assume that only half adders are available in your laboratory. Hierarchy Level ( Mi ) Access Time (ti ) Probability of access ( pi ) Page Transfer time (Ti ) M1 10−6 0.001 sec M2 10−5 0.com SECTION II . Each question carries 5 marks. and more. pi denotes the probability that an access request will refer to Mi . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.99000 0. RegR specifies a CPU register and Mode specifies an addressing mode. Calculate the average time t A required for a processor to read one word from this memory system.00002 -- If a miss occurs at level Mi .2007 conducted by GATE Forum in over 25 cities all over India.com Join discussion of this test paper at http://forum. All India Rank. (a) What is the address of the operand? (b) Assuming that this is a non-jump instruction.gatementor.1 sec M3 10−4 0.GATE CS . interaction with IISc alumni in our online discussion forums.gateforum. Attempt all questions. visit www. An instruction at memory location 2000 specifies Mode = 2 and the RegR refers to program counter (PC). Join All India Mock GATE Classroom Test Series . The instruction format of a CPU is: OP CODE MODE RegR One Memory word Mode and RegR together specify the operand. Mode = 2 specifies that ‘the register RegR contains the address of the operand.gateforum. All India Rank. compute the size of the data and index areas in terms of number of blocks. Percentile. K .j: index. K . How many levels of tree do you have for the index? 15. B . visit www.gateforum. Fill up the boxes to complete the program and write against A .j]>max then max:=A[i. d2 . Join All India Mock GATE Classroom Test Series .GATE CS . begin max:= A . d j . Assume that max is a variable to store the largest value and i.1993 www. d j −1 .gatementor. 0 K n − 1 using a single loop. i:=0. begin for i:=1 to n-1 do if A[i] > A [i+1] then begin temp : A[i]. i:= D end end end. K dn are stored in these n nodes.gateforum. For more details. If the disk block size is 512 bytes and there are 16 K records. var i. including key field of size 14 bytes. d2 . temp : item.com Think GATE Think GATE Forum . Let X be a pointer to the j-th node (1≤j≤n) in which dj is stored.j are the indices to the array. A[i]:=A[i+1]. An address of a disk block takes 2 bytes.j:=0. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Consider the recursive algorithm given below: procedure bubblersort (n).j] if C then j:=j+1 else begin j:=0. Give an algorithm to insert d into the list to obtain a list having items d1 . An ISAM (indexed sequential) file consists of records of size 64 bytes each. 14. The data items d1 . C and D in your answer book. dn in the order without using the header.2007 conducted by GATE Forum in over 25 cities all over India.com Join discussion of this test paper at http://forum. 13. A new data item d stored in node with address Y is t be inserted. interaction with IISc alumni in our online discussion forums. Consider a singly linked list having n nodes. while B do begin if A[i. The following Pascal program segments finds the largest number in a twodimensional integer array A 0 K n − 1.com 12. B A B A DA A A P Clock P B DB B B B A A Join All India Mock GATE Classroom Test Series . In case more than five questions are attempted. in which every non-leaf node has 2 descendants. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Solve for an . Prove by the principal of mathematical induction that for any binary tree.GATE CS . Out of a group of 21 persons.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum. and more. Each question carries 5 marks.C INSTRUCTIONS: There are TEN questions in this section.gateforum. 9 eat vegetables. 16. All India Rank. How many persons eat at least two out the three dishes? 18.gatementor. and P is control input.2007 conducted by GATE Forum in over 25 cities all over India. bubblesort (n -1 ) end Let an be the number of times the ‘if…then…. Develop the state transition table for this controller. 10 eat fish and 7 eat eggs : 5 persons eat all three. Attempt any FIVE questions. 17. the number of leaves in the tree is one more than the number of non-leaf nodes. the first five answers alone will be evaluated.1993 www. Show that proposition C is a logical consequence of the formula A ∧ ( A → ( B ∨ C ) ) ∧ ( B →~ A ) Using truth tables. which A and B are state variable implemented by D flip-flops. SECTION: II .com A[i+1]:=temp end. For more details. visit www. A control algorithm is implemented by the NAND – gate circuitry given in figure below.’ Statement gets executed when the algorithm is run with value n. interaction with IISc alumni in our online discussion forums.gateforum. 19. Set up the recurrence relation by defining an in terms of an −1. Percentile. enrollment of students in courses and teachers of courses. LHLD 5000 MVI B. were generated by a program: 1 2 3 4 1 3 5 2 1 5 4 3 2 3 This program is run on a demand paged virtual memory system. interaction with IISc alumni in our online discussion forums. Attributes for primary key in each relation are marked by ‘*’. Percentile. S1 S2 S3 S4 S5 S6 For questions 23 and 24: The following relations are used to store data about students.com Think GATE Think GATE Forum . and more. with main memory size equal to 4 pages. Write a concurrent program using parbegin-parend and semaphores to represent the precedence constraints of the statements S1 to S6 . A INX H DCR B JNZ GET The following page addresses.com Join discussion of this test paper at http://forum. 5 IN 20 MOV M.com 20. as shown in figure below.2007 conducted by GATE Forum in over 25 cities all over India. For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. visit www. and (b) List the roles of the registers used and the address referred to by it. Given that the following is an 8085 program segment: (a) Identify the function performed by it. Indicate the page references for which page faults occurs for the following page replacement algorithms. Join All India Mock GATE Classroom Test Series .GATE CS .gateforum. (a) LRU (b) FIFO Assume that the main memory is empty initially. All India Rank. courses. GET: 21.gateforum. in the given sequence. 22.1993 www. prove that it is in 3 NF. (a) If a procedure P has two parameters as described in procedure definition: procedure P (var x :integer. (b) In the generated code for the body of procedure P.gatementor. Write a SQL query for retrieving roll number and name of students who got A grade in at least one course taught by teacher named Ramesh for the above relational database. Percentile.2007 conducted by GATE Forum in over 25 cities all over India.…. (i) assignment statement e.com Students (rollno*. P(a. cno grade rd (a) Is the database in 3 normal form (3NF)? (b) If yes. A stack is used to pass parameters to procedures in a procedure call. the relations so that they are in 3 NF (without proving). (iii) sequencing e.gateforum.b) State precisely in a sentence what is pushed on stack for parameters a and b. 24. Assume that expression has already been defined. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.sdaddr tno cno cname tname rollno. and if P is called by .1993 www. interaction with IISc alumni in our online discussion forums. For more details. x:=expression (ii) loop construct e. Do not use optional parentheses and * operator in CFG. cname is course name. saddr) courses (cno*. etc. tname is teacher name.) 23.com Think GATE Think GATE Forum .cao*) (cno is course number.com Join discussion of this test paper at http://forum. visit www. statement end (a) Write a context-free grammar (CFG) for statements in the above language.grade) teach(tno*.g. If not.gateforum. For the relational database given above. for i:=expression to expression do statement. tno is teacher number. how will the addressing of formal parameters x and y differ? Join All India Mock GATE Classroom Test Series . begin statement .g. (b) Show the parse tree for the following statement: for j:=2 to 10 do begin x:=expr1. sname is student name. A simple Pascal like language has only three statements. y: integer). y:=expr2 end 26.tname. sname.GATE CS .g. 25. and more. normalize. All India Rank. cno*. the following functional dependencies hold: rollno sname. cname) enroll(rollno*. interaction with IISc alumni in our online discussion forums.1993 www. 28.gateforum. such that no string has 3 consecutive occurrences of the letter b.2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet {a. Percentile. visit www. Let ({p.GATE CS . For more details.com 27.gatementor.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum. q {. *) be a semigroup where p * p = q. All India Rank. and more. Show that: (a) p * q = q * p and (b) q * q = q Join All India Mock GATE Classroom Test Series . b} .gateforum. Percentile. Section – A 1.4 1. and more. Begin answer for this section on a fresh page. 1.5 (a) y n +1 = y n + hf ( xn . y ) is dx specified by. For more details.GATE CS .gateforum.2007 conducted by GATE Forum in over 25 cities all over India. There will be no negative marking. y n+1 ) Let A and B be any two arbitrary events. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Then which one of the following is true? (a) AA′ = 1 1. y n+1 ) (c) y n +1 = y n−1 + 2hf ( xn . Section A has EIGHT questions. Choose one of the alternatives for the following questions: 1.com Read (i) (ii) (iii) (iv) (v) (vi) the following instructions carefully: This question paper consists of two sections: A & B. (choose one of the following). y n ) (b) y n +1 = y n + hf ( xn+1 .gateforum.1994 www. Section B has TWENTY questions. All India Rank. Answer all questions in this section. then. Answer any TEN questions in this section. Answer to questions in each section should appear together in the same sequence in which they appear in the question paper.gatementor. visit www.1 FORTRAN implementation do not permit recursion because (a) they use static allocation for variables (b) they use dynamic allocation for variables (c) stacks are not available on all machines (d) it is not possible to implement recursion on all machines 1. y n ) (d) y n +1 = (1 + h ) f ( xn+1 .com Join discussion of this test paper at http://forum.com Think GATE Think GATE Forum . which one of the following is true? (a) P ( A ∩ B ) = P ( A ) P ( B ) (b) P ( A ∪ B ) = P ( A ) + P ( B ) (c) P ( A B ) = P ( A ∩ B ) P ( B ) (d) P ( A ∪ B ) ≤ P ( A ) + P ( B ) An unrestricted use of the “goto” statement is harmful because (a) it makes it more difficult to verify programs (b) it increases the running time of the programs (c) it increases the memory required for the programs (d) it results in the compiler generating longer machine code Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums.2 Let A and B be real symmetric matrices of size n × n .3 (b) A = A−1 (c) AB = BA (d) ( AB )′ = BA Backward Euler method for solving the differential equation dy = f ( x. Percentile. j ) element of the lower triangular matrix in this new representation is: (a) i + j 1. non-zero elements (i.12 (b) i + j − 1 (c) j+ i ( i − 1) 2 (d) i + j ( j − 1) 2 Generation of intermediate code based on an abstract machine model is useful in compilers because (a) it makes implementation of lexical analysis and syntax analysis easier Join All India Mock GATE Classroom Test Series . For more details. which one of the following is true for G? (a) g = g −1 for every g ∈ G (c) 1. k a constant 2 n (b) T ( n ) = 2T + k .2007 conducted by GATE Forum in over 25 cities all over India.10 (b) 1 Some group (G. the index of the th ( i.gateforum.8 (b) 10 (c) 7 (d) 9 The recurrence relation that arises in relation with the complexity of binary search is: n (a) T ( n ) = T + k .com Think GATE Think GATE Forum . o ) is (c) 2 (d) 3 known to be abelian. h ∈ G (b) g = g2 for every g ∈ G (d) G is of finite order In a compact single dimensional array representation for lower triangular matrices (i.9 0 0 −3 The rank of matrix 9 3 5 is: 3 1 1 (a) 0 1.com Join discussion of this test paper at http://forum.e elements of the lower triangle) of each row are stored one after another.1994 www.gatementor. k a constant 2 n (c) T ( n ) = T + log n 2 n (d) T ( n ) = T + n 2 The logic expression for the output of the circuit shown in figure below is: (a) AC + BC + CD A B (b) AC + BC + CD (c) ABC = CD C (d) A B + B C + C D D 1. All India Rank. Then. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and more. visit www.com 1.7 1.gateforum. starting from the first row.6 The number of distinct simple graphs with upto three nodes is (a) 15 1.11 2 ( goh ) = g2 oh2 for every g.GATE CS . interaction with IISc alumni in our online discussion forums.e all the elements above the diagonal are zero) of size n × n. 1. 1 (b) n2 (c) n ( n − 1) 2 (d) n ( n + 1) 2 Which of the following conversions is not possible (algorithmically)? (a) Regular grammar to context free grammar (b) Non-deterministic FSA to deterministic FSA (c) Non-deterministic PDA to deterministic PDA (d) Non-deterministic Turing machine to deterministic Turing machine 1. All India Rank.gatementor.15 (c) 1. 4.com Think GATE Think GATE Forum . 4. For more details. 5.17 1.gateforum. 5. 2 1. 5 in that order? (a) 3.com Join discussion of this test paper at http://forum. 4. and more. Percentile. 1. interaction with IISc alumni in our online discussion forums. 5. 4 (d) 5.gateforum.18 Linked lists are not suitable data structures of which one of the following problems? (a) Insertion sort (b) Binary search (c) Radix sort (d) Polynomial manipulation Which of the following features cannot be captured by context-free grammars? (a) Syntax of if-then-else statements (b) Syntax of recursive procedures (c) Whether a variable has been declared before its use (d) Variable names of arbitrary length Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India.com (b) syntax-directed translations can be written for intermediate code generation (c) it enhances the portability of the front end of the compiler (d) it is not possible to generate code for real machines directly from high level language programs 1. 3. 2 The number of substrings (of all lengths inclusive) that can be formed from a character string of length n is (a) n 1. 2.1994 www.13 A memory page containing a heavily used variable that was initialized very early and is in constant use is removed when (a) LRU page replacement algorithm is used (b) FIFO page replacement algorithm is used (c) LFU page replacement algorithm is used (d) None of the above 1. 2. visit www. 4. 3.14 Which of the following permutations can be obtained in the output (in the same order) using a stack assuming that the input is the sequence 1.16 (b) 3. 3. 2.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. com Join discussion of this test paper at http://forum.22. interaction with IISc alumni in our online discussion forums.com 1.23. (d) Depth-first search can be used to find connected components of a graph. 1. In which one of the following cases is it possible to obtain different results for call-by reference and call-by-name parameter passing methods? (a) Passing a constant value as a parameter (b) Passing the address of an array as a parameter (c) Passing an array element as a parameter (d) Passing an array following statements is true 1.com Think GATE Think GATE Forum .21. and more.19.1994 www. Percentile. visit www. For more details. the binary tree cannot be uniquely constructed. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.20. Which of the following algorithm design techniques is used in the quicksort algorithm? (a) Dynamic programming (b) Backtracking (c) Divide and conquer (d) Greedy method 1. All India Rank.gateforum. (b) Breadth-first search cannot be used to find converted components of a graph (c) Given the prefix and postfix walks over a binary tree. Consider the following two functions: n3 for 0 ≤ n ≤ 10.GATE CS . 000 g1 ( n ) = 2 n for n ≥ 10.2007 conducted by GATE Forum in over 25 cities all over India. Which one of the following statements is true? (a) Macro definitions cannot appear within other macro definitions in assembly language programs (b) Overlaying is used to run a program which is longer than the address space of computer (c) Virtual memory can be used to accommodate a program which is longer than the address space of a computer (d) It is not possible to write interrupt service routines in a high level language 1. 000 n for 0 ≤ n ≤ 100 g2 ( n ) = 3 n for n > 100 Which of the following is true? ( ) (a) g1 ( n ) is 0 ( g2 ( n ) ) (b) g1 ( n ) is 0 n3 (c) g2 ( n ) is 0 ( g1 ( n ) ) (d) g2 ( n ) is 0 ( n ) Join All India Mock GATE Classroom Test Series . Which one of the following statements is false? (a) Optimal binary search tree construction can be performed efficiently using dynamic programming.gatementor.gateforum. gateforum.5 and 0. transitivity} the relation R ={(x. N. K n} with odd cardinality is __________ 2. the binary operation __________ is associative and non-commutative. Percentile.com Think GATE Think GATE Forum . P2 and P3 is __________ 2. The probability of occurrence of at least one of the event is __________ 2.GATE CS .8.1 The number of flip-flops required to construct a binary modulo N counter is __________ 2.7. and more. Join All India Mock GATE Classroom Test Series .5. Consider n-bit (including sign bit) 2’s complement representation of integer number. The Hasse diagrams of all the lattices with up to four elements are __________ (write all the relevant Hasse diagrams). that can be represented is __________ ≤ N ≤ __________ 2.6.y) ∈ N 2 x ≠ y } satisfies __________ 2.com Join discussion of this test paper at http://forum. The number of edges in a regular graph of degree d and n vertices is _________ 2.gatementor. visit www. 50 150 300 350 600 Increasing addresses The sequence of requests for blocks of size 300. The number of subsets {1.com 1.2.2007 conducted by GATE Forum in over 25 cities all over India.3. symmetry. Amongst the properties {reflexivity. 0. The probability of the event A in terms of P1 .9. The range of integer values. B and C be independent events which occur with probabilities 0. 50 can be satisfied if we use (a) either first fit or best fit policy (any one) (b) first fit but not best fit policy (c) best fit but first fit policy (d) None of the above 2. Consider the following heap (figure) in which blank regions are not in use and hatched region are in use.1994 www. 125.8. anti-symmetry. All India Rank. Fill in the blanks: 2.24. For more details. On the set N of non-negative integers. Let A. The probability of an event B is P1.4.3 respectively. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 25. 2.gateforum. The probability that events A and B occur together is P2 while the probability that A and B occur together is P3. interaction with IISc alumni in our online discussion forums.2. gatementor. Percentile.gateforum. The regular expression for the language recognized by the finite state automaton of figure is __________ 0 A 1 1 B 0 0 C 1 3.com Join discussion of this test paper at http://forum. visit www. Answer the following questions as indicated. (Reduced Instruction Set Computers) machines.10.3.gateforum. 3. 3. and more. 3. interaction with IISc alumni in our online discussion forums.1.4. For more details. 3. Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson’s Rule (d) Solutions of Systems of Linear Equations Match the following items (i) Backus-Naur form (a) Regular expressions (ii) Lexical analysis (b) LALR(I) grammars (iii) YACC (c) LL(I) grammars (iv) Recursive descent parsing (d) General context-free grammars Join All India Mock GATE Classroom Test Series . State True or False with one line explanation Expanding opcode instruction formats are commonly employed in RISC. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. State True or False with one line explanation A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits). All India Rank.2007 conducted by GATE Forum in over 25 cities all over India.2. State True or False with one line explanation Multiplexing of address/data lines in 8085 microprocessor reduces the instruction execution time. 3.GATE CS .com 2.5.1994 www.com Think GATE Think GATE Forum . modest speed and packing density (iii) TTL (c) Bipolar.9. An instance of a relational scheme R(A.gateforum. visit www. B. 1 0 1 Find the inverse of the matrix −1 1 1 0 1 0 3.8. low packing density (iv) CMOS (d) Bipolar.com Join discussion of this test paper at http://forum.12. good resistance to radiation (ii) Ga As (b) Unipolar. very high speed difficult to fabricate. inexpensive 3.10. interaction with IISc alumni in our online discussion forums. Percentile. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Can you conclude that A is a candidate key for R? 3.6. 3. Every subset of a countable set is countable. B and C: AB + AC = 1 AC + B = 0 Join All India Mock GATE Classroom Test Series . and more. − ) which is equivalent to R ∩ S. low power. Using only the truth table decide whether p ⇔ q does not imply p q is true or false. 3. (a) Let * be a Boolean operation defined as A * B = AB + A B If C = A * B then evaluate and fill in the blanks: (i) A * A = _______ (ii) C * A = _______ (b) Solve the following boolean equations for the values of A. All India Rank. 4. highest speed silicon IC.13. State True or False with reason Logical data independence is easier to achieve than physical data independence 3. Match the following items (i) ECL (a) Unipolar. State True or False with reason There is always a decomposition into Boyce-Codd normal form (BCNF) that is lossless and dependency preserving.7.com Think GATE Think GATE Forum .com 3. 3. Give a relational algebra expression using only the minimum number of operators from ( ∪.1994 www. For more details.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. Let p and q be propositions. C) has distinct values for attribute A.11.gateforum. modes packing density.GATE CS . State whether the above statement is true or false with reason. Assume all variables are suitably declared. n div 2).gateforum. n is computed by this program? Function what (x.2007 conducted by GATE Forum in over 25 cities all over India. interaction with IISc alumni in our online discussion forums. end. and more. Join All India Mock GATE Classroom Test Series . i=0. An incomplete algorithm for doing this in linear time. min:=n. while _____do begin temp:=A[i]. j:=i. 6. All India Rank. i:=____________.GATE CS .gateforum. 7. without using another is given below. ………………. For more details. Percentile. where 1≤K≤n-1.com Think GATE Think GATE Forum .A[1]. j:=(j+K) mod n. if j<min then min:=j. value:=value*what(x*x.A[n-1]. A 3-ary tree is a tree in which every internal node has exactly three children. Use induction to prove that the number of leaves in a 3-ary tree with n interval nodes is 2 ( n − 1) + 3. end. It is required to shift the elements of the array cyclically to the left by K places.1994 www. end. visit www. A[(n+i-K)mod n]:=_____. An array A contains n integers in locations A[0]. Complete the algorithm by filling in the blanks.gatementor. What function of x.. begin value:=1 if n>0 then begin if n mod 2 = 1 then value:=value*x. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. what:value end.com 5.com Join discussion of this test paper at http://forum. n:integer): integer: Var value : integer. while _____do begin A[j]:=_____. Assume Q2Q1Q0 = 000 initially.{R j ← Ri ⊕ R j . 1.gatementor. find the parent of each node.1994 www. for i. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 2. Percentile. Following 7 bit single error correcting Hamming coded message is received.2007 conducted by GATE Forum in over 25 cities all over India. (Higher order register in the register pair contains higher order digits of operand) 11.com Join discussion of this test paper at http://forum. (figure below): 7 6 5 4 3 2 1 1 0 0 0 1 1 0 bit No.gateforum. 4. and show the tree diagrammatically. 7. that is. J CK Q2 D Q1 CK K T Q0 CK Q0 1 Clock (Four clock pulses given here) 12.gateforum. and more. after giving four clock pulses to the clock terminal. Q1 and Q0 in the circuit of figure. Assume the two input operands are in BC and DE Register pairs. 12. 10. Write a program in 8085 Assembly language to Add two 16-bit unsigned BCD(84-2-1 Binary Coded Decimal) number. (a) Assume that a CPU has only two registers R1 and R2 and that only the following instruction is available XOR Ri . The result should be placed in the register pair BC. j = 1. R j . When the tree is traversed in post-order. Find the contents of the flip-flop Q2 . All India Rank. A rooted tree with 12 nodes has its nodes numbered 1 to 12 in pre-order. 5.GATE CS . 8. 9. 10. the nodes are visited in the order 3. For more details. 11. Reconstruct the original tree from this information. 9. visit www. If the message contains an error find the bit which is erroneous and gives the correct message. 2} Join All India Mock GATE Classroom Test Series . 6. interaction with IISc alumni in our online discussion forums. Determine if the message is correct (assuming that at most 1 bit could be corrupted).com 8.com Think GATE Think GATE Forum . SECTION – B Answer any TEN questions in this section. The ‘year’ attribute for the STUDENTS relation indicates the year in which the student is currently studying (First year.gateforum. Determine an input test to detect the fault.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. visit www. All India Rank. Percentile.com Using this XOR instruction. (b) The line p of the circuit shown in figure has stuck at 1 fault. Consider B + − tree of order d shown in figure? (A) B + − tree of order d contains between d and 2d keys in each node (a) Draw the resulting B + − tree after inserted in the figure. rollno) The underlined attributes indicate the primary keys for the relations. age. find an instruction sequence in order to exchange the contents of the registers R1 and R2 . Consider the following relational schema: COURSES (cno. Second year etc. cname) STUDENTS (rollno. interaction with IISc alumni in our online discussion forums.com Think GATE Think GATE Forum .2007 conducted by GATE Forum in over 25 cities all over India.) (a) Write a relational algebra query to Print the roll number of students who have registered for cno 322. For more details. the number of nodes accessed during a search is 0 ( − ) . Join All India Mock GATE Classroom Test Series . 14. and more. year) REGISTERED FOR (cno. p A B 94-7 s-a-1 B C 13.gateforum. 10 15 25 36 25 38 39 41 69 47 93 69 71 75 83 95 99 101 105 (b) For a B + − tree of order d with n leaf nodes.gatementor.GATE CS .1994 www. sname. (b) Write a SQL query to Print the age and year of the youngest student in each year. 17. All India Rank. Percentile. (b) A symbol declared as ‘external’ in assembly language is assigned an address outside the program by the assembler itself.gateforum. Join All India Mock GATE Classroom Test Series . State whether the following statements are True or False with reasons for your answer (a) A subroutine cannot always be used to replace a macro in an assembly language program.1994 www.gatementor. For more details. interaction with IISc alumni in our online discussion forums. (i) S is regular (ii) S is recursively enumerable (iii) S is not recursively enumerable (iv) S is recursive (b) Given that a language L1 is regular and that the language L1 ∪ L2 is regular. 19. visit www. and more. 18. (a) Use the patterns given to prove that n −1 ∑ (2i + 1) = n 2 i =0 (You are not permitted to employ induction) etc 1 4 9 (b) Use the result obtained in (a) to prove that n n ( n + 1) i =1 2 ∑i = 16.com 15. Every element a of some ring ( R.com Think GATE Think GATE Forum . State whether the following statements are True or False with reasons for your answer: (a) Coroutine is just another name for a subroutine. Decide whether or not the ring is commutative. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Join discussion of this test paper at http://forum.gateforum. is the language L2 always regular? Prove your answer.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. (b) A two pass assembler uses its machine opcode table in the first pass of assembly. +. 0 ) satisfies the equation aoa = a. (a) Given a set S = { x there is an x-block of 5's in the decimal expansion of π } (Note: x-block is a maximal block of x successive 5’s) Which of the following statements is true with respect to S? No reasons need to be given for the answer. and place the result . A grammar G is in Chomsky-Normal Form (CNF) if all its productions are of the form A BC or A a.gateforum. are non-terminals and a is a terminal.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. then how long is a derivation of w in G? 21. The above function is run on a computer with a stack of 64 bytes. Give reasons for your answer. end. two. Consider the following recursive function: function fib (1:integer). begin r:=5 two. B and C. load register . begin if (n=0) or (n=1) then fib:=1 else fib:=fib(n-1) + fib(n-2) end.1994 www. at addren ADD addren . add register to . end begin r:=2. For more details.GATE CS . and more. visit www. Consider the program below: Program main. and that an integer value and an address takes 2 bytes each.gatementor. What is printed by the above program if (i) Static scoping is assumed for all variables. estimate the maximum value of n for which the stack will not overflow. (ii) Dynamic scoping is assumed for all variables. procedure one. in the register Join All India Mock GATE Classroom Test Series . Suppose we have a computer with a single register and only three instructions given below: LOAD addren . Percentile. contents of addren .com Think GATE Think GATE Forum . Give reasons for your answer.com Join discussion of this test paper at http://forum. two. store register . procedure two. where A.2007 conducted by GATE Forum in over 25 cities all over India. begin write (r) end.com 20.integer. one. var r:integer. Suppose G is a CFG in CNF and w is a string in L(G) of length. var r:integer. interaction with IISc alumni in our online discussion forums. from addren STORE addren . 22. 23. All India Rank. Assuming that only return address and parameter and passed on the stack. 25. It is required to transfer all the items from the queue to the stack. The statements are numbered from S1 to S6 S1 read n S2 i:=1 S3 if i>n goto next S4 a(i):=i+1 S5 i:=i+1 S6 next : Write a(i) Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums. All India Rank. j exist.gateforum.com Consider the following grammar: A id :=E E E +T T T ( E ) id Write a syntax directed translation to generate code using this grammar for the computer described above. Insert. Describe. Do not assume any implementation of the queue or stack. An independent set in a graph is a subset of vertices such that no two vertices in the subset are connected by an edge.2007 conducted by GATE Forum in over 25 cities all over India.gateforum. An incomplete scheme for a greedy algorithm to find a maximum independent set in a tree is given below: V: Set of all vertices in the tree.com Join discussion of this test paper at http://forum. ∈ V such that V:=V – {u}. 27. Percentile. visit www. and more. An array a contains n integers in non-decreasing order. (a) Draw a precedence graph for the following sequential code. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. a linear time algorithm to find i. if u is such that then 1:= I ∪ {u} end. using Pascal like pseudo code. 26.GATE CS . While I:=φ. V ≠ φdo begin select a vertex u. A queue Q containing n items and an empty stack S are given. For more details. if such i.1994 www. and the order of all other items is preserved. Note that the only operations which can be performed on the queue and stack are Delete.gatementor. 24. Push and Pop.com Think GATE Think GATE Forum . (a) Complete the algorithm by specifying the property of vertex u in each case (b) What is the time complexity of the algorithm. so that the item at the front of queue is on the top of the stack. Show how this can be done in O(n) time using only a constant amount of additional storage. j. output(I). such that A i + A j = a given integer M. A 1 ≤ A 2 ≤ K ≤ A n. gateforum.com Join discussion of this test paper at http://forum. All India Rank.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. find a safe sequence.2007 conducted by GATE Forum in over 25 cities all over India.gatementor.com Think GATE Think GATE Forum .com (b) Can this graph be converted to a concurrent program using parbegin-parend construct only? 28. Percentile. r2 r1 p3 p1 p2 p0 r3 (a) Find if the system is in a deadlock state. Consider the resource allocation graph given in the figure. and more. Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums. (b) Otherwise. For more details.gateforum. visit www.1994 www. If X > Y then if X < 0 then X:=abs(X) else X:=2*X. For more details.2007 conducted by GATE Forum in over 25 cities all over India.A 1.3 In a vectored interrupt (a) the branch address is assigned to a fixed location in memory (b) the interrupt source supplies the branch information to the processor through an interrupt vector (c) the branch address is obtained from a register in the processor (d) none of the above 1. All India Rank.gatementor.gateforum. and more.5 1.7 (b) -20 (c) -10 (d) None Merge sort uses (a) Divide and conquer strategy (b) Backtracking approach (c) Heuristic search (d) Greedy approach The principle of locality justifies the use of (a) interrupts (b) DMA (c) Polling (d) Cache Memory In a paged segmented scheme of memory management. Percentile. (a) 10 1. Choose the correct alternative for each part. This question has 25 parts.com Think GATE Think GATE Forum . Each part carries 1 mark.com Join discussion of this test paper at http://forum. Y:=20. what is the value of X after the execution of the program segment? X:=-10.6 1.gateforum.1995 www. visit www.com SECTION . 1.GATE CS . interaction with IISc alumni in our online discussion forums. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. the segment table itself must have a page table because (a) the segment table is often too large to fit in one page (b) each segment is spread over a number of pages Join All India Mock GATE Classroom Test Series .4 In the following Pascal program segment.2 (b) ANI FOH (c) XRI FOH (d) ANI OFH Which of the following statements is true? (a) ROM is a Read/Write memory (b) PC points to the last instruction that was executed (c) Stack works on the principle of LIFO (d) All instructions affect the flags 1.1 A single instruction to clear the lower four bits of the accumulator in 8085 assebly language? (a) XRI OFH 1. 000111.gateforum. 011001. 111111? (a) 2 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 010101. visit www.gateforum.9 Which of the following page replacement algorithms suffers from Belady’s anamoly? (a) Optimal replacement (b) LRU (c) FIFO (d) Both (a) and (c) In some programming languages.1995 www.GATE CS . Percentile.12 (a) Variables (b) Identifiers (c) Actual parameters (d) Formal parameters What is the distance of the following code 000000. If L and D denote the sets of letters and digits respectively. begin II. and more.com (c) segment tables point to page table and not to the physical locations of the segment (d) the processor’s description base register points to a page table 1.11 (a) Context free (b) Regular (c) Context sensitive (d) LR(k) What are x and y in the following macro definition? macro Add x.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. an identifier is permitted to be a letter following by any number of letters or digits. interaction with IISc alumni in our online discussion forums. For more details. All India Rank.13 (b) 3 (c) 4 (d) 1 Which of the following strings can definitely be said to be tokens without looking at the next input character while compiling a Pascal program? I.D ) Consider a grammar with the following productions S → a ∝ b b ∝ c aB S →∝ S b S →∝ b b ab S ∝→ bd b b The above grammar is: 1. ( L. which of the following expressions defines an identifier? (a) 1. program III.D ) * (d) L.10 (L ∪ D) + * (b) L ( L ∪ D ) (c) * ( L.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum.8 1.y Load y Mul x Store y end macro 1. <> Join All India Mock GATE Classroom Test Series . 2007 conducted by GATE Forum in over 25 cities all over India.17 Which scheduling policy is most suitable for a time shared operating system? (a) Shortest Job First (b) Round Robin (c) First Come First Serve (d) Elevator For merging two sorted lists of sizes m and n into a sorted list of size m+n. Percentile. All India Rank.16 1.com Think GATE Think GATE Forum .com (a) I (b) II (c) III (d) All of the above 1.20. Then (a) R is reflexive and hence an equivalence relation (b) R is reflexive and hence a partial order (c) R is reflexive and hence not an equivalence relation (d) None of the above 1.GATE CS .gatementor.gateforum.com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums.15 1. The number of nodes of degree 2 in T is: (a) log2 n 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. visit www. Let R be a symmetric and transitive relation on a set A.1995 www. we required comparisons of (a) O ( m ) (b) O ( n ) (c) O ( m + n ) (d) O (log m + log n ) A binary tree T has n leaf nodes.1. (2. and more. The number of elements in he power set P ( S ) of the set S = {(φ ) .14 A linker is given object modules for a set of programs that were compiled separately. What information need to be included in an object module? (a) Object code (b) Relocation bits (c) Names and locations of all external symbols defined in the object module (d) Absolute addresses of internal symbols 1.gateforum.19. For more details. 3)} is: (a) 2 (b) 4 (c) 8 (d) None of the above Join All India Mock GATE Classroom Test Series .18 (b) n − 1 (c) n (d) 2n The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 7 is: (a) 16 25 3 9 (b) 10 (c) 27 75 (d) 18 25 1. and more. Choose the correct alternative for each part. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. 2.1 A sequence of two instructions that multiplies the contents of the DE register pair by 2 and stores the result in the HL register pair (in 8085 assembly language) is: 2. 16 data lines (b) 11 address.com Join discussion of this test paper at http://forum.24.2007 conducted by GATE Forum in over 25 cities all over India.1 (b) n (c) n + 1 (d) None of the above 2. The value of k for which 4 x 2 − 8 xy + ky 2 = 0 does not represent a pair of straight lines (both passing through the origin) is: (a) 0 (b) 2 (c) 9 (d) 3 1. The rank of the following ( n + 1) × ( n + 1) matrix.2.GATE CS .com 1.1995 www.22. This question has 25 parts. 8 data lines Join All India Mock GATE Classroom Test Series . the slope of the tangent equals −2x the y curve is (a) a straight line (b) a parabola (c) a circle (d) an ellipse 1.gatementor.gateforum.25 The minimum number of edges in a connected cyclic graph on n vertices is: (a) n . where a is a real number is 1 1 M M 1 a a2 L an a a2 L an M M M M M M a a2 L an (a) 1 (b) 2 (c) n (d) Depends on the value of a 1. Each part carries 2 Marks. Percentile. In the interval 0.23. visit www.gateforum. π the equation x = cos x has (a) No solution (b) Exactly one solution (c) Exactly two solutions (d) An infinite number of solutions 1.21. All India Rank. If at every point of a certain curve. For more details. (a) XCHG and DAD B (b) XTHL and DAD H (c) PCHL and DAD D (d) XCHG and DAD H The capacity of a memory unit is defined by the number of words multiplied by the number of bits/word. How many separate address and data lines are needed for a memory of 4 K × 16? (a) 10 address. GATE CS . procedure FIND (X:real).1995 www. D = 0 (c) A = 1. What is the value of X printed by the following program? program COMPUTE (input. end. C = 0. C = 0. and more. What does the following Pascal program segment do? while X <>Y do if X > Y then X:=X – Y else Y:=Y – X. interaction with IISc alumni in our online discussion forums.gateforum. For more details. 12 data lines Assume that X and Y are non-zero positive integers.5.3. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. D = 1 (b) A = 1. (d) 12 address. begin X:=2 Find(X) Writeln(X) end 2.gatementor.2007 conducted by GATE Forum in over 25 cities all over India. (a) Computes the LCM of two numbers (b) Divides the larger number by the smaller number (c) Computes the GCD of two numbers (d) None of the above 2. B = 0. AB = AC .4. var X:integer.com (c) 12 address. C = 0. D = 1 (d) A = 1. C and D satisfy the following simultaneous Boolean equations? A + AB = 0. begin X:=sqrt(X).com Join discussion of this test paper at http://forum. AB + AC + CD = CD (a) A = 1. 2 (a) 2 (b) (c) Run time error (d) None of the above What values of A. Percentile. 16 data lines 2. B.gateforum. output). All India Rank. B = 0. visit www. B = 1.com Think GATE Think GATE Forum . B = 0. D = 0 Join All India Mock GATE Classroom Test Series . C = 1. write(X). 6 5 3 1. 1 . 0499.GATE CS . 0260.com Think GATE Think GATE Forum . 0320. 0120. The sequence …………… is an optimal non-preemptive scheduling sequence for the following jobs which leaves the CPU idle for …………………….gateforum. All India Rank. 1 + 2 ω.1 2. (b) bc (c) ab (d) cc A shift reduce parser carries out the actions specified within braces immediately after reducing with the corresponding rule of grammar S → xxW {print"1"} S → y {print"2"} W → Sz {print"3"} What is the translation of xxxxyzz using the syntax directed translation scheme described by the above rules? (a) 23131 (b) 11233 (c) 11231 (d) 33211 Join All India Mock GATE Classroom Test Series .0 (c) {3.0 1 (b) (2.8.2. 0200.3}. Job Arrival time Burst time 1 0. -1 + 2 ω2 A language with string manipulation facilities uses the following operations head(s): first character of a string tail(s): all but the first character of astring concat(s1.1995 www. 0220. ω and ω2. (b) 8 (c) 7 (d) 10 If the cube roots of unity are 1.0 9 2 0.9. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 1 .gateforum.2 ω2 (c) -1. head(tail(tail(s)))) (a) ac 2. For more details.2 ω. 0430.com 2.10.1).gatementor. (a) -1. and more. 0240.3}. visit www. 0510.5 The address sequence generated by tracing a particular program executing in a pure demand paging system with 100 records per page with 1 free main memory frame is recorded as follows.2 ω2 (d) -1. 1 . 0560. interaction with IISc alumni in our online discussion forums.2. Percentile.2. (a) {3. 1 .2007 conducted by GATE Forum in over 25 cities all over India. 1 + 2 ω.s2):s1 s2 for the string acbc what will be the output of concat(head(s). What is the number of page faults? 0100.7. 1 + 2 ω2 (b) 1.1. unit(s) of time.com Join discussion of this test paper at http://forum.0 (d) {1. 0370 (a) 13 2.1).6. 0530. then the roots of the following equation 3 are ( x − 1) + 8 = 0 2.2 ω. The number of 1’s in 3 * 4096 + 15 * 256 + 5 * 16 + 3 are: ( ) (a) 8 (c) 2000 the (b) 9 1 3 (i + j + k) (b) 1 (i + j − k ) 3 binary representation (c) 10 2. smaller (d) larger. var2: (p.gateforum.GATE CS .14.y : integer). larger (c) larger. larger Join All India Mock GATE Classroom Test Series .16. interaction with IISc alumni in our online discussion forums.: real) end end Suppose an array of 100 records was declared on a machine which uses 4 bytes for an integer and 8 bytes for a real. For more details.var2) of var1: (x.com Think GATE Think GATE Forum . visit www.q.com 2.1995 www. All India Rank. How much space would the compiler have to reserve for the array? (a) 2800 (b) 2400 2. In a virtual memory system the address space specified by the address lines of the CUP must be __________ than the physical memory size and _______ than the secondary storage size.11. and more.15.com Join discussion of this test paper at http://forum. Two balls are drawn in succession.gateforum. Percentile. A bag contains 10 white balls and 15 black balls. case (var1. A unit vector perpendicular a = 2i − 2 j + k and b = 1 + j − 2k is: (a) (d) 1200 to (c) of (d) 12 both 1 (i − j − k ) 3 the (d) vectors 1 3 (i + j − k) 2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. smaller (b) smaller.12. The iteration formula to find the square root of a positive real number b using the Newton Raphson method is (a) xk +1 = 3 ( xk + b ) 2 xk (c) xk +1 = xk − 2 xk (x 2 k (b) xk +1 = 3 ( xk + b ) 2 xk +b ) (d) None of the above 2. A variant record in Pascal is defined by type varirec = record number : integer.2007 conducted by GATE Forum in over 25 cities all over India.13. (a) smaller. The probability that one of them is black and the other is white is: (a) 2 3 (b) 4 5 (c) 1 2 (d) 2 1 2.gatementor. ‘V’ is inclusive or and ⇒ is implication. Then (a) A is closed under* but < A. II.17. x y x + xyy + ( ) III. interaction with IISc alumni in our online discussion forums. E → xE y xy II. the number of collisions increases. Let A be the set of all non-singular matrices over real number and let* be the matrix multiplication operation. and more. Binary search using a linear linked list is efficient. is (a) true (b) multiple valued (c) false (d) cannot be determined 2. where L = x n y n such that n >= 1 ? { } I.21.gatementor. (a) I and II (b) II and III (c) I and IV (d) I and III Join All India Mock GATE Classroom Test Series . If the proposition ¬p ⇒ ν is true. The worst case complexity for Quicksort is O n2 IV. visit www. where ¬ is negation. As the number of entries in a hash table increases.com Think GATE Think GATE Forum . *> is not a semigroup (b) <A. *> is a group but not an abelian group 2. The solution of differential equation y ′′ + 3y ′ + 2y = 0 is of the form (a) C1e x + C2 e2 x (b) C1e − x + C2e3 x (c) C1e − x + C2e −2 x (d) C1e −2 x + C2 2− x 2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum.2007 conducted by GATE Forum in over 25 cities all over India. *> is a semigroup but not a monoid (c) <A.1995 www.19.18.com Join discussion of this test paper at http://forum. Recursive programs are efficient ( ) III. Percentile.gateforum. then the truth value of the proposition ¬pV ( p ⇒ q ) . *> is a monoid but not a group (d) <A.com 2.22.GATE CS . For more details.20. x + y + (a) I only (b) I and II (c) II and III (d) II only 2. All India Rank. (a) AB + CD + *F/D + E* (b) ABCD + *F/DE*++ (c) A *B + CD/F *DE++ (d) A + *BCD/F* DE++ Which of the following statements is true? I. Which of the following definitions below generates the same language as L. The postfix expression for the infix expression A + B * ( C + D ) / F + D * E is: 2. A finite state machine with the following state table has a single input x and a single out z. Y and Z after the execution of the program segment. visit www.1} . 1 C.com Think GATE Think GATE Forum . B. The values of the variables A and B are 5 CH and 92H. Percentile. Let ∑ = {0.1995 www. interaction with IISc alumni in our online discussion forums. var A. A computer system has a 4K word cache organized in block-set-associative manner with 4 blocks per set. 1 C B. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 1 C. 6 Consider the following high level program segment.GATE CS . (b) 6. respectively. (each integer is represented by two bytes) begin X :=A+B Y :=abs(bA-b). Also indicate error conditions if any. 40 3. X. 1 D B. All India Rank. 0 B. Y :unsigned byte. W.com 2. The number of bits in the SET and WORD fields of the main memory address format is: (a) 15. Give the contents of the memory locations for variables W. Join All India Mock GATE Classroom Test Series . X.25.23. not regular (d) not regular.24. and more.com Join discussion of this test paper at http://forum. 2 (d) 4. regular (b) not regular. then the shortest input sequence to reach the final state C is: (a) 01 (b) 10 (c) 101 { (d) 110 } 2. For more details. 0 If the initial state is unknown. 4 (c) 7.gateforum. present state next state. L = ∑* and R = 0n1n such that n > 0 then the languages L ∪ R and R are respectively (a) regular.gatementor. W :=A-B Z :=A*B End. Z :unsigned integer. 0 D. no regular 2. 64 words per block. 0 B B. z x=1 x=0 A D.gateforum. regular (c) regular.2007 conducted by GATE Forum in over 25 cities all over India. .1995 www.com 4. (b) The Pascal procedure given for computing the transpose of an N × N (N>1) matrix A of integers has an error.GATE CS .MAXSIZE. Procedure TRANSPOSE (var A: INTARR.B:integer). The jobs arrive and finish in the following sequences. What is the value of GET(3.B-1) end .gateforum. J.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum.B)+GET(A-1. interaction with IISc alumni in our online discussion forums. N : integer). A computer installation has 1000k of main memory. Find the error and correct it. and more..J]. Job 1 requiring 200k arrives Job 2 requiring 350k arrives Job 3 requiring 300k arrives Job 1 finishes Job 4 requiring 120k arrives Join All India Mock GATE Classroom Test Series . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.MAXSIZE] of integer. All India Rank. TMP. For more details. integer. type INTARR=array [1. begin if B = 0 then GET:=1 else if A < B then GET:=0 else GET:=GET(A-1. A[I.integer. 5. Percentile. visit www. var I.I}:=TMP end end.2007 conducted by GATE Forum in over 25 cities all over India. A(J. Assume that the following declaration are made in the main program const MAXSIZE=20.I]. (a) Consider the following Pascal function where A and B are non-zero positive integers.gateforum.2)? function GET(A.1. begin for I:=1 to NO – 1 do for J:=1 to N do begin TMP: = A[I.J]:=A[J.gatementor. Expr (Expr) 3.com Job 5 requiring 150k arrives Job 6 requiring 80k arrives (a) Draw the memory allocation table using Best Fit and First fit algorithms. X.gateforum. var A: record A. 9. 7. 8. Percentile.gateforum. B.2007 conducted by GATE Forum in over 25 cities all over India. visit www. (b) Which algorithm performs better for this sequence? 6. ExprTail _Expr 5. (b) Compute without using power series expansion lim x →0 sin x 0 SECTION – B Answer any TEN questions. VarTail (Expr) 8. procedure T(U. and more. C? Draw all these binary trees. 1. Expr Var Expr Tail 4. interaction with IISc alumni in our online discussion forums. All India Rank. 10. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.1995 www. Expr _Expr 2. (b) A grammar is said to have cycles if it is the case that A ⇒ +A Show that no grammar that has cycles can be LL(I). Y: integer). What is the number of binary trees with 3 nodes which when traversed in postorder give the sequence A. VarTail λ 9. B : integer end. Var Id Var Tail 7.com Join discussion of this test paper at http://forum. For more details. V. Goal Expr$ (a) Translate the arithmetic expression a * − ( b + c ) into syntax tree.gatementor.GATE CS . Construct the LL(1) table for the following grammar. (a) Determine the number of divisors of 600. (a) Using the scope rules of Pascal determine the declaration that apply to each occurrence of the names A and B in the following program segment. ExprTail λ 6.com Think GATE Think GATE Forum . Join All India Mock GATE Classroom Test Series . gateforum. 11.com Think GATE Think GATE Forum . A : integer end. 37. Show that Lc is also in NP. 25 Use bubblesort to arrange the sequence in ascending order.com Join discussion of this test paper at http://forum. Suppose L satisfies the two conditions given below (i) L is in NP and (ii) For every n.. and more.1 mm Join All India Mock GATE Classroom Test Series . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. then B = 2.2007 conducted by GATE Forum in over 25 cities all over India.1995 www. 13. with B do begin A:=X. 52. For more details.gatementor. interaction with IISc alumni in our online discussion forums. B:=Y end end. there is exactly one string of length n that belongs to L.com B: record B. (b) Find the lexical errors in the following Pascal statement: if A > 1. ‘v’ is inclusive or and ¬ is negation. Consider the following sequence of numbers 92. All India Rank. B:=V end. L ≤ ∑* . 11. If the overhead for formatting a disk is 96 bytes for 4000 byte sector.gateforum. begin with A do begin A:=4. 12. 12. Give the sequence at the end of each of the first five passes.5A else read (C). Obtain the principal (canonical) conjunctive normal form of the propositional formula ( p ∧ q ) V ( ¬q ∧ r ) Where ‘ ∧ ’ is logical and. Let L be a language over ∑ i.GATE CS .e. Let Lc be the complement of L over ∑* . Percentile. (a) Compute the unformatted capacity of the disk for the following parameters: Number of surfaces: 8 Outer diameter of the disk: 12 cm Inner diameter of the disk: 4 cm Inter track space: 0. 14. visit www. 00 1 The following is an 8085 assembly language program: MVI B.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. visit www. 15. OAH MVI A. The transmission rate is 1200 bits/second. one parity bit (odd parity) and one step bit. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. All India Rank.gatementor. determine the effective data transfer rate which is defined as the number of bytes transferred per second between disk and memory. For more details. 05H LXI H. (a) Implement a circuit having the following output expression using an inverter and NAND gate Z = A + B + C. (i) What is the complete bit stream that is transmitted for the string ‘0110101’? (ii) How many such strings can be transmitted per second? Join All India Mock GATE Classroom Test Series . and more.com Number of sectors per track: 20 (b) if the disk in (a) is rotating at 360 rpm.2007 conducted by GATE Forum in over 25 cities all over India. (a) An asynchronous serial communication controller that uses a start stop scheme for controlling the serial I/O of a system is programmed for a string of length seven bits. (b) What is the equivalent minimal Boolean expression (in sum of products form) for the Karnaugh map given below? AB CD 00 01 11 1 1 1 11 1 1 1 10 1 01 10 16. Percentile.gateforum.1995 www.gateforum. IC40H CALL SUB HLT SUB CMP M RZ INX H DCR B JNZ SUB RET (a) What does the program do? (b) What are the contents of registers A and B initially? (c) What are the contents of HL register pair after the execution of the program? 17.com Join discussion of this test paper at http://forum.GATE CS . S2. h. All India Rank. 19. var a.gateforum. f. The following is an incomplete Pascal function to convert a given decimal integer (in the range -8 to +7) into a binary integer in 2’s complement representation. visit www. and more. What is the size of the video buffer RAM for the display to be used in monochrome (1 bit per pixel) graphics mode? 18. BINARY:=BINARY + B*EXPONENT. V(b) end. i. e. S4. V(c) end.gatementor. B. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. begin cobegin begin S1. Draw the precedence graph for the statements S1 to S9. V(c). BINARY :integer. Consider the following program segment for concurrent processing using semaphore operators P and V for synchronization. V(d) end. For more details.1995 www. j. C that complete program. k : semaphore. g. begin if(N>=-8) and (N<=+7) then begin if N<0 then N : = A.com (b) Consider a CRT display that has a text mode display format of 80 × 25 characters with a 9 × 12 character cell. V(a). EXPONENT:=EXPONENT*10. interaction with IISc alumni in our online discussion forums.2007 conducted by GATE Forum in over 25 cities all over India. EXPONENT:integer. function TWOSCOMP (N:integer):integer. BINARY:=0.com Think GATE Think GATE Forum .GATE CS . begin P(a). d.com Join discussion of this test paper at http://forum. N :=C end TWOSCOMP:=BINARY end end. Percentile. var RAM.gateforum. b. begin P(c). c. Join All India Mock GATE Classroom Test Series . EXPONENT:=1. while N<>0 do begin REM:=N mod 2. Determine the expression A. V(j) end. P(f). 25. V(f) end. All India Rank. interaction with IISc alumni in our online discussion forums.V(g).com Think GATE Think GATE Forum . 23. How many minimum spanning trees does the following graph have? Draw them. begin P(e). The head of a moving head disk with 100 tracks numbered 0 to 99 is currently serving a request at tract 55. S3. (b) Determine the number of positive integers ( ≤ 720 ) which are not divisibly by any of numbers 2. and 5. S7. Join All India Mock GATE Classroom Test Series . V(i) end. A B 2 3 3 4 C 4 5 E D 23. Percentile. begin P(h). S6. For more details. 75.com begin P(d).gatementor. 65 Which of the two disk scheduling algorithms FCFS (First Come First Served) and SSTF (Shortest Seek Time First) will require less head movement? Find the head movement for each of the algorithms. S8. 2n > n2 24. S5. S9 end. begin P(b). (a) Show that G1 ∩ G2 is also a group of G (b) Is G1 ∪ G2 always a subgroup of G? 22. If the queue of requests kept in FIFO order is 10. the number of vertices of odd degree is always even. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Let G1 and G2 be subgroups of a group G. Prove using mathematical induction for n ≥ 5. Prove that in finite graph. V(k) end. 70.GATE CS .V(h) end. P(k). 20. 3. (a) Find the minimum value of 3 − 4 x + 2 x 2 . begin P(g).com Join discussion of this test paper at http://forum.1995 www. visit www.2007 conducted by GATE Forum in over 25 cities all over India. 21.gateforum.gateforum. (Weights are assigned to the edge). coend end. P(i). and more. P(j). begin P(j). (a) Get the names of all publishers. C) with the following functional dependencies: A.gateforum. ANAME. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com 26. For more details.gatementor. PROJECT. visit www. AUTHOR (ANAME. (a) Consider the relation scheme R(A. AGE) PUBLISHER (PNAME.com Think GATE Think GATE Forum . Consider the relation scheme. Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum.gateforum. JOIN and DIVIDE operations. (b) Get values of all attributes of all authors who have published a book for the publisher with PNAME = ‘TECHNICAL PUBLISHERS’. interaction with IISc alumni in our online discussion forums. B. B C.1995 www.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. CA Show that the scheme R is the Third Normal Form (3NF) but not in BoyceCode Normal Form (BCNF). Percentile. 27. ACITY. PNAME) Express the following queries using (one or more of )SELECT. (b) Determine the minimal keys of relation R. and more. PCITY) BOOK (TITLE. (c) Get the names of all authors who have published a book for any publisher located in Madras. INSTITUTION. All India Rank. 1. Percentile.GATE CS . the set (a – b) ∪(b-a) ∪(a∩b) is equal to.5 Two dice are thrown simultaneously. (d) The set of real numbers excluding zero in an abelian group under multiplication. Y = 1 (c) X = 97.4 (a) X = 1.≤) is (a) 3 (b) 4 (c) 9 (d) None of the above Suppose X and Y are sets and X and Y are their respective cardinalities. Let ≤ be the partial order defined by X ≤ Y if x divides y. and more.12.2 1. It is given that there are exactly 97 functions from X to Y. (c) The set of rational numbers form an abelian group under multiplication.com Join discussion of this test paper at http://forum.A 1. c or d against the sub-question number. Y = 97 (d) None of the above Which of the following statements is false? (a) The set of rational numbers is an abelian group under addition.3 (d) Ac ∩ Bc (c) A ∩ B Let X = {2. visit www.gateforum.3.com Think GATE Think GATE Forum .1 Let A and B be sets and let Ac and Bc denote the complements of the sets A and B. b.2007 conducted by GATE Forum in over 25 cities all over India. (a) (c) f ( x0 + h ) + f ( x0 − h ) (b) 2 f ( x0 + h ) + 2f ( x0 ) + f ( x0 − h ) 2 h (d) f ( x0 + h ) − f ( x0 − h ) 2h f ( x0 + h ) − 2f ( x0 ) + f ( x0 − h ) h2 Join All India Mock GATE Classroom Test Series . from this one can conclude that 1. For more details. Number of edge as in the Hasse diagram of (X. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. The probability that at least one of them will have 6 facing up is (a) 1.gatementor. (b) Ac ∪ Bc (a) A ∪ B 1.6. 1. interaction with IISc alumni in our online discussion forums.24}. Y = 97 (b) X = 97.1996 www.6 1 36 (b) 1 3 (c) 25 36 (d) 11 36 The formula used to compute an approximation for the second derivative of a function f at a point X0 is. All India Rank.com SECTION . Write in your answer book the correct or the most appropriate answer to the following multiple choice questions by writing the corresponding letter a. (b) The set of integers in an abelian group under addition.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. then the system has infinitely many solutions. Percentile. b}. (b) Determining whether a context-free grammar is ambiguous is undecidbale.2007 conducted by GATE Forum in over 25 cities all over India. both A and the augmented matrix [A b] have the same rank.10 Let L ⊆ Σ* where Σ = {a.com Join discussion of this test paper at http://forum.gateforum.gatementor. (b) If m < n and b is the zero vector.1996 www. visit www.gateforum. b is the zero vector and rank (A) = n.GATE CS .com Think GATE Think GATE Forum .8 Which two of the following four regular expressions are equivalent? (ε is the empty string). n ≥ 1 is regular 1. interaction with IISc alumni in our online discussion forums. (c) Given two arbitrary context-free grammars G1 and G2 it is undecidable whether L(G1) = L(G2).7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a m × 1 column vector and X is a n × 1 column vector of unknows. which of the following is true? { (a) L = x x has an equal number of a's and b's { } is regular } (b) L = an bn n ≥ 1 is regular { (c) L = x x has more a's and b's { } is regular } (d) L = am bn m ≥. Which of the following is false? (a) The system has a solution if and only if. and more. For more details. 1. 1.11 Which of the following is false? n log n (a) 100n log = 100 (b) ( ) (c) If 0 < x < y then n x = 0 ny log n = 0 (loglog n ) (d) 2n ≠ 0 ( nk ) Join All India Mock GATE Classroom Test Series . (i) (00) * (ε + 0) (ii) (00)* (iii) 0* (iv) 0(00)* (a) (i) and (ii) 1. (d) The system will have only a trivial solution when m = n. (d) Given two regular grammars G1 and G2 it is undecidable whether L(G1) = L(G2).com 1. All India Rank. (c) If m = n and b is non-zero vector. then the system has a unique solution.9 (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv) Which of the following statements is false? (a) The Halting problem of Turing machines is undecidable. interaction with IISc alumni in our online discussion forums. how many nodes will become unbalanced when a node is inserted as a child of the node “g”? a e b c d f g (a) 1 1.14? (a) f e g c d b a 1.com 1. 1 (c) 2.15 1. Percentile. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 2 (d) 1.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum.2007 conducted by GATE Forum in over 25 cities all over India. 2 (b) 2.13 (a) (ii) and (iii) are true (b) (i) and (ii) are true (c) (iii) and (iv) are true (d) (ii) and (iv) are true An advantage of chained hash table (external hashing) over the open addressing scheme is (a) Worst case complexity of search operations is less? (b) Space used is less (c) Deletion is easier (d) None of the above 1.1996 www.14 In the balanced binary tree in Fig. All India Rank. and more.16 (b) 3 (b) g c b d a f e (c) g c d b f e a (d) f e d g c b a Relative mode of addressing is most relevant to writing (a) coroutines (b) position – independent code (c) shareable code (d) interrupt handlers The (i) (ii) (iii) (iv) pass numbers for each of the following activities object code generation literals added to literal table listing printed address resolution of local symbols that occur in a two pass assembler respectively are (a) 1.gateforum. (ii) Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations. 1.14 given below. For more details.17 (c) 7 (d) 8 Which of the following sequences denotes the post order traversal sequence of the tree of question 1. 2.gateforum. 1.gatementor. 2 Join All India Mock GATE Classroom Test Series . 1. visit www. 1. 2.1.12 Consider the following statements: (i) First-in-first out types of computations are efficiently supported by STACKS.GATE CS . 2. 1. (iii) Implementing QUEUES on a circular array is more implementing QUEUES on a linear array with two indices. 2. efficient than (iv) Last-in-first-out type of computations are efficiently supported by QUEUES. 18 The process state transition diagram in Fig.23.1010 (b) 100000 …. P and V 1. Which of the following is an example of spooled device? (a) A line printer used to print the output of a number of jobs.19.com Think GATE Think GATE Forum .0001 (c) 111111 ….com 1..22. Number of machine cycles required for RET instruction in 8085 microprocessor is (a) 1 (b) 2 (c) 3 (d) 5 1. (d) A graphic display device. Both’s algorithm for integer multiplication gives worst performance when the multiplier pattern is (a) 101010 …. visit www.21. Percentile.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. A critical section is a program segment (a) which should run in a certain specified amount of time (b) which avoids deadlocks (c) where shared resources are accessed (d) which must be enclosed by a pair of semaphore operations.. 1. and more.1111 (d) 011111 …. 1.1996 www. For more details.20.8 is representative of TERMINATED NEW RUNNING (a) a batch operating system READY BLOCKED (b) an operating system with a preemptive scheduler (c) an operating system with a non-preemptive scheduler (d) a uni-programmed operating system. (c) A secondary storage device in a virtual memory sytem..gatementor.2007 conducted by GATE Forum in over 25 cities all over India.1110 Join All India Mock GATE Classroom Test Series .. The size of ROM required is (a) 256 × 16 (b) 64 K × 8 (c) 4 K × 16 (d) 64 K × 16 1. (b) A terminal used to enter input data to a running program.gateforum. A ROM is sued to store the table for multiplication of two 8-bit unsigned integers. All India Rank.1.GATE CS . interaction with IISc alumni in our online discussion forums.gateforum. gatementor. and more. y ) = 2 ( x − y ) .com 1. x + y ) x+y x −y (c) f −1 ( x. 2 ( x + y ) Let R be a non-empty relation on a collection of sets defined by A R B if and only if A ∩ B = φ.gateforum. Let f:R×R R×R be a bijective function defined by f(x. which of the following statements is true? (a) It gives non-uniform priority to various devices. y ) = .2007 conducted by GATE Forum in over 25 cities all over India. the inverse function of f is given by 2. Percentile. The range of the magnitude of the normalized numbers in this representation is (a) 0 to 1 (b) 0.25 Consider the following floating-point number representation.5 to 1-2-23 ( ) 2. visit www. c or d against the sub-question number.GATE CS .y)=(x+y. y ) = . y ) = ( x − y . (c) It is only useful for connecting slow devices to a processor device. interaction with IISc alumni in our online discussion forums. Write in your answer book the correct or the most appropriate answer to the following multiple choice questions by writing the corresponding letter a.24.com Join discussion of this test paper at http://forum. (pick the true statement) (a) R is reflexive and transitive (b) R is symmetric and not transitive (c) R is an equivalence relation (d) R is not reflexive and not symmetric Join All India Mock GATE Classroom Test Series . b. For the daisy chain scheme of connecting I/O devices. For more details.com Think GATE Think GATE Forum .5 to 1 (c) 2−23 to 0.1996 www.gateforum.1 Let R denotes the set of real numbers.x-y). Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (d) It requires a separate interrupt pin on the processor for each device. (b) It gives uniform priority to all devices. x + y x −y (b) f −1 ( x. 1 1 (a) f −1 ( x. All India Rank. 2 2 (d) f −1 ( x.5 (d) 0. 31 24 23 0 Exponent Mantissa The exponent is in 2’s complement representation and mantissa is in the sign magnitude representation. 2. 1. Then.2. (d) A subset s ≠ φ of G is a subgroup of the group <G. where c > 0 is. a* b-1 ∈ s.2. (b) xn +1 = 3xn2 2 xn3 + c (d) xn +1 = 3xn2 cos θ The matrices sin θ 2 xn3 − 3 c 3xn2 2 xn3 − c 3xn2 − sin θ a 0 and commute under multiplication cos θ 0 b (a) if a = b or θ = nπ. 2.gateforum.2007 conducted by GATE Forum in over 25 cities all over India.5..com Think GATE Think GATE Forum .4.8. is an integer (b) always (c) never (d) if a cos θ ≠ b sin θ The probability that top and bottom cards of a randomly shuffled deck are both aces in (a) 2. ∨ as OR.7.6. (( x → y ) ∧ x ) → y ( x → ( x ∨ ψ )) (b) (d) (( x → y ) ∧ ( x ∧ y )) → x (( x ∨ y ) ↔ ( x → y )) Which one of the following is false? (a) The set of all bijective functions on a finite set forms a group under function composition. and more. Which one? (a) L1. (b) The set {1. b ∈ s. …….com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums. ~ as NOT.GATE CS . (a) (c) 2. L2 (b) L1 ∩ L2 (c) L1 ∩ R (d) L1 ∪ L2 Join All India Mock GATE Classroom Test Series . Which of the following is false? Read ∧ as AND.gatementor. Newton-Raphson iteration formula for finding 3 c . 2.3. 2 xn3 + 3 c 4 4 × 52 52 (b) 4 3 × 52 52 (c) 4 3 × 52 51 (d) 4 4 × 52 51 If L1 and L2 are context free languages and R a regular set. visit www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (a) xn +1 = (c) xn +1 = 2. Percentile. one of the languages below is not necessarily a context free language. All India Rank. For more details.gateforum. *> if and only if for any pair of elements a. p –1} forms a group under multiplication mod p where p is a prime number.com 2. (c) The set of all strings over a finite alphabet forms a group under concatenation.1996 www. as one way implication and ↔ as two way implication. Define a context free languages L ≤ {0. 6. 10.2007 conducted by GATE Forum in over 25 cities all over India. Percentile.GATE CS . 5.9.11. (d) None of the above 2.gateforum. For more details.gateforum.10.com Think GATE Think GATE Forum .com 2. interaction with IISc alumni in our online discussion forums. 7. and more. init(L) is the set of prefixes of L) Let L {w/w is nonempty and has on equal number of 0’s and 1’s Then init (L) is (a) the set of all binary strings with unequal number of 0’s and 1’s (b) the set of all binary strings including the null string (c) the set of all binary strings with exactly one more 0’s than the number of 1’s or one more 1 than the number of 0’s. visit www. 2. 17. 19. The grammar whose productions are if id then <stmt> if id then <stmt> else <stmt> id:=id is ambiguous because (a) the sentence if a then if b then c:=d (b) the left most and right most derivations of the sentence if a then if b then c:=d give rise top different parse trees (c) the sentence if a then if b then c:=d else c:=f has more than two parse trees (d) the sentence if a then if then c:=d else c:=f has two parse trees 2.1} init (L) = {u/uv ∈ L for some ν in {{0.gatementor. All India Rank. The minimum number of interchanges needed to convert the array 89. 12.com Join discussion of this test paper at http://forum. The recurrence relation T(1) = 2 n T(n) = 3T + n 4 Has the solution T(n) equal to (a) O(n) (b) O (log n) 3 (c) O n 4 (d) None of the above Join All India Mock GATE Classroom Test Series . 40. 70 (a) 0 (b) 1 (c) 2 (d) 3 2.1996 www. 11.1}} (in other words. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 9.12. 2. Quick-sort is run on two inputs shown below to sort in ascending order (i) 1. X if X=0 then …. 15. 62.gateforum. 58. 91.GATE CS . X M2 X ENDC IF NE. X WORD X + 1 ENDC ENDM (a) (ii) only (b) (i) only (c) both (i) and (ii) (d) None of the above Join All India Mock GATE Classroom Test Series .15.gatementor.gateforum.13. (a) C1 < C2 (b) C1 > C2 (c) C1 = C2 (d) we cannot say anything for arbitrary n. Percentile. 24 The number of nodes in the left subtree and right subtree of the root respectively is (a) (4. 37. n – 1. and more.14. 2. 5. 3) (d) (3. All India Rank. Then. 2. 3. M1 X + 1 ENDC IF NE. 8. ….com 2.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. n – 2. 20.3 …. 60. A binary search tree is generated by inserting in order the following integers: 50. 8) 2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. visit www.16. 4) (c) (8. 1 Let C1 and C2 be the number of comparisons made for the inputs (i) and (ii) respectively. X: M1.1996 www. X: if X ≠ O then …… WORD X: address (X) is stored here ENDC ENDM (ii) MACRO M2.n (ii) n.com Join discussion of this test paper at http://forum. For more details. Which of the following macros can put a macro assembler into an infinite loop? (i) MACRO IF EQ.2007 conducted by GATE Forum in over 25 cities all over India. The average number of key comparisons done on a successful sequential search in list of length n is (a) log n (b) n −1 2 (c) n 2 (d) n +1 2 2.X IF EQ. 7) (b) (7. and more.21.19.gatementor.21 which has a four fit binary number b3 b2 b1b0 as input and a five bit binary number.com 2. Consider the circuit in Fig. d4 ‘φ’ Binary adder d3 d2d1 d0 Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India.1 (d) A – 3 B – 4 C – 2 D .2 (c) A – 4 B – 3 C – 2 D . 8.20. C. A 1000 Kbyte memory is managed using variable partitions but to compaction.GATE CS .gateforum. It currently has two partitions of sizes 200 Kbytes and 260 Kbytes respectively.gateforum. d4d3d2d1d0 as output. The completion time of A under round robin scheduling with time slice of one time unit is (a) 10 (b) 4 (c) 8 (d) 9 2. B. and that all other philosophers pick up the right fork before the left fork (d) None of the above 2. All India Rank. A solution to the Dining Philosophers Problem which avoids deadlock is (a) ensure that all philosophers pick up the left fork before the right fork (b) ensure that all philosophers pick up the right fork before the left fork (c) ensure that one particular philosopher picks up the left fork before the right fork. 1 time units respectively.17.1996 www. b3 b2 b1 b0 ‘φ’ (a) Binary of Hex conversion (b) Binary to BCD conversion (c) Binary to grey code conversion C in C out (d) Binary to radix-12 conversion.18.com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums.2 (b) A – 4 B – 3 C – 1 D . D.com Think GATE Think GATE Forum . 1. visit www. Percentile.2. The smallest allocation request in Kbytes that could be denied is for (a) 151 (b) 181 (c) 231 (d) 541 2. their burst CPU time requirements are 4. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. The correct matching for the following pairs is (A) Activation record (1) Linking loader (B) Location counter (2) Garbage collection (C) Reference counts (3) Subroutine call (D) Address relocation (4) Assembler (a) A – 3 B – 4 C – 1 D .1 2. For more details. Four jobs to be executed on a single processor system arrive at time 0+ in the order A. All India Rank. For more details. Minimum number of bits required in the control word to generate the required control signals will be (a) 2 (b) 2.24. interaction with IISc alumni in our online discussion forums. Percentile. visit www.25.2.gatementor.2.22. AB CD (a) BD + BD (b) (c) (d) ( B + C + D )( B + C + D ) ( B + D )( B + D ) ( B + D )( B + D ) 00 00 01 11 1 1 20 01 1 1 11 1 1 10 1 1 2. What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in Fig.5 (c) 10 (d) 12 Join All India Mock GATE Classroom Test Series .2. Consider the following state table in Fig. and more.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India.23.com Think GATE Think GATE Forum .gateforum. Assume that during any microinstruction. Consider the circuit in Fig. at most two control signals are active.gateforum.com 2.22 f implements C 0 C C C 1 Multiplex 2 3 A f B (a) A BC + ABC + ABC (b) A + B + C (c) A ⊕ B ⊕ C (d) AB+BC+CA 2.1996 www.24.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. The number of states in the minimized machine will be input x Present state (a) 4 0 1 A D0 B1 B A0 C1 C A0 B1 D A1 C1 (b) 3 (c) 2 (d) 1 2. A micro program control unit is required to generate a total of 25 control signals.23 for a sequential machine. and two control inputs C0 and C1. Let f be a function defined by x2 for x ≤ 1 2 f ( x ) = ax + bx + c for 1 x ≤ 2 x+d for x > 2 Find the values for the constants a. 4. An 8085 based system has an output port with address 00H.gateforum. 5. one 2-input OR gate and one Inverter. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Consider the following assembly language program. Which of the following probe sequences are possible and which are not? Explain. Join All India Mock GATE Classroom Test Series . and more. interaction with IISc alumni in our online discussion forums. (a) 61 52 14 17 40 43 (b) 2 3 50 40 60 43 (c) 10 65 31 48 37 43 (d) 81 61 52 14 41 43 (e) 17 77 27 66 18 43 A logic network has two data inputs A and B. For more details. one 2-input AND gate. visit www. It implements the function F according to the following table. b.com Think GATE Think GATE Forum .com 3. ORG 0100H MVI A. 0105H PCHL HLT (a) What does the program do with respect to the output port φφ H? (b) Show the waveforms at the three least significant bits of the port φφ H. 00H LXI H. Percentile.com Join discussion of this test paper at http://forum. 6.2007 conducted by GATE Forum in over 25 cities all over India. All India Rank.GATE CS . C1 C2 F 0 0 A+B 0 1 A+B 1 0 A⊕B Implement the circuit using one 4 to AB Multiplexor. one 2-input Exclusive OR gate.1996 www. A binary search tree is used to locate the number 43.gatementor.gateforum. c and d so that f is continuous and differentiable everywhere on the real line. S ABAC A aA|ε B bB ε Cd Join All India Mock GATE Classroom Test Series . f3 K fn } is defined by the following recurrence: fn + 2 = fn +1 + fn . B. Percentile. If f and g ∈ F. and (iii) page replacements. visit www.gateforum. Let C = A and CD = 1. and more. interaction with IISc alumni in our online discussion forums.3} {1. All India Rank. All questions carry equal marks. whose current status (page numbers in decimal) is 17 1 63 LRU page For each hexadecimal address in the address sequence given below. d}.2007 conducted by GATE Forum in over 25 cities all over India. a Let A = 11 a21 a12 b11 and B = a22 b21 b12 be two matrices such that b22 1 0 AB = I.gateforum. define an equivalence relation ~ by f ~ g if and only if f(3) = g. if any.2. {a. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. n ≥ 1. (i) the new status of the list (ii) page faults. Let G be a context-free grammar where G = ({S.com Join discussion of this test paper at http://forum. LRU page replacement is implemented using list. if any.2.com Think GATE Think GATE Forum . A. b. page size of 256 bytes. 11. For more details. 10FF 11B0 indicate.GATE CS . (a) Find the number of equivalence classes defined by ~ (b) Find the number of elements in each equivalence class. 010D. Let F be the collection of all functions f:{1. 00FF. 10. f2 = 1 : f1 = 1 : Prove by induction that every third element of the sequence is even. f2 .com 7. C}. SECTION – B Answer any TEN questions from this section.1996 www.3}. Express the elements of D in terms of the 1 1 elements of B. and has 1 Kbyte of main memory. The Fibonacci sequence {f1 . 8. 9. P.S) with the productions in P given below.gatementor. A demand paged virtual memory system uses 16 bit virtual address. and more. All India Rank. KK} {( q2 . Transform the grammar G to an equivalent contextfree grammar G that has no ε productions and no unit productions. ε .gateforum. ε )} δ ( q2 . b. ( A unit production is of the form x y. b. b ) = {( q2 .12) for two finite state machines M1 and M2 recognizing languages L1 and L2 respectively. and y are non terminals). q2) (a. φ) be a pushdown automaton accepting by empty stack for the language which is the set of all nonempty even palindromes over the set {a. 12. b. a. Zb )} (1) δ ( q1 . interaction with IISc alumni in our online discussion forums. Z) δ. (a) Display the transition diagram for a machine that recognizes L1 L2.1996 www. a. b. (b) Modify the transition diagram obtained in part (a) obtain a transition diagram for a machine that recognizes (L1 L2) by adding only ε transitions and no new states.gateforum. Za)} δ ( q1 . visit www. a.com (ε denoted the null string). qi. a ) = {KK . {( q1.GATE CS . obtained from transition diagrams for M1 and M2 by adding only and transitions and no new states.com Join discussion of this test paper at http://forum. a ) = (6) (7) Join All India Mock GATE Classroom Test Series . Z ) = {( q1 . b ) = {KK .b). Given below are the transition diagrams (Fig. Z. Z ) = (2) (3) δ ( q1 . (a. ε )} δ ( q2 . Below is an incomplete specification of the transition d. complete the specification. KK} (4) δ ( q1 .2007 conducted by GATE Forum in over 25 cities all over India. For more details.gatementor. (Final states are enclosed in double circles). Percentile. 0 1 Start A M1 B 0 1 a Start C b b D a a E b 13. Z ) = {( q2 . The top of stack is assumed to be at the right end of the string representing stack contents. ε )} (5) δ ( q2 .b}. Let Q = (q1.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. com 14. All India Rank. Complete the following O(n) procedure to insert item x (which is guaranteed to be smaller than any item in the last row or column) still keeping A partially sorted. and more. i: =i + 1 (5) end (6) else begin (7) (8) end (9) A [i] [j]:= end 15. n – 1} for any fixed ‘n’. For more details. v) is |u – v| (b) the weight of the edge (u. A complete. (2) while (x > or x >) do (3) if A[ i + 1] [j] ∩ [i] ]j] then begin (4) A [i] [j]:= A[i +1] [j].gatementor.com Think GATE Think GATE Forum ..com Join discussion of this test paper at http://forum. 1 ….gateforum. j:=A[i] [j]:=x. interaction with IISc alumni in our online discussion forums. Draw the minimum spanning tree of G if (a) the weight of the edge (u. Use the hash funtion H(x) = (ord (x) – ord (‘a’) + 1) mod 10 And linear probing to resolve collisions. visit www. A two dimensional array A[1. (a) Which insertions cause collisions? (b) Display the final hash table? 16. Percentile. jε 1 − n − 1 A i j < A i j + 1 and A i + 1 j A i j < Fill in the blanks: (a) The smallest item in the array is at A[i] [j] where i = and j = ………… (b) The smallest item is deleted. v) is u + v Join All India Mock GATE Classroom Test Series .1996 www.gateforum. weighted graph G is given on the vertex {0. Insert the characters of the string K R P C S N Y T J M into a hash table of size 10.2007 conducted by GATE Forum in over 25 cities all over India. var begin (1) i: =1.GATE CS . undirected. procedure insert (x integer) j ′ j:integer. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.n] [1 – n] of integers is partially sorted if ∀i. 19.com Join discussion of this test paper at http://forum. and more.gatementor. (b) Write down sequence of vertices in the shortest path from A to E. What is printed by the program if parameter a is procedure test 1 is passed as (i) call-by-reference parameter? (ii) call-by-value-result parameter? program Example (input. Consider the following program that attempts to locate an element x in an array a [ ] using binary search. begin i:1.com Think GATE Think GATE Forum .GATE CS . Percentile. repeat k:(i+j) div 2. weighted graph shown below in Fig.1996 www. Assume N > 1. if a [k] < x then i:=k else j:=k until (a =x) or (i∩=j). output) var b: integer.4 B 41 6 12 9φ A 22 C 12 2 6φ D 5φ E 15 7φ 1φ F We are interested in the shortest paths from A.com 17. x:integer.j. Let G be the directed. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.k:integer. Consider the following program in pseudo-Pascal syntax. (a) Output the sequence of vertices identified by the Dijkstra’s algorithm for single source shortest path when the algorithm is started at node A. Under what conditions does the program fail? var i. visit www. For more details. a:=array.2007 conducted by GATE Forum in over 25 cities all over India. The program is erroneous. Join All India Mock GATE Classroom Test Series . All India Rank. (c) What is the cost of the shortest path from A to E? 18.gateforum. procedure test 2. [1 … N] of integer. interaction with IISc alumni in our online discussion forums.gateforum.=n. if (a [k] = x) then writeln (‘x is not in the array’) else writeln (‘x’ is not in the array’) end. The concurrent programming constructs fork and join are as below: fork <label> which creates a new process executing from the specified label join <variable> which decrements the specified synchronization variable (by 1) and terminates the process if the new value is not 0.gateforum. test ] (b). 21. writeln (‘point 3: ‘b) end 20. test 2. interaction with IISc alumni in our online discussion forums.com begin b: = 10 end procedure test 1 (a:integer). begin (*Example*) b:=3. Show the precedence graph for S1. visit www.”} E id {print id. S3.2007 conducted by GATE Forum in over 25 cities all over India. end. N=2 M=2 fork L3 fork L4 S1 L1 : join N S3 L2: join M S5 L3:S2 goto L1 L4:S4 Join All India Mock GATE Classroom Test Series . S4 and S5 of the concurrent program below. (a + b)* (c + d).com Think GATE Think GATE Forum .1996 www. and more.b). writeln (‘point 1: ‘a. wrote.b). begin a:5.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS .name} E (E) An LR – parser executes the actions associated with the productions immediately after a reduction by the corresponding production.m(‘point: ‘a. using SDTS given above.gatementor.com Join discussion of this test paper at http://forum. All India Rank. Draw the parse tree and write the translation for the sentence. Consider the syntax-directed translation schema (SETS) shown below: E E + E {print “+”} E E * E {print “. For more details. S2. Percentile. D1 Q1 D2 CK Q2 CK D3 Q3 CK Clock Fig. Use the following names for the states corresponding to the values of flip-flops as given below.com goto L2 next: 22. Join All India Mock GATE Classroom Test Series . where P0.GATE CS .com Think GATE Think GATE Forum . P2 are processes. Percentile.1996 www.2007 conducted by GATE Forum in over 25 cities all over India. The disk is used as follows: Disk-block 0: File Allocation Table.5. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. A computer system uses the Banker’s Algorithm to deal with deadlocks. Disk block 3: Data block 2. visit www. For more details.com Join discussion of this test paper at http://forum. Its current state is shown in the tables below.gateforum. with one 32 bit entry per file: Disk block 2: Data block 1. etc. and R0.gatementor. All India Rank.5 (a) Draw a state diagram. R2 are resoures types. representing the data block address of the next date block in the file Disk block 1: Directory. interaction with IISc alumni in our online discussion forums. consisting of one 8-bit entry per date block. which is implemented by the circuit. R1. and more. Consider the synchronous sequential circuit in Fig.gateforum. (a) What is the maximum possible number of files? (b) What is the maximum possible file size in blocks? 24. Maximum Need Current Allocation R0 R1 R2 P0 4 1 2 P1 1 5 P2 1 2 Available R0 R1 R2 R0 R1 R2 P0 1 0 2 2 2 0 1 P1 0 3 1 3 P2 1 0 2 (a) Show that the system can be in this state. (b) What will system do on a request by process P0 for one unit of resource type R1? 23. A file system with a one-level directory structure is implemented on a disk with disk block size of 4 K bytes. P1. 98 16 Kbytes 0. which are not reachable.98 16 M byte 0.90 16 Kbytes 0. What fraction of the processor time is consumed by the disk. For more details.1996 www.com Think GATE Think GATE Forum . and assume that the handling of the interrupt at DMA completion requires 500 clock cycles for the processor. Assume that the initial set-up of a DMA transfer takes 1000 lock cycles for the processor. A hard disk is connected to a 50 MHz processor through a DMA controller.995 Size Hit ratio 250 M bytes 1. The hard disk has a transfer rate of 2000 Kbytes/sec and average block size transferred is 4 K bytes.99 64 Kbytes 0.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. 25.80 4M byte 0.99 Size Hit ratio 260 Mbyte 1.gateforum. if the disk is actively transferring 100% of the time? Level 1 (Cache memory) Level 1 (Cache memory) Access time = 50 nsec/byte Access time = 200 nsec/byte Size Hit ratio Size Hit ratio 8 Kbytes 0.95 64 Kbytes 0. and more.com Q1 Q2 Q3 State 0 0 0 S0 0 0 1 S1 - - - - - - - - - - - - 1 1 1 S7 (b) Given that the initial of the circuit is S4.gatementor. All India Rank. visit www.com Join discussion of this test paper at http://forum. identify the set of states. 26.gateforum.0 Join All India Mock GATE Classroom Test Series .0 A computer system has a three level memory hierarchy.90 16 M byte 0. interaction with IISc alumni in our online discussion forums. with access time and hit ratios as shown below: Level 1 (Cache memory) Level 2 (main memory) Level 3 Access time = 50 nsec/byte Access time = 200 nsec/byte Access time = 5 µsec/byte Size Hit ratio Size Hit ratio 8 M byte 0. Percentile.80 4 Kbytes 0. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Date) Explain in one English sentence.995 (a) What should be the minimum sizes of level 1 and 2 memories to achieve an average access time of less than 100 nsec? (b) What is the average access time achieved using the chosen sizes of level 1 and level 2 memories? 27. User Name.1996 www. All India Rank. For more details.gateforum. visit www. interaction with IISc alumni in our online discussion forums. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.95 64 M byte 0.com 64 M byte 0.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India.com Join discussion of this test paper at http://forum. and more. Percentile. Book Title ((USERS ISSUED) BOOKS)) (b) σ Author Name (BOOKS (σ Home Town) = Delhi (USERS ISSUED))) Join All India Mock GATE Classroom Test Series . what each of the following relational algebra queries is designed to determine (a) σ User #=6 (11 User #. Home Town) BOOKS (Books # Book Title.com Think GATE Think GATE Forum .gatementor. A library relational database system uses the following schema USERS (User #. Author Name) ISSUED (Book #. User #.gateforum. Each sub-part contains a multiple-choice question. Percentile.2 (d) not converge 2 The determinant of the matrix (a) 11 1.gateforum. All India Rank.3 (b) A – 3 B – 4 C – 1 D . For more details.3 1.1997 www.com Think GATE Think GATE Forum .25 (a) converge to -1 (b) converge to (c) converge to .2007 conducted by GATE Forum in over 25 cities all over India.4 (c) 0.gateforum.2 (c) A – 3 B – 4 C – 2 D . the iterations will 6 −8 0 2 0 0 0 0 1.gatementor. interaction with IISc alumni in our online discussion forums.1 The probability that it will rain today is 0. b. If the iterations are started form –1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 1.1 (d) A – 4 B – 1 C – 2 D . Which of the following implementations of a list should be used? (a) Singly linked list (b) Doubly linked list (c) Circular doubly linked list (d) Array implementation of list The correct matching for the following pairs is (A) All pairs shortest paths (1) Greedy (B) Quick Sort (2) Depth-First search (C) Minimum weight spanning tree (3) Dynamic Programming (D) Connected Components (4) Divide and Conquer (a) A – 2 B – 4 C – 1 D .5.3 (b) 0.7.com Join discussion of this test paper at http://forum. Write in your answer book the sub-part number and the letter a. visit www. This question contains 10 sub-parts each carrying ONE mark.5 (d) 0.35 1 4 6 is: 4 8 0 −1 1 (b) -48 (c) 0 (d) -24 The concatenation of two lists is to be performed on 0(1) time. and more.4 The Newton-Raphson method is used to find the root of the equation x 2 − 2 = 0 .GATE CS . c or d corresponding to the most appropriate answer.6. The probability that it will rain either today or tomorrow is 0.com SECTION – A 1.3 Join All India Mock GATE Classroom Test Series . What is the probability that it will rain today and tomorrow? (a) 0. The probability that it will rain tomorrow is 0.2 1. 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile.com 1. It is required to make efficient use of memory.8 A language L allows declaration of arrays whose sizes are not known during compilation. For more details.gatementor. All India Rank. Which one of the following is true? (a) A compiler using static memory allocation can be written for L (b) A compiler cannot be written for L. interaction with IISc alumni in our online discussion forums.GATE CS . 1. and more. (c) A compiler using dynamic memory allocation can be written for L (d) None of the above 1.6 In the following grammar Y Y Y Y ::= Z * Z Z ::= id X ::= X ⊕ Which of the following is true? (a) ‘⊕’ is left associative while ‘*’ is right associative (b) Both ‘⊕’ and ‘*’ is left associative (c) ‘⊕’ is right associative while ‘*’ is left associative (d) None of the above 1. (a) that support recursion (b) that support dynamic data structures (c) that use dynamic scope rules (d) None of the above Join All India Mock GATE Classroom Test Series .com Think GATE Think GATE Forum . an interpreter must be used.gateforum.gateforum.1997 www.9 The conditional expansion facility of macro processor is provided to (a) test a condition during the execution of the expanded program (b) to expand certain model statements depending upon the value of a condition during the execution of the expanded program (c) to implement recursion (d) to expand certain model statements depending upon the value of a condition during the process of macro expansion.7 Which of the following is essential for converting an infix expression to the postfix form efficiently? (a) An operator stack (b) An operand stack (c) An operand stack and an operator stack (d) A parse tree 1.10 Heap allocation is required for languages. visit www.com Join discussion of this test paper at http://forum. gatementor. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. c or d corresponding to the most appropriate answer. The question contains 5 subparts.1997 www.1 An N-bit carry lookhead adder. c or d corresponding to the most appropriate answer. where Z is the set of integers and the operation * is defined by n*m = maximum (n.*) is a monoid (b) (Z.5 The correct matching for the following pairs is (A) DMA I/O (1) High speed RAM (B) Cache (2) Disk (C) Interrupt I/O (3) Printer (D) Condition Code Register (4) ALU (a) A – 4 B – 3 C – 1 D .gateforum.5 interrupt in 8085 microprocessor executes service routing from interrupt vector location (a) 0000H 2. The minimum addition time using the best architecture for this adder is (a) proportional to N (b) proportional to log N (c) a constant (d) None of the above 3. each carrying 1 mark.GATE CS . Each subpart contains a multiple-choice question. All India Rank. Let z = x*y.*) is an Abelian group (c) (Z. visit www. and more. each carrying 1 mark.3 (b) x (b) 0075H (c) 003CH (d) 0034H Purpose of a start bit in RS 232 serial communication protocol is (a) to synchronize receiver for receiving every byte (b) to synchronize receiver for receiving a sequence of bytes (c) a parity bit (d) to synchronize receiver for receiving the last byte 2. 3. Each subpart contains a multiple-choice question.1 (d) A – 2 B – 3 C – 4 D .2 (c) 0 (d) 1 RST 7.1 Let (Z. Write in your answer book the subpart number and the letter a.com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums.com Think GATE Think GATE Forum . Write in your answer book the subpart number and the letter a.2007 conducted by GATE Forum in over 25 cities all over India. value of z*x is (a) x +y 2. where N is a multiple of 4.4 (c) A – 4 B – 3 C – 2 D .4 2. For more details. b.2 (b) A – 2 B – 1 C – 3 D .1 Let * be defined as x*y= x +y.*)? (a) (Z.*) be an algebraic structure. employs ICs 74181 (4 bit ALU) and 74182 (4 bit carry lookhead generator).com 2. The question contains 10 subparts.*) is a group (d) None of the above Join All India Mock GATE Classroom Test Series . Percentile.m). which of the following statements is true for (Z. 2. b.gateforum. Percentile.com Think GATE Think GATE Forum . how many a complements does the element ‘e’ have? (a) 2 b (b) 3 c g (c) 0 d e (d) 1 f 3. and more.com 3.3 (b) p ∨ (q p) (c) p ∨ (p q) (d) p (p q) In the lattice defined by the Hasse diagram given in following figure.7 The correct matching for the following pairs is: (A) Disk scheduling (1) Round robin (B) Batch processing (2) SCAN (C) Time sharing (3) LIFO (D) Interrupt processing (4) FIFO (a) A – 3 B – 4 C – 2 D .gatementor.1997 www.GATE CS .4 Given Σ={a.gateforum. All India Rank.2007 conducted by GATE Forum in over 25 cities all over India.3 (d) A – 3 B – 4 C – 3 D .b}. interaction with IISc alumni in our online discussion forums. which one of the following sets is not countable? (a) Set of all strings over Σ (b) Set of all languages over Σ (c) Set of all regular languages over Σ (d) Set of all languages over Σ accepted by Turing machines 3.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.5 Locality of reference implies that the page reference being made by a process (a) will always be to the page used in the previous page reference (b) is likely to be to one of the pages used in the last few page references (c) will always be to one of the pages existing in memory (d) will always lead to a page fault 3.gateforum.6 3.2 Which of the following propositions is a tautology? (a) (p ∨ q) p 3. For more details.1 (b) A – 4 B – 3 C – 2 D . visit www.2 I/O redirection (a) implies changing the name of a file (b) can be employed to use an existing file as input file for a program (c) implies connection 2 programs through a pipe (d) None of the above Join All India Mock GATE Classroom Test Series .1 (c) A – 2 B – 4 C – 1 D . an operating system (a) ignores the interrupt (b) always changes state of interrupted process after processing the interrupt (c) always resumes execution of interrupted process after processing the interrupt (d) may change state of interrupted process to ‘blocked’ and schedule another process 3. Then AI12 is such that its first (a) row is the same as its second row (b) row is the same as the second row of A (c) column is the same as the second column of A (d) row is all zero 4.1997 www.com Join discussion of this test paper at http://forum.GATE CS . each carrying 2 marks.9 Thrashing (a) reduces page I/O (b) decreases the degree of multiprogramming (c) implies excessive page I/O (d) improve the system performance 3. visit www.3 Using a forward Euler method to solve y ′′ (t) =f(t). b. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2]? (a) 6 4.8 When an interrupt occurs. interaction with IISc alumni in our online discussion forums. All India Rank.gateforum.gatementor. hf (0). and more. y ′′ (0)=0 with a step size of h.10 Dirty bit for a page in a page table (a) helps avoid unnecessary writes on a paging device (b) helps maintain LRU information (c) allows only read on a page (d) None of the above 4. Write in your answer book the subpart number and the letter a. 4.2 (b) 10 (c) 12 (d) 5. h(f(0) + f(h)) and h(f(0) + f(h) = f(2h)) (b) 0. y(0). For more details.com 3. 0 h2 f(0) and 2h2f(0)+f(h) Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. we obtain the following values of y in the first four iterations: (a) 0.gateforum. c or d corresponding to the most appropriate answer.1 What is the maximum value of the function f ( x ) = 2 x 2 − 2 x + 6 in the interval [0.com Think GATE Think GATE Forum . Each subpart contains a multiple-choice question. The question contains 10 subparts. Percentile.5 ( ) Let a= aij be an n-rowed square matrix and I12 be the matrix obtained by interchanging the first and second rows of the n-rowed Identify matrix. h2f(0) 3h2f(0) (d) 0.gatementor. For more details. x. S2 end C. visit www. K) where K is an appropriate integer key chosen by the implementation.com Think GATE Think GATE Forum . 7. For a sequence of operations. interaction with IISc alumni in our online discussion forums.com Join discussion of this test paper at http://forum. hf(0) + h2f(0) and hf (0) + h2f(0)+hf(h) 4. T(n) = 2T Which of the following statements is true? n 2 (a) T ( n ) = O n (b) T(n) = O(n) (c) T(n) = O (log n) (d) None of the above + n for n≥2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 2. C. x. PUSH (C) is implemented INSERT (Q. and more.GATE CS . p(1) = 4. 4.4 A polynomial p(x) is such that p(0) = 5. 5.z:real S1 end B. 3.7 4. 0. Join All India Mock GATE Classroom Test Series . Which of the following sequences is a valid output? (a) 5 3 1 2 4 7 8 6 (b) 5 3 1 2 6 4 8 7 (c) 5 3 2 4 1 6 7 8 (d) 5 3 1 2 4 7 6 8 Let T(n) be the function defined by T(1) = 1. p(2) = 9 and p(3) = 20. i:integer. Procedure B.1997 www.8 (b) 2 (c) 3 (d) 4 A binary search tree contains the value 1.2007 conducted by GATE Forum in over 25 cities all over India.5 4. Percentile. the keys chosen are in (a) non-increasing order (b) non-decreasing order (c) strictly increasing order (d) strictly decreasing order Given the following Pascal like program segment Procedure A.com (c) 0. All India Rank.y:intger. end A. 0. 6. 8.gateforum. POP is implemented as DELETEMIN(Q).6 4.gateforum. the minimum degree it can have is (a) 1 4. The tree is traversed in pre-order and the values are printed out. A priority queue Q is used to implement a stack that stores characters. Procedure C. The minimum number of trapezoids 1 guaranteed to ensure E ≤ 10-4 is computing in 7 using f = is x (a) 60 (b) 100 (c) 600 (d) 10000 5.gatementor.1997 www. i and y in S2 (d) None of the above 4. All India Rank. c or d corresponding to the most appropriate answer. y . z and y in S1 and x of A. y and z in S1 and x of B. Each subpart contains a multiple-choice question. 5.com Think GATE Think GATE Forum . Which one of the following is 5.10 The trapezoidal method to numerically obtain ∫ b a f ( x ) dx has an error E bounded by b−a 2 h max f ′′ ( x ) x ∈ a.2007 conducted by GATE Forum in over 25 cities all over India.com The variables accessible in S1 and S2 are (a) x or A.gateforum.9 The expression (a * b) * c op…. i and z in S2 (c) x or B. and more. Write in your answer book the subpart number and the letter a. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. For more details. ‘*’ and ‘↑’ (exponentiation) can be evaluated on a CPU with a single register without storing the value of (a * b) if (a) ‘op’ is ’+’ or ‘*’ (b) ‘op’ is ’↑’ or ‘*’ (c) ‘op’ is ’↑’ or ‘+’ (d) not possible to evaluate without storing 4.GATE CS . z ) = x + yx + xz be a switching function. y. x of B and z in S1 and x of B.1 Let f ( x.2 valid? (a) y x is a prime implicant of f (b) xz is a minterm of f (c) xz is an implicant of f (d) y is a prime implicant of f Contents of A register after the execution of the following 8085 microprocessor program is MVIA.gateforum. y and i in S2 (b) x or B.com Join discussion of this test paper at http://forum. b. 55 H MVI C. Percentile. visit www. where ‘op’ is one of ‘+’. 25 H ADDC DAA (a) 7AH (b) 80H (c) 50H (d) 22H Join All India Mock GATE Classroom Test Series . b 12 where h is the width of the trapezoids. each carrying 2 marks. interaction with IISc alumni in our online discussion forums. The question contains 5 subparts. y . c or d corresponding to the most appropriate answer.14. x.2.4 (a) 9 (b) 5 (c) 8 (d) None of the above Given 224 )r = 13)r . Write in your answer book the subpart number and the letter a.gatementor.com 5. The number of connected components in G is (a) 8 6. z ) = Σ8.gateforum.15 6.1997 www.12. The question contains 10 subparts. each carrying 2 marks. f2 and f (in canonical sum of products form in decimal notation) are: f1 (w.15 f (w.10. a2 . The value of the radix r is: (a) 10 5. Each subpart contains a multiple-choice question. where n ≥1. visit www. 8. The functions f1 . b.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums.1 A partial order ≤ is defined on the set S = { x.2007 conducted by GATE Forum in over 25 cities all over India.10 f2 (w.2 (d) 1 (b) 4 (c) 12 (d) 25 The number of equivalence relations of the set {1. y } as x ≤ ai for all i and a1 ≤ y for all i. Percentile. z ) = Σ8. 9. The number of total orders on the set S which contain the partial order ≤ is (a) n! 6.GATE CS . 9 f f3=? The function f3 is (a) Σ9. 8. For more details.10 f1 f2 (b) Σ9 (c) Σ1. y .gateforum.3 A micro instruction is to be designed to specify (a) none or one of the three micro operations of one kind and (b) none or upto six micro operations of another kind The minimum number of bits in the micro-instruction is 5. x.3. 9 (d) Σ8. 6. K an .5 (b) 8 (c) 5 (d) 6 Consider the logic circuit shown in Figure below. and more. Two vertices i and j are adjacent if i − j = 8 or i − j = 12. x.4 (c) n Let G be a graph with 100 vertices numbered 1 to 100.4} is (a) 15 6. All India Rank. a1 .3 (b) n+2 (b) 16 (c) 24 (d) 4 Which one of the following regular expressions over {0.13. y .com Think GATE Think GATE Forum .1} denotes the set of all strings not containing 100 as a substring? (a) 0*(1+0)* (b) 0*1010* (c) 0*1*01 (d) 0(10+1)* Join All India Mock GATE Classroom Test Series . z ) = Σ7. 6. a stings s and an integer k.d).c} is accepted by a deterministic pushdown automata? (a) (c) (d) {w ⊂ w w ∈ {a. c} * n n n Note: wR is the string obtained by reversing ‘w’.b. d include only atomic values. b.b. For more details.gateforum. visit www. c.c. the minimum number of units of r such that no deadlocks will ever arise is (a) 3 6.i=1……9 is coded as follows repeat P(mutex) {critical section} v(mutex) forever The code for P10 is identical except that it uses v(mutex) in place of P(mutex). All India Rank. c}} R (b) {ww R } w ∈ {a.2007 conducted by GATE Forum in over 25 cities all over India. b.gateforum.1997 www.com Join discussion of this test paper at http://forum. b} *} {a b c n ≥ 0} {w w is a palindrome over {a.GATE CS . What is the largest number of processes that can be inside the critical section at any moment? (a) 1 (b) 2 (c) 3 (d) None of the above 6.gatementor. only the following functional dependencies and those that can be inferred from them hold: ac bd This relation is (a) in first normal form but not in second normal form (b) in second normal form but not in third normal form Join All India Mock GATE Classroom Test Series . where the domains of a. b.6 Which of the following language over {a. Percentile. and more.7 An operating system contains 3 user processes each requiring 2 units of resource R. M accepts s within k steps (b) Equivalence of two given Turing machines (c) Language accepted by a given finite state machine is not empty (d) Language generated by a context free grammar is non empty 6.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums.9 For a database relation R(a.5 Which one of the following is not decidable? (a) Given a Turing machine M.com 6.8 (b) 5 (c) 4 (d) 6 Each process Pi. gateforum. 9.gateforum. 2. end 13. else if p ↑ next = nil then change : 6. if p = nil then change : = p 5. :=change(t) 12. The following function returns a list in which 1. 10. 8. 3. 11. All India Rank. ON and OFF periods of the square wave should be 7 bus cycles each. :=p.2007 conducted by GATE Forum in over 25 cities all over India. Write the line number and the content of the box in your answer sheet. Percentile. (c) and (d) can cause its violation (c) Both (a) and (d) can cause its violation (d) Both (b) and (c) can cause its violation 7. Data bit D3 should be involved in the data transfer from CPU to the flip-flop. function change (p: ↑ list): ↑ list.com (c) in third normal form (d) None of the above 6.1997 www. val : integer end n a2i and a2i −1 . t : q ↑ next.GATE CS . draw the required interface logic circuit (only the relevant signals should be shown) (b) Write a program to generate a squarewave on the output of the flip-flop. var q. Complete the function by filling the boxes. else begin 7. A D flip-flop is to be connected to an 8085-microprocessor chip as a 1-bit output port with a port address of FF hex. (c) or (d) can cause its violation (b) All of (a). one NOT gate and one D flip-flop. :=q.com Join discussion of this test paper at http://forum. Let L = {a1.10 Let R (a. Consider the following four operations R and S (a) Insert into R (b) Insert into S (c) Delete from R (d) Delete from S Which of the following is true about the referential integrity constraint above? (a) None of (a).t : ↑ list.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. e. visit www. (a) Using only one NAND gate (fan in of 10).. (b). For more details. 8.. and more. c) and S(d.gatementor. a2. end Join All India Mock GATE Classroom Test Series . The flip-flop should be cleared on power ON. an) n≥0 be a list whose Pascal representation is type list = record next:↑ list. b. q : p ↑ next. begin 4. ……. f) be two relations in which d is the foreign key of S that refers to the primary key of R. interaction with IISc alumni in our online discussion forums. (b). 1≤i≤ are 2 interchanged. interaction with IISc alumni in our online discussion forums. Consider the following program in Pseudo-Pascal syntax. y1 ) . z:=x+10 end end(*recur*) begin (*what*) z =10. Two vertices ( x1 .com 9. program what: var z: integer procedure recur (x): begin if x ≤ 40 then begin x: x + z. recur (x). writeln(z) end (a) Suppose the parameter to the procedure ‘recur’ is passed by value. recur(z). y2 )} is ( x1 − x2 )2 + ( y1 − y2 )2 (a) What is the weight of a minimum weight-spanning tree in this graph? Write only the answer without any explanations. (b) What is the weight of a maximum weight-spanning tree in this graph? Write only the answer without any explanations? 10. visit www.1997 www.GATE CS . All India Rank.com Join discussion of this test paper at http://forum. Consider the grammar S bSc S PQR P bPc Pε Q cQd Qε R dRe Rε Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. Percentile.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. ( x2 . Consider a graph whose vertices are points in the plane with integer co-ordinates (x. For more details. and more. (i) What value is printed by the program? (ii) How many time is ‘recur’ called? (b) What value is printed by the program if the parameter is passed by reference? 11.gateforum.gateforum. where n≥2 is an integer. y2 ) are adjacent iff x1 − x2 ≤ 1 and y1 − y2 ≤ 1 . y1 ) and ( x2 .gatementor.y) such that 1≤x≤n and 1≤y≤n. The weight of an edge {( x1. b ∈ E2 and (a. em for some i..…. 1≤i≤n? (c) How many functions f in F satisfy the property f(i)<f(j) for some 1≤i≤j≤n? 14. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. R are non-terminal symbols with S being the start symbol.m:integer):integer. (a) How many functions are members of F? (b) How many functions f in F satisfy the property f(i)=1 for some i. Function F(n. Let R be a reflexive and transitive relation on a set A. and more. (a) What is the probability that bucket number 1 is empty after the Kth insertion? (b) What is the probability that no collision has occurred in any of the K insertisons? (c) What is the probability that the first collision occurs at the Kth insertions? 13. (b) Define a relation ≤ on the equivalence classes of E as E1 ≤ E2 is ∃ a.n} to the set {1. Consider a hash table with n buckets.com Where S.m) + F(n. visit www. begin If (n <=0) or (m <=0) then F:=1 else F:F(n . c.gateforum.b)∈R.. The hash function is such that the probability that a key 1 value is hashed to a particular bucket is . Join All India Mock GATE Classroom Test Series . j. 12.m – 1). d k . k.gateforum.b such that a ∈ E1 . For more details. All questions carry equal marks.GATE CS .1. e are terminal symbols and ‘ε’ is the empty string. b. This grammar generates strings of the form bi . Q.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. Let F be the set of one-to-one functions from the set {1. b) ∈ R and ( b. where external (overflow) chaining is used to resolve collisions.k.2. m ≤ 0. Consider the following function. 15. (a) What is the condition on the values of i. a) ∈ R} (a) Prove that E is an equivalence relation on A.com Think GATE Think GATE Forum . SECTION – B Answer any TEN questions from this section. define a new relation E on a as E = {( a. All India Rank.…. interaction with IISc alumni in our online discussion forums.com Join discussion of this test paper at http://forum.1997 www.2.j.m? (b) Find the smallest string that has two parse trees. b) ( a. The hash table is initially empty and K n distinct values are inserted in the table. Prove that ≤ is a partial order. Percentile. d.m} where m≥n≥1. c j .. P. end. the following program fragment prints the length of a shortest sequence of consecutive elements of A.…. 17. Write only the answers without any explantion.2)? (b) What is the value of F(n. by using induction on h. The height of a binary tree is the maximum distance of a leaf node from the root. While not finish do 6. Assume that n. (a) Prove.. If 7. min:n. Percentile. visit www. 9. For more details.gateforum. (b) In a size-balanced binary tree of height h≤1.m)? (c) How many recursive calls are made to the function F. Join All India Mock GATE Classroom Test Series . The distance of a node from the root is the length of the path from the root to the node. interaction with IISc alumni in our online discussion forums. sum:= 12. It prints ‘n+1’ if no such sequence exists. 16.gateforum.com Join discussion of this test paper at http://forum. end 13. if j = n then finish:=true. else 14.2007 conducted by GATE Forum in over 25 cities all over India. and more. .GATE CS .. 1.com n n − 1 n − 1 = + to answer the following k k k − 1 questions. A size balanced binary tree is a binary tree in which for every node the difference between the number of nodes in the left and right subtree is at most 1. that a size-balance binary tree of height h contains at least 2h nodes. when evaluating F(n. then 8. begin 15. j:=j+1. Complete the program by filling the boxes. including the original call.A[n]. A[I].j:=1. 5. sum:=sum – A[i].A[i+1]. 16.A[2]. begin 2. In each case use the simplest possible expression. how many nodes are at distance h – 1 from the root? Write only the answer without any explanations. finish:= false. i :+1.A[j]such that the sum of their values is ≥M.com Think GATE Think GATE Forum .……. If(j – I) < min then min:=j – 1.m). Write only the line number and the contents of the box. 11. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. An array A contains n≥1 positive integers in the locatios A[1]. 17. All India Rank. a given positive number. Sum := 4. 3. else begin 10.1997 www. Use the recurrence relation (a) What is the value of F(n. i:=i+1. m are positive integers.gatementor. int *j) { Node *t1. } t1 next =NULL. end 19. *j=0. 18. *t2. typedef struct node Node. Consider the following piece of ‘C’ code fragment that removes duplicates from an ordered list of integers. interaction with IISc alumni in our online discussion forums. while t2 ! = NULL) { if (t1. (a) How many times is the comparison in statements S1 made? (b) What is the minimum and the maximum number of times statements marked S2 get executed? (c) What is the significance of the value in the integer pointed to by j when the function completes? Join All India Mock GATE Classroom Test Series . t1 = t2: -----------(S2) } t2 = t2 next.com Join discussion of this test paper at http://forum.GATE CS .val) ------------------ (S1) { (*j)++. struct nod *next. writeln (min +1).com 18. {. end.2007 conducted by GATE Forum in over 25 cities all over India. struct node{ int val. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and more.gatementor. All India Rank.gateforum. Percentile.1997 www. else return head: *j = 1. For more details.com Think GATE Think GATE Forum . return head.val! = t2. if (t2 == NULL) return head. if (t1! = NULL) t2 = t1 next. t1 = head. } Assume the list contains n elements (n – 2) in the following questions. t1 next = t2.gateforum. Node *remove-duplicates (Node*head. 20. visit www. 23. where { } LP = s ss ′ ∈ L some string. (a) What is the total number of key values in the internal nodes of a B+ . defined by the following grammar. All India Rank.tree of order d is a tree in which each internal node has between d and 2 d key values. The language L. A language L is a subset of Pascal with the following constructs: (a) Expressions involving the operators ‘+’ and ‘<’ only (b) Assignment statements (c) ‘while’ statements and (d) Compound statements with the syntax ‘begin…end’ Give an unambiguous grammar of L.r).com 19.com Think GATE Think GATE Forum . and more.1997 www. A B+ .i). 21.2007 conducted by GATE Forum in over 25 cities all over India. Percentile. visit www.gateforum.gatementor.i) (+. s' . All leaves are at the same distance from the root. Given that L is a language accepted by a finite state machine. An internal node with M key values M + 1 children. assign-stmt :: LHS := E E ::= E + T T T ::= T * V V V ::= id (E) ( LHS ) :: id It is required to convert expression and assignment strings of L into postfix strings that use the type-specific operations (+. (*. The height of the tree is the distance of a leaf fro the root. For more details. The root (if it is an internal node) has between 1 and 2d key values. 22. The distance of a node from the root is the length of the path from the root to the node. (:=.b) such that the number of a’s is divisible by two and the number of b’s is divisible by three.com Join discussion of this test paper at http://forum.gateforum. { } LP = s s obtainable by reversing some string in L .i) and (:=. Construct a finite state machine with minimum number of states. interaction with IISc alumni in our online discussion forums.tree with 1 leaves (1 ≥ 2)? (b) What is the maximum number of internal nodes in a B+-tree of order 4 with 52 leaves? (c) What is the minimum number of leaves in a B+-tree of order d and height h(n≥1)? 20.GATE CS . allows use of real or integer data in expressions and assignment statements. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. show that LP and LR are also accepted by some finite state machines. accepting all strings over (a.r). (*.r) Join All India Mock GATE Classroom Test Series . 24.GATE CS . procedure A. var Z: integer. (*call to A*) : end (*procedure B*) begin (* procedure A*) : B.gateforum. visit www. Consider the following program fragment in Pascal: Program Main. var Y: integer. For more details. and more. interaction with IISc alumni in our online discussion forums. You may assume that the name and type of a variable can be obtained by making the function calls’ give type (id) and givename (id)* respectively.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2007 conducted by GATE Forum in over 25 cities all over India. var Z: integer. procedure B. var X: integer.com Write a syntax directed translation scheme to convert expression and assignment strings into the post-fix form.com Join discussion of this test paper at http://forum. (*call to C*) A.1997 www. procedure C. (*call to B*) : end (*procedure A*) begin (*Main*) Join All India Mock GATE Classroom Test Series . begin (*procedure C*) : end (*procedure C*) begin (*procedure B*) : C. All India Rank.com Think GATE Think GATE Forum . Percentile.gatementor. In this interval. Percentile.GATE CS . 1. interaction with IISc alumni in our online discussion forums. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Think GATE Think GATE Forum . B.1998 www.1 A die is rolled three times. 1.gateforum.3 (a) has unique solution (b) has no solutions (c) has finite number of solutions (d) has infinite number of solutions Which of the following statements applies to the bisection method used for finding roots of functions: (a) converges within a few iterations (b) guaranteed to work for all continuous functions (c) is faster than the Newton-Raphson method (d) requires that there be no error in determining the sign of the function. The probability that exactly one odd number turns up among the three outcomes is (a) 1. This question consists of 35 THIRTY-FIVE multiple questions of ONE mark each.4 Consider the function y = x in the interval [-1. For more details.gatementor.2007 conducted by GATE Forum in over 25 cities all over India.5 What is the converse of the following assertion? I stay only if you go (a) I stay if you go (b) If I stay then you go (c) If you do not go then I do not stay (d) If I do not stay then you go Join All India Mock GATE Classroom Test Series .A 1.com Join discussion of this test paper at http://forum. out of which ONLY ONE is correct.com SECTION . the function is (a) continuous and differentiable (b) continuous but not differentiable (c) differentiable but not continuous (d) neither continuous nor differentiable 1. four possible alternatives (A. visit www. All India Rank. For each question. C and D) are given. and more.gateforum.1]. Indicate the correct answer in the boxes corresponding to the questions only on the FIRST sheet of the answer book.2 1 6 (b) 3 8 (c) 1 8 (d) 1 2 Consider the following set of equations: x + 2y = 5 4 x + 8y = 12 3x + 6y + 3z = 15 This set 1. ………… written in binary (b) The numbers 1.1998 www.8 The number of functions from an m element set to an n element set is (a) m + n 1.. (d) The set {1. 2. (b) Non-deterministic Push-down automata are equivalent to deterministic Pushdown automata.} 1.2007 conducted by GATE Forum in over 25 cities all over India.9 1. Consider the following assertions: (i) R1 ∪ R2 is an equivalence relation (ii) R1 ∩ R2 is an equivalence relation Which of the following is correct? (a) Both assertions are true (b) Assertion (i) is true but assertion (ii) is not true (c) Assertion (ii) is true but assertion (i) is not true (d) Neither (i) nor (ii) is true 1.com 1. and more. 1110111. Join All India Mock GATE Classroom Test Series . (d) Non-deterministic Turing machines are equivalent to deterministic Turing machines.7 (b) n2 (c) 1 (d) n + 1 Let R1 and R2 be two equivalence relations on a set. For more details. ……….gatementor. 8. 4. All India Rank. visit www.GATE CS . 11011.written in unary (c) The set of binary string in which the number of zeros is the same as the number of ones. which of the following statements is false? (a) The non-deterministic finite-state automata are equivalent to deterministic finite-state automata..6 Suppose A is a finite set with n elements.gateforum. (e) Multi-tape Turing machines are equivalent to Single-tape Turing machines. ………………. which of the following is true? (a) A ⊂ B (b) B ⊂ A (c) A and B are incomparable (d) A = B Which of the following set can be recognized by a Deterministic Finite state Automaton? (a) The numbers 1. 2n .gateforum.10 (b) mn (c) nm (d) m*n If the regular set A is represented by A = (01 + 1)* and the regular set ‘B’ is represented by B = ((01)*1*)*. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 4. 2. The number of elements in the largest equivalence relation of A is (a) n 1. …………. (c) Non-deterministic Turing machines are equivalent to deterministic Push-down automata.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. 2n .com Join discussion of this test paper at http://forum.. ……………. Percentile. 101.11 Regarding the power of recognition of languages. com Think GATE Think GATE Forum . the minimum band rate required to sustain a transfer rate of 300 characters per second is (a) 2400 band (b) 19200 band (c) 4800 band (d) 1200 band The octal representation of an integer is 3428. If this were to be treated as an eight-bit integer is an 8085 based computer.8 V and 5.19 (b) -98 (c) 76 (d) -30 Which of the following devices should get higher priority in assigning interrupts? (a) Hard disk (b) Printer (c) Keyboard (d) Floppy disk Which of the following addressing modes permits relocation without any change whatsoever in the code? (a) Indirect addressing (b) Indexed addressing (c) Base register addressing (d) PC relative addressing Join All India Mock GATE Classroom Test Series .1998 www. All India Rank.14 1. Percentile. For more details.0 V (d) any voltage below Vcc but above 2. a parity bit and 2 stop bits. its decimal equivalent is (a) 226 1.5 V (b) any voltage between 0.com Join discussion of this test paper at http://forum.GATE CS .gateforum. visit www.2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.16 1.gateforum.0 V (c) any voltage below 5.8 V 1.18 1. interaction with IISc alumni in our online discussion forums.gatementor. and more.17 In serial communication employing 8 data bits.12 1.15 A multiplexor with a 4 bit data select input is a (a) 4:1 multiplexor (b) 2:1 multiplexor (c) 16:1 multiplexor (d) 8:1 multiplexor The threshold level for logic 1 in the TTL family is (a) any voltage above 2.com 1.13 The string 1101 does not belong to the set represented by (a) 110*(0 + 1) (b) 1 ( 0 + 1)* 101 (c) (10)* (01)* (00 + 11)* (d) (00 + (11)*0)* What happens when a bit-string is XORed with itself n-times as shown: B ⊕ B ⊕ B ⊕ ( B K n times ( ( (a) complements when n is even (b) complements when n is odd (c) divides by 2n always (d) remains unchanged when n is even 1. Percentile.com 1.com Think GATE Think GATE Forum . (b) Loop instructions cannot be interrupted till they complete.S (b) A – R B – P C – S D .21 1. a CPU will not be able to process interrupts. For more details. (c) A processor checks for interrupts before executing a new instruction.20 Which of the following is true? (a) Unless enabled. and more. (c) A complete binary tree with n internal nodes has (n + 1) leaves.2007 conducted by GATE Forum in over 25 cities all over India.23 (a) A – R B – P C – Q D .25 In a resident – OS computer.22 Which one of the following algorithm design techniques is used in finding all pairs of shortest distances in a graph? (a) Dynamic programming (b) Backtracking (c) Greedy (d) Divide and Conquer Give the correct matching for the following pairs: (A) O (log n) (P) Selection (B) O (n) (Q) Insertion sort (C) O (n log n) (R) Binary search ( ) (D) O n2 1.24 (S) Merge sort (b) n2 (c) 2n (d) n ( n + 1) 2 Which of the following statements is false? (a) A tree with a n nodes has (n – 1) edges (b) A labeled rooted binary tree can be uniquely constructed given its postorder and preorder traversal results.Q (d) A – P B – S C – R D .Q How many sub strings of different lengths (non-zero) can be found formed from a character string of length n? (a) n 1. (d) Only level triggered interrupts are possible on microprocessors 1.Q (c) A – P B – R C – S D .com Join discussion of this test paper at http://forum.gateforum.1998 www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS . interaction with IISc alumni in our online discussion forums.gateforum. which of the following systems must reside in the main memory under all situations? (a) Assembler (b) Linker (c) Loader (d) Compiler Join All India Mock GATE Classroom Test Series .gatementor. ( ) (d) The maximum number of nodes in a binary tree of height h is 2h+1 − 1 1. All India Rank. visit www. 2007 conducted by GATE Forum in over 25 cities all over India. 500.com 1. interaction with IISc alumni in our online discussion forums. 500. with n processes competing for them.GATE CS . what is the result of the operation R1A = CAB = DR2? (a) R1 ∪ R2 (b) R1 × R2 (c) R1 − R2 (d) R1 ∩ R2 Join All India Mock GATE Classroom Test Series . All India Rank. 800. 1300. 1. 700. 200. respectively.28 1.30 1.31 When the result of a computation depends on the speed of the processes involved there is said to be (a) cycle steating (b) rare condition (c) a time lock (d) a deadlock A counting semaphore was initialized to 10. and more. 600 (b) 0. 800 (d) 200.com Join discussion of this test paper at http://forum.gatementor.33 (b) 8 (b) 5 (c) 4 (d) 3 Given two union compatible relations R1(A.32 (c) 10 (d) 12 A computer has six tape drives.29 Type checking is normally done during (a) lexical analysis (b) syntax analysis (c) syntax directed translation (d) code optimization A linker reads four modules whose lengths are 200. 1600 (c) 200. Then 6 P (wait) operations and 4V (signal) operations were completed on this semaphore.27 1. (d) The parsers SLR. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (c) The secondary memory device in a virtual storage system (d) The swapping area on a disk used by the swapper. 1000.gateforum. If they are loaded in that order.B) and R2 (C.26 Which of the following statements is true? (a) SLR parser is more powerful than LALR (b) LALR parser is more powerful than Canonical LR parser (c) Canonical LR parser is more powerful than LALR parser. Percentile.gateforum. Each process may need two drives. what are the relocation constants? (a) 0. Canonical CR. The resulting value of the semaphore is (a) 0 1. 200. visit www.1998 www.D). and LALR have the same power 1. 2100 Which of the following is an example of a spooled device? (a) The terminal used to enter the input data for the C program being executed (b) An output device used to print the output of a number of jobs. 600 and 500 words. 600.com Think GATE Think GATE Forum . What is the maximum value of n for the system to be deadlock free? (a) 6 1. For more details. 3.com 1. All India Rank.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 2.com Join discussion of this test paper at http://forum.5 and 4. 1 4 8 7 0 0 3 0 4 2 3 1 3 12 24 2 (b) 1 (c) 2 (d) 4 1 a bc Consider the following determinant ∆ = 1 b ca .gateforum.1998 www.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. visit www.35 (b) 5 NF (c) 4 NF (d) 3 NF There are five records in a database.20) of TWO marks each.1 The rank of the matrix given below is: (a) 3 2. and more. Percentile. The answers to the multiple choice questions of this section MUST be written only in the boxes corresponding to the questions.2. in the second page of the answer book.gateforum. This question consists of 20 (TWENTY) multiple-choice questions (2.1 – 2.gatementor. Name Age Occupation Category Rama 27 CON A Abdul 22 ENG A Jeniffer 28 DOC B Maya 32 SER D Dev 24 MUS C There is an index file associated with this and it contains the values 1.2.34 Which normal form is considered adequate for normal relational database design? (a) 2 NF 1.2007 conducted by GATE Forum in over 25 cities all over India. 1 C ab Which of the following is a factor of ∆ ? (a) a+b (b) a-b (c) a+b+c (d) abc Join All India Mock GATE Classroom Test Series .Which one of the fields is the index built from? (a) Age (b) Name (c) Occupation (d) Category 2. For more details. (2.2) . 4) on the set A = {1.2.8. nor irreflexive but transitive (c) irreflexive. symmetric and transitive (b) neither reflexive.7. 9 persons speak both English and Hindi. symmetric and transitive (d) irreflexive and antisymmetric 2.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.1) . 3) . 0 (b) AB+BC+CA 0 1 (c) B ⊕ C (d) A.gateforum. The binary relation R = {(1. 3) . (3. In a room containing 28 people. (c) 7 (d) 6 Let L be the set of all binary strings whose last two symbols are the same. (2. 1 (b) OR (c) NAND (d) EXOR Formatting for a floppy disk refers to (a) arranging the data on the disk in contiguous fashion (b) writing the directory (c) erasing the system area (d) writing identification information on all tracks and sectors Join All India Mock GATE Classroom Test Series .B 2.4} is (a) reflexive. interaction with IISc alumni in our online discussion forums. (3.gatementor. (3. visit www.5. The function represented by the Karnaugh map given below is BC 00 01 10 11 A 0 1 0 1 1 1 (a) A. (2. (b) 8 (b) 5 (c) 8 (d) 3 Which of the following statements is false? (a) Every finite subset of a non-regular set is regular (b) Every subset of a regular set is regular (c) Every finite subset of a regular set is regular (d) The intersection of two regular sets is regular 2.BC Which of the following operations is commutative but not associative? (a) AND 2. 15 people who speak Hindi and 22 people who speak Kannada.3.4.1) . there are 18 people who speak English.9.com Think GATE Think GATE Forum . and more.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India.1998 www. The number of states in the minimum state deterministic finite 0 state automaton accepting L is (a) 2 2. How many people speak all three languages? (a) 9 2. Percentile. 11 persons speak both Hindi and Kannada whereas 13 persons speak both Kannada and English.com 2.gateforum. All India Rank. 4) .1)} .6.3. (3. For more details. 2) . (2. GATE CS . Percentile. What value would the following function return for the input x = 95? Function fun (x:integer):integer. What is the result of the following program? program side-effect (input. All India Rank. what is the address of the element A[i][j]? (a) 15i + j + 84 (b) 15j + i + 84 (c) 10i + j + 89 (d) 10j + i + 89 Join All India Mock GATE Classroom Test Series . and more.10.1998 www.com Think GATE Think GATE Forum . Assuming that each integer takes one memory locations the array is stored in row-major order and the first element of the array is stored at location 100.gateforum. output).12.gatementor. 10] [1 …… 15] of integer. the number of leaves in it is given by (a) x(n – 1) +1 (b) xn . Begin If x > 100 then fun : x – 10 Else fun : fun(fun (x + 11)) End. result: integer: fucntion f (var x:integer):integer. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2007 conducted by GATE Forum in over 25 cities all over India. For more details. The address space of 8086 CPU is (a) one Megabyte (b) 256 Kilobytes (c) 1 K Megabytes (d) 64 Kilobytes 2. end begin x:=5 result:=f(x)*f(x) writeln(result) end (a) 5 (b) 25 (c) 36 (d) 42 2. var x.14. (a) 89 (b) 90 (c) 91 (d) 92 2.com 2. A complete n-ary tree is one in which every node has O or n sons. Let A be a two-dimensional array declared as follows: A: array [1 ….11.1 (c) xn + 1 (d) x(n+1) 2.f:=x.com Join discussion of this test paper at http://forum.gateforum. interaction with IISc alumni in our online discussion forums. If x is the number of internal nodes of a complete n-ary tree. visit www. begin x:x+1.13. C2 are selection conditions and A1. replacing the l.2007 conducted by GATE Forum in over 25 cities all over India.16. If an instruction takes i microseconds and a page fault takes an additional j microseconds.com 2.18. All India Rank. A2 are attributes of R1? ( ) ( (a) σ c1 σ c1 ( R1 ) → σ c 2 σ c 2 ( R1 ) ) (c) σ c1 ( R1 ∪ R2 ) → σ c1 ( R1 ) ∪ σ c1 ( R2 ) ( ) ( ) π A1 (σ c1 ( R1 ) ) → σ c1 (π A1 ( R1 ) ) (b) σ c1 π A1 ( R1 ) → π A1 σ c1 ( R1 ) (d) Join All India Mock GATE Classroom Test Series . expression) is incorrect? R1 and R2 are relations. The overlay tree for a program is as shown below: Root A D B 4 KB E 6 KB 8 KB F 2 KB 6 KB C 2 KB G 8 KB 4 KB What will be the size of the partition (in physical memory) required to load (and run) this program? (a) 12 KB (b) 14 KB (c) 10 KB (d) 8 KB 2. expression by the r. the effective instruction time if on the average a page fault occurs every k instruction is: (a) i + j k (b) i + j * k (c) i+ j k (d) ( i + j ) * k 2.1998 www. Faster access to non-local variables is achieved using an array of pointers to activation records called a (a) stack (b) heap (c) display (d) activation tree 2.h.gateforum. Percentile.com Join discussion of this test paper at http://forum.s. Consider n processes sharing the CPU in a round-robin fashion.com Think GATE Think GATE Forum .h.gateforum. visit www.GATE CS .e. For more details.s. and more. C1.15. what must be the quantum size q such that the overhead resulting from process switching is minimized but at the same time each process is guaranteed to get its turn at the CPU at least every t seconds? (a) q ≤ t − ns n −1 (b) q ≥ t − ns n −1 (c) q ≤ t − ns n +1 (d) q ≥ t − ns n +1 2.19.17. Which of the following query transformations (i. interaction with IISc alumni in our online discussion forums. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. Assuming that each process switch takes s seconds. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and more. What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form? (a) 80% 3. 1}*|w interpreted as binary number (ignoring the leading zeros) is divisible by five. interaction with IISc alumni in our online discussion forums. the output is 1 except when x = 1 and y = 0. What is the probability that the two will not meet? (b) Give a regular expression for the set of binary strings where 0 every is immediately followed by exactly k 1’s and preceded by at least k 1’s (k is a fixed integer) 4. ice-cream) indicating what ice-creams each student likes. SERVES (parlor. Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language: L = {w ∈ {0. and will see if the other has already arrived. LIKES (student. visit www. Percentile.m.1998 www.com Think GATE Think GATE Forum . 5. If not.gateforum.0 p. 6. (b) 20% (c) 60% (d) 40% (a) Two friends agree to meet at a park with the following conditions. and 5. (a) Solve the following recurrence relation xn = 2 xn −1 − 1.2007 conducted by GATE Forum in over 25 cities all over India. shown below has two inputs (x and y). (a) Suppose we have a database consisting of the following three relations. parlor) giving the parlors each student visits. FREQUENTS (student. (Assume that each student likes at least one ice-cream and frequents at least one parlor) Express the following in SQL: Join All India Mock GATE Classroom Test Series .20. (b) show that the implication gate is functionally complete.gatementor.00 p. 7. realize f = xy + xy using only four implication gates.m. Suppose the domain set of an attribute consists of signed four digit numbers. (a) The implication gate. For more details. ice-cream) indicating what kind of ice-creams each parlor serves.com Join discussion of this test paper at http://forum.com 2. they will wait for 10 minutes or the end of the hour whichever is earlier and leave. n > 1 x1 = 2 (b) Consider the grammar S Aa|b A Ac|Sd|∈ Construct an equivalent grammar with no left recursion and with minimum number of production sales.gateforum. All India Rank. Each will reach the park between 4.GATE CS . GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. c. (Answers to all parts of a question must appear together). and more.gateforum.gatementor. if any. the following situation was encountered: Partitions sizes in KB 4K 8K 20K 2K Jobs sizes in KB 2K 14K 3K 6K 6K 10K 20K 2K Time for execution 4 10 2 1 4 1 8 6 When will the 20K job complete? SECTION – B This section consists of TWENTY questions numbered 8 to 27 of FIVE marks each. h} represented by the following two component digraph.com Print the students that frequent at least one parlor that serves some icecream that they like. (a) Find the points of local maxima and minima. Assume that one operation refers to a multiplication followed by an addition. f. 10. b. x 3 − 6 x 2 + 9 x + 15 (b) Integrate π ∫ π x cos xdx − 9. All India Rank.com Join discussion of this test paper at http://forum. Attempt ANY TEN questions. (a) Prove by induction that the expression for the number of diagonals in a n ( n − 3) polygon of n sides is 2 (b) Let R be a binary relation on A = {a. Answers must be given in the answer book provided. e. visit www. g.gateforum. e b d f a c h g Join All India Mock GATE Classroom Test Series . For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.1998 www. (b) In a computer system where the ‘best-fit’ algorithm is used for allocating ‘jobs’ to ‘memory partitions’. of the following function defined in 0≤x≤6. Answer for each question must start on a fresh page and must appear at one place only. Derive the expression for the number of operations required to solve a system of linear equations in n unknowns using the Gaussian Elimination Method. 8. d.com Think GATE Think GATE Forum . Percentile. interaction with IISc alumni in our online discussion forums. Find the smallest integers m and n such that m < n and Rm = Rn. 1. N = {S1. X ) = {( q1 . if a ≠ b.b. b in A a*b*a =a (c) Show that for every a.2007 conducted by GATE Forum in over 25 cities all over India. {b} . {z0 .gateforum. refines Let (A. (a) Let G1 = (N. ∈)} δ ( q0 .gateforum. {d}} Π3 = {{a. z0 ) = {( q0 . Π 4 } . X )} δ ( q0 . q1} . {Π1 .c}{d}} (a) List the ordered pairs of the equivalence relations induced by Π1 . {C} .com 11. z0 ) = {( q0 .com Think GATE Think GATE Forum .1998 www.d} and Π1 is the following partition of A Π1 ={{a. B} T = {a. b}{c. (a) Show that for every a in A a*a =a (b) Show that for every a. interaction with IISc alumni in our online discussion forums. q0 . b. Percentile. A. c in A a*b*c = a*c 13. 12. visit www. Let M = ({q0 . For more details. φ ) be a Pushdown automation where δ is given by δ ( q0 . All India Rank. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 14.1} .c. xz0 )} δ ( q0 .1. X } . then a*b.1. b} and P is given by Join All India Mock GATE Classroom Test Series . z0 . X ) = {( q1 . z0 ) = {( q0 . d}} (c) Let Π2 = Draw a Poset diagram of the poset.GATE CS .b. Π2 . and more. ∈. T. 0. Furthermore. {{a} . X ) = {( q0 .gatementor. (b) Draw the graph of the above equivalence relation. z0 )} (a) What is the language accepted by this PDA by empty store? (b) Describe informally the working of the PDA. d}} and Π 4 = {{a. Π3 . {0. b ≠ b*a. *) be a semigroup.com Join discussion of this test paper at http://forum. c. for every a and b in A. ∈)} δ ( q0 . δ . b. Suppose A = {a. 0. P. XX )} δ ( q1 . S1) be a CFG where. gateforum. 1. 2. Calculate the total time required to read 35 sectors on a 2-sided floppy disk. k.gatementor. 3. For more details. The first sector to be read is sector 3 on track 10. Assume that the diskette is soft sectored and the controller has a 1-sector buffer. 16. Percentile. j.1 ≥ 1. 4 …………… 17.com Think GATE Think GATE Forum . which generates it. State all your assumptions clearly. 2. All India Rank. 1. Give the value of the hit ratio for 1 = 1 Join All India Mock GATE Classroom Test Series . and n = k*m is a non-zero integer and 1 < m ≤ 1. visit www.1998 www. the head is on track 10. 18. and more.com Join discussion of this test paper at http://forum. (a) Draw the schematic of 8085 based system that can be used to measure the width of a pulse. (b) Write the 8085 Assembly Language program to measure the width of the pulse. 4.GATE CS . For a set-associative Cache Organization. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Assume that the pulse is given as a TTL compatible signal by the source.com S1 a. Design a synchronous counter to go through the following states: 1. the parameters are as follows: tc -- Cache access time tm -- Main memory access time l -- number of sets b -- block size k*b -- set size Calculate the hit ratio for a loop executed 100 times where the size of the loop is n * b. S1 b S1 a B b S1 a A b B Bb AaA Bb Aa What is L(G1)? (b) Use the grammar in Part (a) to give a CFG for ( ) L2 = ai bi ak b1 i. (c) Is L2 inherently ambiguous? 15. The diskette spins at 300 RPM and initially. interaction with IISc alumni in our online discussion forums.2007 conducted by GATE Forum in over 25 cities all over India. 4. Assume that each track has 8 sectors and the track-to-track step time is 8 milliseconds. i = j or k = 1 by adding not more than 5 production rules.gateforum. 3. 2007 conducted by GATE Forum in over 25 cities all over India. Derive a regular expression for the identifier. (a) An identifier in a programming language consists of up to six letters and digits of which the first character must be a letter. Percentile. and more. Join All India Mock GATE Classroom Test Series . to determine S.com Think GATE Think GATE Forum . c. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. p cell i cell(i+1) cell(i+2) cell(i+3) What do the following assignment statements achieve? q: = p next p next:=q next p next:=(q next) next (p next) next:=q (b) Compute the post fix equivalent of the following expression. f and g for which the inorder and postorder traversals result in the following sequences. interaction with IISc alumni in our online discussion forums. 3 * log ( x + 1) − 20.gateforum. a 2 Draw the binary tree with node labels a.625 Construct a syntax directed translation scheme using only synthesized attributes. All India Rank. 21.101 give S. e. (b) What is the size of the smallest AVL tree with height 8? (c) 22. an input 101. Inorder afbcdge Postorder afcgedb (a) Derive a recurrence relation for the size of the smallest AVL tree with height h. (a) Let p be a pointer as shown in the figure in a single linked list. ………….gatementor. (b) Build an LL (1) parsing table for the language defined by the LL(1) grammar with productions Program begin d semi X end X d semi X | sY Y semi s Y | ∈ 23. Let the attribute ‘val’ give the value of a binary number generated by S in the following grammar: S L. For more details. b.com 19.GATE CS .L | L L LB | B B0|1 For example. …………. visit www. d.com Join discussion of this test paper at http://forum.val = 5.1998 www.val.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (a) What is the highest normal form satisfied by this relation? (b) Suppose the attributes Book – title and Author – address are added to the relation. Derive the formula to calculate the disk address (i.com 24.sL). Their expected run times are 6. (a) Free disk space can be kept track of using a free list or a bit map. S1 S3 S2 S4 S5 25.2007 conducted by GATE Forum in over 25 cities all over India. 26. in what order should they be run to minimize the average response time? (b) Write a concurrent program using par begin-par end to represent the procedure graph shown below.GATE CS .gateforum. visit www. respectively. interaction with IISc alumni in our online discussion forums. 5 and x.tL. PRE-REQ gives the information about which courses are pre-requisites for a given course. pre-Cno) COMPLETED (student – no.e.com Think GATE Think GATE Forum . cylinder. Consider the following database relations containing the attributes Book – id Subject – Category – of – book Name – of – Author Nationality – of – Author With book – id as the primary key.gateforum. track and sector numbers.1998 www. COMPLETED indicates what courses have been completed by students. track and sector) of a logical record n assuming that rl = sl. and the primary key is changed to {Name – of – Author. Express the following using relational algebra: List all the courses for which a student with student-no 2310 has completed all the pre-requisites.gatementor. For more details. All India Rank.com Join discussion of this test paper at http://forum. when CL. and more. Percentile. Disk addresses require d bits. (b) Consider a disk with C cylinders. A logical file dl with fixed record length rl is stored continuously on this disk starting at location (cL. Join All India Mock GATE Classroom Test Series .name) PRE-REQ(Cno. For a disk with B blocks. Book – title}. F of which are free. (a) Four jobs are waiting to be run. Cno) COURSES gives the number and name of all the available courses. what will be the highest normal form satisfied by the relation? 27. s sectors per track and a sector length sl. 3. t tracks per cylinder. tL and SL are the cylinder. Consider the following relational database schemes: COURSES (Cno. state the condition under which the free list uses less space than the bit map. 5 1.1 Suppose that the expectation of a random variable X is 5. Indicate the correct answer in the boxes corresponding to the questions only on the FIRST sheet of the answer book.com Join discussion of this test paper at http://forum. 1. Kleene closure Let LD be the set of all languages accepted by a PDA by final state and LE the set of all languages accepted by empty stack. The minimum state finite automation that recognizes the language represented by this regular expression contains (a) n states (b) n + 1 states (c) n + 2 states (d) None of the above Context-free languages are closed under: (a) Union. four possible alternatives (A. C and D) are given. B.gatementor. interaction with IISc alumni in our online discussion forums. out of which ONLY ONE is correct.GATE CS . intersection (b) Union. N times.com Think GATE Think GATE Forum . visit www.com SECTION .1999 www.gateforum.4 1. For each question. and more. (d) None of the above 1. All India Rank. Kleene closure (c) Intersection. Percentile.gateforum. This question consists of TWENTY-FIVE multiple questions of ONE mark each. complement (d) Complement.3 1.A 1.6 1. Which of the following statements is true? (a) There is a sample point at which X has the value 5. (b) There is a sample point at which X has value greater than 5. (c) There is a sample point at which X has a value greater than or equal to 5.7 (d) None of the above The number of binary strings of n zeroes and k ones that no two ones are adjacent is (a) n −1 (b) (c) n (d) None of the above Ck C k +1 n Ck Consider the regular expression (0 + 1) (0 + 1)….2 The number of binary relations on a set with n elements is: (a) n2 (b) 2n 2 (c) 2n 1. For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Which of the following is true? (a) LD = LE (b) LD ⊃ LE (c) LE = LD (d) None of the above Which of the following expressions is not equivalent to x ? (a) x NAND X (b) x NOR x (c) x NAND 1 (d) x NOR 1 Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. 12 Which of the following functions implements the Karnaugh map shown below? CD AB 00 00 11 10 00 0 0 1 0 01 X X 1 X 11 0 1 1 0 10 0 1 1 0 (a) AB + CD (b) D(C +A) (c) AD + AB (d) ( C + D ) C + D + ( A + B ) ( ) Listed below are some operating system abstractions (in the left column) and the hardware components (in the right column)? (A) Thread 1.gateforum. interaction with IISc alumni in our online discussion forums. Interrupt (B) Virtual address space 2.1999 www.1 (b) (A) – 1 (B) – 2 (C) – 3 (D) – 4 (c) (A) – 3 (B) – 2 (C) – 4 (D) . Percentile.2007 conducted by GATE Forum in over 25 cities all over India.1 (d) (A) – 4 (B) – 1 (C) – 2 (D) – 3 Which of the following disk scheduling strategies is likely to give the best through put? (a) Farthest cylinder next (b) Nearest cylinder next (c) First come first served (d) Elevator algorithm System calls are usually invoked by using (a) a software interrupt (b) polling (c) an indirect jump (d) a privileged instruction A sorting technique is called stable if (a) it takes O (nlog n) time (b) it maintains the relative order of occurrence of non-distinct elements (c) it uses divide and conquer paradigm (d) it takes O(n) space Join All India Mock GATE Classroom Test Series . Memory (C) File system 3.com 1.gatementor.8 1. CPU (D) Signal 4. Disk (a) (A) – 2 (B) – 4 (C) – 3 (D) .9 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Join discussion of this test paper at http://forum. visit www. All India Rank.11 1. and more. For more details.10 1.com Think GATE Think GATE Forum .gateforum.GATE CS . 47. 15.14 Suppose we want to arrange the n numbers stored in any array such that all negative values occur before all positive ones. 15. 40. 30.com Join discussion of this test paper at http://forum. 9. 8. 4.GATE CS .15 The number of articulation points of the following graph is 1 5 2 7 3 6 4 (a) 0 1.gatementor.16 (d) 3 (b) n (c) n -1 (d) n Which of the following is the most powerful parsing method? (a) LL (1) 1. 30. 4. 9.gateforum. visit www. 40 1. interaction with IISc alumni in our online discussion forums. 15. 12. 8. 17. then the minimum number of multiplications needed to compute a* is (a) log2n 1. 20. 9.18 (c) 2 If n is a power of 2. 15.17 (b) 1 (b) Canonical LR (c) SLR (d) LALR Consider the join of a relation R with a relation S. 8.com Think GATE Think GATE Forum . 40 (b) 8. For more details. 12. 47. 47. 17. 12. Minimum number of exchanges required in the worst case is (a) n . 30. 4.gateforum. 12. 9. 12. 47. 17 (d) 4.2007 conducted by GATE Forum in over 25 cities all over India. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are (a) m + n and 0 (b) mn and 0 (c) m + n and |m – n| (d) mn and m + n Join All India Mock GATE Classroom Test Series . 40.1999 www. 17 then the order of these elements after second pass of the algorithm is: (a) 8. 20.13 1. All India Rank. 4. 30.1 (b) n (c) n + 1 (d) None of the above If one uses straight two-way merge sort algorithm to sort the following elements in ascending order: 20. 47. 40. 17 (c) 15. 30. 9. Percentile.com 1. 20. 20. 25 (b) EC (c) AE (d) AC Which of the following is correct? (a) B-trees are for storing data on disk and B+ trees are for main memory. c.com Think GATE Think GATE Forum . e a.23.20. d. Let R = (a.gateforum. then block k of the main memory maps to the set (a) (k mod m) of the cache (b) (k mod c) of the cache (c) (k mod 2c) of the cache (d) (k mod 2 cm) of the cache 1.com Join discussion of this test paper at http://forum. ec d. The method converges (a) always (b) only if f is a polynomial (c) only if f ( xo ) < 0 (d) None of the above 1. (b) Range queries are faster on B* trees. The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit number is ( ) (a) O n2 (b) O(n) (c) O(log n) (d) O(1) 1. The relational algebra expression equivalent to the following tuple calculus expression: {t t ∈ r ∧ (t A = 10 ∧ t B = 20)} is (a) σ ( A =10 ∨ B = 20) ( r ) (b) σ ( A =10 ) ( r ) ∪ σ ( B = 20 ) ( r ) (c) σ ( A =10 ) ( r ) ∩ σ ( B = 20 ) ( r ) (d) σ ( A =10 ) ( r ) − σ ( B = 20) ( r ) 1. The Newton-Raphson method is to be used to find the root of the equation f(x)=0 where xo is the initial approximation and f ′ is the derivative of f. a b. visit www.1999 www. interaction with IISc alumni in our online discussion forums. and more. Join All India Mock GATE Classroom Test Series . Which of the following is a key for R? (a) CD 1.19. b. If the cache uses the set associative mapping scheme with 2 blocks per set.GATE CS . (d) The height of a B* tree is independent of the number of records.24.1 1. All India Rank.21. f) be a relation scheme with the following dependencies c f.gateforum. The main memory of a computer has 2 cm blocks while the cache has 2 c blocks. Percentile.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. e.22. Booth’s coding in 8 bits for the decimal number –57 is (a) 0 – 100 + 1000 (b) 0 – 100 + 100 -1 (c) 0 – 1 + 100 – 10 + 1 (d) 0 0 – 10 + 100 . (c) B-trees are for primary indexes and B* trees are for secondary indexes.com 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. For more details. (vii).1 Consider two events E1 and E2 such that probability of E1. Which of the following is/are true? (a) L is a poset (b) L is a Boolean algebra (c) -L1 is context free (d) -L2 is regular If L is context free language and L2 is a regular language which of the following is/are false? (a) L1 – L2 is not context free (b) L1 ∩ L2 is context free (c) ~L1 is context free (d) ~L2 is regular Given the programming constructs (i) assignment (ii) for loops where the loop parameter cannot be changed within the loop (iii) if-then-else (iv) forward go to (v) arbitrary go to (vi) non-recursive procedure call (vii) recursive procedure/function call (viii) repeat loop. What is the number of ways they can divide the flowers amongst themselves? (a) 1638 (b) 2100 (c) 2640 (d) None of the above Let L be a set with a relation R which is transitive. (viii) (c) (vi). Which of the 3 5 following statements is/are true? of E2. halting) function in the same programming language.4. visit www. B.com 2.1999 www. out of which ONLY ONE is correct.5. (iv) (b) (v).com Think GATE Think GATE Forum . Pr E21 = (a) Pr E1 or E2 is 2 3 (b) Events E1 and E2 are independent (c) Events E1 and E2 are not independent E 4 (d) Pr 1 = E2 5 2.gatementor. Pr [E1]= 1 . This question consists of TWENTY-FIVE sub-questions.b) exist.b) and the greatest lower bound glb (a. and more. (vii). Percentile. 2.e. (vii). 2. 2.com Join discussion of this test paper at http://forum. b ∈ L let the least upper bound lub (a.gateforum. (viii) Join All India Mock GATE Classroom Test Series ..gateforum. For more details.2007 conducted by GATE Forum in over 25 cities all over India. which constructs will you not include in a programming language such that it should be possible to program the terminates (i. Indicate the correct answers in the boxes corresponding to the questions only on the SECOND sheet of the answer book. (iii). C and D) are given. four possible alternatives (A. (viii) (d) (iii). 2. Two girls have picked 10 roses. For each of these sub-questions. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. All India Rank. probability 2 1 1 .GATE CS .2. Pr[E1 and E2]= . interaction with IISc alumni in our online discussion forums. 15 sunflowers and 15 daffodils. of TWO marks each. and probability of E1 and E2. anti-symmetric and reflexive and for any two elements a. (a) (ii).3. 7. The decomposition is (a) not in 2NF (b) in 2NF but not 3NF (c) in 3NF but not in 2NF (d) in both 2NF and 3NF Consider the circuit shown below.8. (a) A = 0. Consider the schema R = (S T U V) and the dependencies S T. XOR gates (d) Three-input gates that output (A. 2.gateforum. For more details. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. All India Rank. What are the possible values of A. B = 1.GATE CS . In a certain steady state. U V and V S. visit www. C = 1 (d) A = 1. C = 1 (c) A = 1. and more. interaction with IISc alumni in our online discussion forums.1999 www.gateforum. B = 1. Let R = (R1 and R2) be a decomposition such that R1 ∩ R2 = ∅ . 2. Percentile. Join All India Mock GATE Classroom Test Series . the line Y is at ‘1’. T U.com Join discussion of this test paper at http://forum.B) + C for the inputs A.com 2. C = 1 (b) A = 0. For the schedule given below. B = 0. B and c in this state? A Y B C 2. which of the following is correct: 1 Read 2 3 Read B Write A 4 Read A 5 Write A 6 Write B 7 Read B 8 Write B (a) This schedule is serialized and can occur in a scheme using 2PL protocol (b) This schedule is serializable but cannot occur in a scheme using 2PL protocol (c) This schedule is not serialiable but can occur in a scheme using 2PL protocol (d) This schedule is not seralisable and cannot occur in a scheme using 2PL protocol. NOT gates (b) 2 to 1 multiplexors (c) AND gates. B = 0. C = 1 Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function? (a) XOR gates.6. B and C.2007 conducted by GATE Forum in over 25 cities all over India.gatementor.com Think GATE Think GATE Forum .9. 25 0.25 0. and more. end.12. All India Rank. show. Which of the following is/are advantage of virtual memory? (a) Faster access to memory on an average. Then the output of the program is: (a) 0.125. (b) Processes can be given protected address spaces.2007 conducted by GATE Forum in over 25 cities all over India. For more details.1999 www.end. (b) Changing address translation tables. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. Percentile. var x: real. interaction with IISc alumni in our online discussion forums. (d) Invalidating the translation look-aside buffer. A multi-user. 2.10.gatementor.125 0. procedure show: begin print(x).11. visit www.125 (d) 0. (c) Linker can assign addresses independent of where the program will be loaded in physical memory. show.125 (b) 0. multi-processing operating system cannot be implemented on hardware that does not support (a) Address translation (b) DMA for disk transfer (c) At least two modes of CPU execution (privileged and non-privileged) (d) Demand paging 2.com Join discussion of this test paper at http://forum. Which of the following actions is/are typically not performed by the operating system when switching context from process A to process B? (a) Saving current register values and restoring saved register values for process B. begin x:=0.GATE CS .25. 2.gateforum.25 (c) 0. begin x: = 0.13.25 2. procedure small.com Think GATE Think GATE Forum .125 0. The number of tokens in the Fortran statement DO 10 I = 1. small end.14.com 2.25 is (a) 3 (b) 4 (c) 5 (d) None of the above Join All India Mock GATE Classroom Test Series . Consider the following program in a language that has dynamic scooping: var x: real. (c) Swapping out the memory image of process A to the disk. (d) Programs larger than the physical memory size can be run. 1999 www.20. (d) vertical micro-programming. The number of full and half-adders required to add 16-bit numbers is (a) 8 half-adders. give the correct matching for the following pairs: (M) Tn = Tn −1 + n (U) Tn = O ( n ) (N) Tn = Tn + n (V) Tn = O ( n log n ) 2 (O) Tn = Tn + n log n 2 (P) Tn = Tn −1 + log n ( ) = O (log n ) (W) Tn = O n2 (X) Tn 2 Join All India Mock GATE Classroom Test Series . Percentile. Raid configurations of the disks are used to provide (a) Fault-tolerance (b) High speed (c) high data density (d) None of the above 2. vertical (b) Hard wired control. Hard wired control. programming. and more. C (with 15 records). Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Arrange the following configuration for CPU in decreasing order of operating speeds: Hard wired control. horizontal micro- vertical micro- (c) horizontal micro-programming. The minimum number of record movements required to merge five files A (with 10 records). is (a) Ambiguous (c) Information is unambiguous (b) Unambiguous not sufficient to decide whether it is ambiguous or (d) None of the above 2. hard wired control.21. 15 full-adders (c) 16 half-adders. vertical micro-programming.16. 0 full-adders (d) 4 half-adders.GATE CS . visit www.com 2. Zero has two representations in (a) Sign magnitude (b) 1’s complement (c) 2’s complement (d) None of the above 2. 8 full-adders (b) 1 half-adder.19.2007 conducted by GATE Forum in over 25 cities all over India. (a) Hard wired control.gateforum.com Think GATE Think GATE Forum . micro-programming. horizontal micro-programming. For more details. B (with 20 records).com Join discussion of this test paper at http://forum.17. All India Rank. 2. programming.18. horizontal microprogramming. horizontal micro-programming. D (with 5 records) and E (with 25 records) is: (a) 165 (b) 90 (c) 75 (d) 65 2. If T1 = O(1). interaction with IISc alumni in our online discussion forums. 12 full-adders 2.gatementor.gateforum.15. A grammar that is both left and right recursive for a non-terminal. vertical microprogramming. score off the answer not to be evaluated.gateforum. visit www. (a) Mr. X offers the following proof: Join All India Mock GATE Classroom Test Series .com Think GATE Think GATE Forum . 3. X claims the following: If a relation R is both symmetric and transitive. and more. Percentile. Consider the following C function definition int Trial (int a. else if (a > = b) return Trial (a.com (a) M – W N – V O – U P . int c) { if ((a > = b) && (c < b) return b. Which of the following programming language features cannot be implemented on this processor? (a) Pointers (b) Arrays (c) Records (d) Recursive procedures with local variable 2.c). b. If more number of questions are attempted. The main differences(s) between a CSIC and A RISC processor is/are that a RISC processor typically (a) has fewer instructions (b) has fewer addressing modes (c) has more registers (d) is easier to implement using hard-wired control logic 2.25. Attempt ANY FIFTEEN questions. All India Rank. then R is reflexive. Mr. Which of the following is/are correct? (a) An SQL query automatically eliminates duplicates (b) An SQL query will not work if there are no indexes on the relations (c) SQL permits attribute names to be repeated in the same relation (d) None of the above SECTION – B This section consists of TWENTY questions of FIVE marks each. else return Trial (b.2007 conducted by GATE Forum in over 25 cities all over India. int b.24. interaction with IISc alumni in our online discussion forums. and c (b) Finds the minimum of a.a.X (b) M – W N – U O – X P .22. A certain processor supports only the immediate and the direct addressing modes.b). b and c (c) Finds the middle number of a. For this.X 2. b. c (d) None of the above 2.1999 www. } The function Trial: (a) Finds the maximum of a.23. else only the first fifteen unscored answers will be considered.GATE CS .c.V (c) M – V N – W O – X P . For more details.com Join discussion of this test paper at http://forum.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.U (d) M – W N – U O – V P .gatementor. D). D)] (ii) {(B. Let Abe an n × n matrix such that the elements in each row and each column are arranged in ascending order. which finds 1st. Now because R is transitive xRy and yRx together imply xRx. F). 2nd and 3rd smallest elements in minimum number of comparisons. (b) Given two finite automata M1. Therefore. (note: strict subset) 7. either aH = bH or aH and bH are disjoint. 6. A E D B C F (a) Which of the following sets of edges is a cut? (i) {(A.GATE CS . 8. Join All India Mock GATE Classroom Test Series . (B. E). visit www. A cut in G is a set of edges whose removal results in G being broken into two or more components. Show that the language L{xcx 1 x ∈ {0. All India Rank. (b) Give an example of a relation R which is symmetric and transitive but not reflexive. F). For more details.gatementor. A min-cut of G is a cut in G of minimum cardinality. and more.B)} (b) What is the cardinality of min-cut in this graph? (c) Prove that if a connected undirected graph G with n vertices has a min-cut of cardinality k. (E. M2. (a) Show that |aH| = |H| (b) Show that for every pair of elements a. (A. Let G be a finite group and H be a subgroup of G. outline an algorithm to decide if L(M1) ⊆ L(M2).com “From xRy. using symmetry we get yRx. B).2007 conducted by GATE Forum in over 25 cities all over India. (a) Given that A is regular and (A ∪B) is regular. For a ∈ G. define aH={ah1 h∈H). which are not connected with each other. R is reflexive”. (A. 5.com Join discussion of this test paper at http://forum. does it follow that B is necessarily regular ? Justify your answer. Percentile.gateforum.1999 www. 4. Consider the following graph. Draw a decision tree.com Think GATE Think GATE Forum . Let G be a connected. (A. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.b ∈G. (c) Use the above to argue that the order of H must divide the order of G.gateforum. D).1}* and c is a terminal symbol} is not context free c is not 0 or 1. (C. then G has at least (nk/2) edges. The size of a cut is called its cardinality. undirected graph. interaction with IISc alumni in our online discussion forums. 1999 www. FUNNY (f) = IF HALTS (f f) THEN not (f f) ELSE TRUE (a) Show that FUNNY terminates for all functions f. Example: Given the following function definition. on input 101. For example.val = 5. 10. interaction with IISc alumni in our online discussion forums. Suppose we have a function HALTS which when applied to any arbitrary function f and its arguments will say TRUE if function f terminates for those arguments and FALSE otherwise. Use induction on the height of the binary tree to prove that the number of full nodes plus one is equal to the number of leaves. 3. algorithm what (n) begin if n = 1 then call A else begin what (n –1). 6. a full node is defined to be a node with 2 children. (a) In binary tree. Let synthesized attribute val give the value of the binary number generated by S in the following grammar.gateforum. 4.gatementor.com Think GATE Think GATE Forum . S LL\L L LB\B B 0\1 Write S-attributed values corresponding to each of the productions to find S.GATE CS . 101. 11. call B(n) end end. visit www.625. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. FACTORIAL (N) = IF (N = 0) THEN 1 ELSE N*FACTORIAL (N-1) Then HALTS (FACTORIAL 4) = TRUE and HALTS (FACTORIAL –5)=FALSE Let us define the function. Assume. and more.2007 conducted by GATE Forum in over 25 cities all over India. 12. Show the result after the deletion of the root of this heap. procedure A and procedure B take ( ) (1) and ( ) (1/n) unit of time respectively. (a) Consider the following algorithms. Derive the time complexity of the algorithm in ( )-notation. (b) Draw the min-heap that results from insertion of the following elements in order into an initially empty min-heap: 7.val. 1. (b) use (a) to prove (by contradiction) that it is not possible to have a function like HALTS which for arbitrary functions and inputs says whether it will terminate on that input or not.gateforum. For more details. All India Rank.com Join discussion of this test paper at http://forum. (b) Write a constant time algorithm to insert a node with data D just before the node with address p of a singly linked list. 2.com 9. S. Join All India Mock GATE Classroom Test Series . Percentile. 5. The 5 instructions in a certain instruction sequence need these stages for the different number of clock cycles as shown by the table below. (b) Let A be a tautology and B be any other formula..gateforum.a). …. Prove that (A∨B) is a tautology. Decode field (D). P(a+b.gateforum. vari i. of clock cycles needed for Instruction F D E W 1 1 2 1 1 2 1 2 2 1 3 2 1 3 2 4 1 3 2 1 5 1 2 1 2 Find the number of clock cycles needed to perform the 5 instructions.a. Join All India Mock GATE Classroom Test Series . What will be the output of the following program assuming that parameter passing is (i) call by value (ii) call by reference (iii) call by copy restore procedure P{x.com Join discussion of this test paper at http://forum. begin a: = : b : =3.2007 conducted by GATE Forum in over 25 cities all over India. procedure readarray.…. begin y: y + 1.. Percentile.x. z: x + x end. Consider the following Pascal program skeleton: program sort (…).y. visit www. 15. and more. 14. Execute (E) and Result Write (W). var a. begin …:=…a… end.gatementor. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS . All India Rank. interaction with IISc alumni in our online discussion forums.1999 www. Print (a) end. (a) Show that the formual [(~p∨q) ⇒ (q ⇒ P)] is not a tautology. An instruction pipeline consists of 4 stages – Fetch (F). 16. No.com 13..com Think GATE Think GATE Forum .z}. For more details. …:=…v…. Shift right R1 by 1 bit Jump to target X Z:…. . The processor has three general purpose registers R1.gatementor. R1 SHR R1 SHL R1 CMP R2.3).3). Join All India Mock GATE Classroom Test Series . Consider the following program fragment in the assembly language of a certain hypothetical processor. qsort (1. visit www. . . following procedures are active: sort. For more details. qsort (1.. exchange (1. function partition (…)….0 . end. procedure qsort(…. var k.gateforum.j. and more. R2 and R3.GATE CS . 17.) after the instructions. . Assume that given points in time during program execution. All India Rank.). Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. R1 JZY INC R3 SHR R1 JMP X .…. . set flags appropriately in status register Jump if zero to target Z.2007 conducted by GATE Forum in over 25 cities all over India.v.com Join discussion of this test paper at http://forum. . …:=…x…. end. begin …:=…a….9). begin : end: begin : end.com procedure exchange (…). begin …:=…a…. . partition (1.1999 www. The meanings of the instructions are shown by comments (starting with . . …. interaction with IISc alumni in our online discussion forums.3) Show snapshots of the runtime stack with access links after each of the activations. Compare R1 and 0. Percentile.gateforum.com Think GATE Think GATE Forum . X: Y: CMP R1. JZZ MOV R2. var i. Copy contents of R1 to R2 Shift right R1 by 1 bit Shift left R1 by 1 bit Compare R2 and R1 and set flag in status register Jump if zero to target Y Increment R3 by 1. Percentile.com (a) Initially R1. It is proposed to provide a TLB (Translation look-aside buffer) for speeding up address translation. R2 and R3 contain the values 5.2007 conducted by GATE Forum in over 25 cities all over India. D0 is the least significant) 19.0 and 0 respectively. R2 and R3 initially contain the values n. D3 (bi-directional data lines. (a) A certain processor provides a ‘test and set’ instruction that is used as follows. The proposed TLB will be capable of storing page table entries for 16 recently referenced virtual pages. (a) What is the minimum page size in bytes so that the page table for a segment requires at most one page to store it? Assume that the page size can only be a power of 2 (b) Now suppose that the pages size is 512 bytes. What is the final value of R3 when control reaches Z? 18.gateforum. 3 bits for page protection and 1 dirty bit. How many bits are available in page table entry for storing the aging information for the page? Assume that the page size is 512 bytes. interaction with IISc alumni in our online discussion forums. Join All India Mock GATE Classroom Test Series . For more details. The virtual address space is divi8ded into 8 nonoverlapping equal size segments. Each of these chips has the following signal pins: (i) CS (Chip select. D1. A0 is the lest significant) (v) D0.1999 www. what are the final values of R1 and R3 when control reaches Z? (b) In general. (b) Consider the following solution to the producer-consumer problem suing a buffer of size 1. Assume that the initial value of account is 0.gatementor. Design a 2K × 8 (2048 locations. D2. The memory is byte addressable. each bit wide) memory system mapped at addresses (1000 )16 to (17FF )16 for the 8085 processor using four 1K × 4 memory chips. Page table are stored in the main memory and consists of 2 byte page table entries. A1. data lines are in high impedance state when it is 1) (ii) RD (0 for read operation) (iii) WR (0 for write operation) (iv) A0. if R1. each entry of which contains the physical address of the page table for the segment.GATE CS . What is the number o tag bits that will need to be associated with each cache entry (c) Assume that each page table entry contains (besides other information) 1 valid bit. and 0 respectively. All India Rank.com Think GATE Think GATE Forum . …A9 (input address lines. TSET register. Both virtual and physical address spaces contain 216 bytes each. and more.gateforum. visit www.com Join discussion of this test paper at http://forum. A certain computer system has the segmented paging architecture for virtual memory. 0. in a fast cache that will use the direct mapping scheme. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Also assume that the testing of count and assignment to count are atomic operations. The memory management unit (MMU) has a hardware segment table. 20.flag This instruction atomically copies flag to register and sets flag to 1. Give pseudopodia for implementing the entry and exit code to a critical region using this instruction. 1999 www.gateforum. and more. Consider a B-tree with degree m.000. Remove item from buffer. Location) Write an SQL query to: (a) Find all employee names who work in departments located at ‘Calcutta’ and whose salary is greater than Rs.1. of any internal node (except the root) is such that m ≤ c ≤ 2m –1. derive the maximum and minimum number of records in the leaf nodes for such a B-tree with height h. Count =1: Wakeup (Consumer).gatementor. Percentile.000.com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums. the number of children.h≥1. visit www.com Think GATE Think GATE Forum .00. Forever: Show that in this solution it is possible that both the processes are sleeping at the same time. if count = 1 then sleep.50. Count = 0 Wakeup (producer). Forever Consumer: Repeat if count = 0 then sleep. All India Rank. for each department number.2007 conducted by GATE Forum in over 25 cities all over India. Join All India Mock GATE Classroom Test Series . For more details. 21. Consider the set of relations EMP (Employee-no.com Producer Repeat Produce an item.GATE CS . (b) Calculate. the number of employees with a salary greater than Rs. that is. Salary) DEPT (Dept-no. Dept-no. Consumer item. (Assume that the root of a tree is at height 0). Dept-name.gateforum. place item in buffer. Employee-name. c. 22. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums. i ≤ i ≤ n. four possible alternatives (A. Indicate the correct answer in the boxes corresponding to the questions only on the FIRST sheet of the answer book. j = i − j for all i.gatementor.7 (b) 11010101 (c) 00101011 (d) 10101011 To put the 8085 microprocessor in the wait state (a) lower the HOLD input (b) lower the READY input (c) raise the HOLD input (d) raise the READY input Join All India Mock GATE Classroom Test Series . C and D) are given. Which of the following is true? (a) S ⊂ T 1. Percentile. j.5 2 The determinant of the matrix 2 8 2 9 1.com Join discussion of this test paper at http://forum.1 ≤ j ≤ n The sum of the elements of the array v is (a) 0 1. 1.A 1. All India Rank.1 – 1. For more details.1 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is (a) 3 1.GATE CS . This question consists of TWENTY-THREE multiple questions of ONE mark each.6 (a) L = 0+ (b) L is regular but not 0+ (c) L is context free but not regular (d) L is not context free The number 43 in 2’s complement representation is (a) 01010101 1. For each question (1.com SECTION .4 ( n + 1) (b) T ⊂ S (c) S = T (d) S ∩T = φ Let L denotes the language generated by the grammar S 0S0/00.23). visit www. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2 (b) 8 (c) 9 (d) 12 (c) n2 − 3n + 2 (d) n2 (c) 15 (d) 20 An n × n array v is defined as follows: ν i.gateforum.b} represented by the regular expressions (a+b*)* and (a+b)*.2000 www. Which of the following is true? 1. B.2007 conducted by GATE Forum in over 25 cities all over India. out of which ONLY ONE is correct. respectively.com Think GATE Think GATE Forum .3 (b) n -1 (a) 4 0 0 0 1 7 2 is: 0 2 0 0 6 1 (b) 0 Let S and T be language over Σ={a.gateforum. a float.2 (c) X – 2 Y – 3 Z .gateforum. All India Rank.GATE CS .1 (d) X – 3 Y – 1 Z . }.com Join discussion of this test paper at http://forum. n->value=5. each element of which is a structure of type node 1. lost memory Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India.1 (b) X – 1 Y – 3 Z . each element of which is a pointer to a structure of type node (b) A structure of 2 fields. (d) by checking the TRAP pin for ‘high’ status at regular intervals. 2: using uninitialized pointers Z: char *p.12 The most appropriate matching for the following pairs X: m=malloc(5). m= NULL.11 (a) X – 3 Y – 2 Z .com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. we can say that (a) T1 ≤ T2 (b) T1 ≥ T2 (c) T1 < T2 (d) T1 is T2 plus the time taken for one instruction fetch cycle 1.gateforum. define s to be (a) An array. struct node *s[10]. Constants is 1. 3. and an array of 10 elements (d) An array. visit www.9 The 8085 microprocessor responds to the present of an interrupt (a) as soon as the TRAP pin becomes ‘high’ (b) by checking the TRAP pin for ‘high’ status at the end of each instruction each (c) by checking the TRAP pin for ‘high’ status at the end of the execution of each instruction.10 The most appropriate matching for the following pairs X: Indirect addressing 1: Loops Y: Immediate addressing 2: Pointers Z: Auto decrement addressing 3.2 The following C declarations struct node{ int i: float j. For more details. *p=’a’.2000 www. interaction with IISc alumni in our online discussion forums. Percentile. each field being a pointer to an array of 10 elements (c) A structure of 3 fields: an integer. and more.com 1. 1. 1: using dangling pointers Y: free(n).8 Comparing the time T1 taken for a single instruction on a pipelined CPU with time T2 taken on a non-pipelined but identical CPU. com is: 1.2 (c) X – 3 Y – 2 Z . Let t(n) denote the time taken for the most efficient algorithm to determined if there are two elements with sum less than 1000 in s.2 The most appropriate matching for the following pairs X: depth first search 1: heap Y: breadth-first search 2: queue Z: sorting 3: stack is: 1.1 Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress.GATE CS .13 (a) X – 1 Y – 3 Z . or further nested.com Join discussion of this test paper at http://forum. } u. visit www. Join All India Mock GATE Classroom Test Series . Note that Y and Z may be NULL. long z. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2007 conducted by GATE Forum in over 25 cities all over India.gateforum. Which of the following represents a valid binary tree? (a) (1 2 (4 5 6 7)) (b) (1 (2 3 4) 5 6) 7) (c) (1 (2 3 4)(5 6 7)) (d) (1 (2 3 NULL) (4 5)) Let s be a sorted array of n integers. interaction with IISc alumni in our online discussion forums.gateforum. respectively. }t.1 (d) X – 2 Y – 3 Z .15 1. For more details. which of the following statements is true? (a) t (n) is 0(1) (b) n ≤ t(n) ≤ n log2 n n (c) n log2 n ≤ t(n) < 2 n (d) t(n) = 2 Aliasing in the context of programming languages refers to (a) multiple variables having the same memory location (b) multiple variables having the same value (c) multiple variables having the same identifier (d) multiple uses of the same variable 1. of node X. and more. Percentile.1 (d) X – 3 Y – 1 Z .3 (b) X – 3 Y – 1 Z .com Think GATE Think GATE Forum .2 (b) X – 2 Y – 1 Z .16 (a) X – 1 Y – 2 Z .17 Consider the following C declaration struct { short s [5] union { float y.14 1.3 (c) X – 3 Y – 2 Z .gatementor.2000 www. All India Rank. ignoring alignment considerations.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and department (deptno. Let m[0]…m[4] be mutexes (binary semaphores) and P[0] …. Which of the following derivations does a top-down parser use while parsing an input string? The input is assumed to be scanned in left to right order. B+ -trees are preferred to binary trees in databases because (a) Disk capacities are greater than memory capacities (b) Disk access is much slower than memory access (c) Disk data transfer rates are much less than memory data transfer rates (d) Disks are more reliable than memory 1. respectively. The memory requirement for variable t.com Join discussion of this test paper at http://forum.21. This could cause (a) Thrashing (b) Deadlock (c) Starvation. is (a) 22 bytes 1.com Think GATE Think GATE Forum .GATE CS .gateforum.2000 www.com Assume that objects of the type short. address) Join All India Mock GATE Classroom Test Series .18 (b) 14 bytes (c) 18 bytes (d) 10 bytes The number of tokens in the following C statement printf(“i=%d. All India Rank. interaction with IISc alumni in our online discussion forums. release (m[(i+1)mod 4]).&i). For more details. deptno).gatementor.23.22. float and long occupy 2 bytes. 4 bytes and 8 bytes. &i=%x”. (a) Leftmost derivation (b) Leftmost derivation traced out in reverse (c) Rightmost derivation (d) Rightmost derivation traced out in reverse 1.20. salary.wait (m[(i+1) mode 4]). Given the relations employee (name. ……… release (m[i]). deptname. Which of the following need not necessarily be saved on a context switch between processes? (a) General purpose registers (b) Translation look-aside buffer (c) Program counter (d) All of the above 1. P[4] be processes.19.2007 conducted by GATE Forum in over 25 cities all over India. Suppose each process P[i] executes the following: wait (m[i].i. is (a) 3 (b) 26 (c) 10 (d) 21 1. visit www. but not deadlock (d) None of the above 1. Percentile. and more. 2. This question consists of TWENTY-SIX multiple questions of TWO marks each. B. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.3. Percentile. The overlap of X and Y is half a unit.26).4. Let S = ∑ i log i =3 and T= ∫ 100 2 2l and x log2 xdx Which of the following statements is true? 2. C and D) are given.com Think GATE Think GATE Forum .2007 conducted by GATE Forum in over 25 cities all over India. the probability of the event E1. E1 and E2 are events in a probability space satisfying the following constraints: • Pr(E1) = Pr(E2) • Pr(E1 ∪ E2) = 1 • E1 and E2 are independent The value of Pr(E1).1 X. The overlap of Y and Z is also half a unit. All India Rank.gatementor.GATE CS .×.1 – 2. For each question (2.com Join discussion of this test paper at http://forum.∪. . Which of the following is true? (a) k must be 1 (b) k must be 0 (c) k can take any value between 0 and 1 (d) None of the above 2.com Which of the following queries cannot be expressed using the basic relational algebra operations (σ.Y and Z are closed intervals of unit length on the real line. 2. out of which ONLY ONE is correct. Let the overlap of X and Z be k units.∩.π. and more.gateforum.−)? (a) Department address of every employee (b) Employees whose name is the same as their department name (c) The sum of all employees’ salaries (d) All employees of a given department 2. four possible alternatives (A. visit www. (a) S > T (b) S = T (c) S < T and 2S > T (d) 2S ≤ T A polynomial p(x) satisfies the following: p(1) = p(3) = p(5) = 1 p(2) = p(4) = -1 The minimum degree of such a polynomial is (a) 1 (b) 2 (c) 3 (d) 4 Join All India Mock GATE Classroom Test Series . is (a) 0 (b) 1 4 (c) 1 2 (d) 1 100 2. For more details. interaction with IISc alumni in our online discussion forums. Indicate the correct answer in the boxes corresponding to the questions only on the SECOND sheet of the answer book.gateforum.2000 www. y. b. visit www.5. Assume that the equivalence a ↔ (b V-b) and b ↔ c hold. For more details. z and w. All India Rank. Let P(S) denotes the powerset of set S.2000 www. or L must be {an| n is even} 2. 2.com Think GATE Think GATE Forum .com Join discussion of this test paper at http://forum. and more. respectively: (a) 0 1 0 0 (b) 1 1 0 1 (c) 1 0 1 1 (d) 1 0 0 0 Join All India Mock GATE Classroom Test Series .9.6. c. x +y + z =1 xy = 0 xz + w = 1 xy + z w=0 have the following solution for x. y. (d) Only (P2) is decidable The simultaneous equations on the Boolean variables x. Consider the following decision problems: (P1) Does a given finite state machine accept a given string (P2) Does a given context free grammar generate an infinite number of stings Which of the following statements is true? (a) Both (P1) and (P2) are decidable (b) Neither (P1) nor (P2) are decidable (c) Only (P1) is decidable 2. Percentile. 2. z and w. A relation R is defined on the set of integers as x Ry iff (x+y) is even.com 2.2007 conducted by GATE Forum in over 25 cities all over India.gatementor.8. Which of the following is always true? (a) P(P(S))=P(S) (b) P(S) ∩P(P(S)) = {φ} (c) P(S) ∩S = P(S) (d) S ∉P(S) Let a.gateforum.GATE CS .7. Which of the following statements is true? (a) R is not an equivalence relation (b) R is an equivalence relation having 1 equivalence class (c) R is an equivalence relation having 2 equivalence classes (d) R is an equivalence relation having 3 equivalence classes 2.10.gateforum. interaction with IISc alumni in our online discussion forums. d be propositions. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Then the truth-value of the formula ( a ∧ b ) → ( a ∧ c ) ∨ d is always (a) True (b) False (c) Same as the truth-value of b (d) Same as the truth-value of d What can be said about a regular language L over {a} whose minimal finite state automation has two states? (a) L must be {an|n is odd} (b) L must be {an|n is even} (c) L must be {an|≥0} (d) Either L must be {an|n is odd}. and the sequence X: = A + B Y:= A + c X: = X + C Y:= Y + B Executed on a computer where floating point numbers are represented with 32 bits.0 Join All India Mock GATE Classroom Test Series .12.com Think GATE Think GATE Forum . Y = 1.gateforum. C = 1.com Join discussion of this test paper at http://forum.0. Y = 1.13.gatementor. Which of the following modes can the card not support? (a) 1600 × 400 resolution with 256 colours on a 17 inch monitor (b) 1600 × 400 resolution with 16 million colours on a 14 inch monitor (c) 800 × 400 resolution with 16 million colours on a 17 inch monitor (d) 800 × 800 resolution with 256 colours on a 14 inch monitor 2.gateforum.2000 www.14. Percentile. interaction with IISc alumni in our online discussion forums. 0 (b) 1. After the clock cycles the output state P.GATE CS . Which functions does NOT implement the Karnaugh map given below? wz 00 01 11 10 00 0 × 0 0 01 0 × 1 1 11 1 1 1 1 10 0 × 0 0 xy↓ (a) (c) (w + x ) y (w + x ) (w + y ) ( x + y ) (b) xy + yw (d) None of the above Q 1 P 2. (a) 1. 1 (respectively).0.2007 conducted by GATE Forum in over 25 cities all over India.0 × 1030. Y = 0.0. 1 2. The following arrangement of master-slave flip flops J K D 1 Clock has the initial state of P.0 (b) X = 1. The values for X and Y will be (a) X = 1. All India Rank.0 (d) X = 0.0 × 1030. Q is (respectively). Q as 0. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Y = 0.com 2. For more details.0. 0 (d) 0.11. visit www. 1 (c) 0. B = -2. A graphics card has on board memory of 1 MB. and more. Consider the values of A = 2.0 (c) X = 0.0. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. Which of the following statements is always true? (a) {u. and let T be the resulting depth-first search tree. and more. k). Lt G be an undirected graph.j) which reverses the order of elements in a between positions i and j (both inclusive).com Join discussion of this test paper at http://forum. For more details. Let G be an undirected connected graph with distinct edge weight. then its removal must disconnect G (c) No minimum spanning tree contains emax (d) G has a unique minimum spanning tree 2. What does the following sequence do.19.v} must be an edge in G.v} is not an edge in G then u and v must have the same parent in T Join All India Mock GATE Classroom Test Series . All India Rank. inorder and preorder traversal.2000 www. 1. n). Which of the following statements is false? (a) Every minimum spanning tree of G must contain emin (b) If emax is in a minimum spanning tree. Consider the following functions f ( n ) = 3n g ( n) = 2 n n log2 n h ( n) = n! Which of the following is true? (a) h(n) is O (f(n)) (b) h(n) is O (g(n)) (c) g(n) is not O (f(n)) (d) f(n) is O(g(n)) 2. where 1 ≤ k ≤n: reverse (s.GATE CS . reverse (s. and v is a descendant of u in T (c) If {u.18. Let emax be the edge with maximum weight and emin the edge with minimum weight.v} must be an edge in G. (a) Rotates s left by k positions (b) Leaves s unchanged (c) Reverses all elements of s (d) None of the above 2.15. Percentile. Respectively. n). and u is a descendant of v in T (b) {u. interaction with IISc alumni in our online discussion forums.2007 conducted by GATE Forum in over 25 cities all over India.16. Let LASTPOST.gateforum.gateforum. Which of the following is always tree? (a) LASTIN = LASTPOST (b) LASTIN = LASTPRE (c) LASTPRE = LASTPOST (d) None of the above 2.com 2.i.com Think GATE Think GATE Forum . k + 1. Let u be a vertex in G and let ν be the first new (unvisited) vertex visited after visiting u in the traversal. 1. Consider a depth-first traversal of G. Suppose you are given an array s[1…n] and a procedure reverse (s.17. LASTIN and LASTPRE denote the last vertex visited in a postorder. visit www.v} is not an edge in G then u is a leaf in T (d) If {u. of a complete binary tree. reverse (s. 9999 milliseconds (b) 1 millisecond (c) 9. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.| id Which of the following is true? 2. Percentile. The value of j at the end of the execution of the following C program int incr (int i) { static int count = 0.j. For more details.com Think GATE Think GATE Forum . and more. All India Rank. (c) Never request a resource after releasing any resource (d) Request and all required resources be allocated before execution. i++) j = incr(i). (a) * has higher precedence than + (b) . interaction with IISc alumni in our online discussion forums. } main () { int i.20.23.com 2. Then a 99.gateforum.9999 microseconds 2.com Join discussion of this test paper at http://forum.999 microseconds (d) 1.2007 conducted by GATE Forum in over 25 cities all over India. } is (a) 10 (b) 4 (c) 6 (d) 7 2. i <=4.21. count = count + i.GATE CS . Join All India Mock GATE Classroom Test Series .22. for (i = 0. visit www. Given the following expression grammar: EE*F|F+E|F F F . while a memory access takes 1 microsecond.99% hit ratio results in average memory access time of (a) 1.gatementor. return (count).has higher precedence than * (c) + and – have same precedence (d) + has higher precedence than * Suppose the time to service a page fault is on the average 10 milliseconds.gateforum.2000 www. Which of the following is NOT a valid deadlock prevention scheme? (a) Release all resources before requesting a new resource (b) Number the resources uniquely and never request a lower numbered resource than the last one requested. 5. Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum.gateforum.GATE CS . interaction with IISc alumni in our online discussion forums.26 In SQL.1}. Suppose all comparisons with a null value are treated as false. If more number of questions are attempted. 6. visit www.24.25. 1. relations can contain null values. x ⊗ y = (xy) mod 8 (a) Prove that ({0. 2 4. that is . and comparisons with null values are treated as unknown.com Think GATE Think GATE Forum . 3. provided (a) r has no duplicates and s is non-empty (b) r and s have no duplicates (c) s has no duplicates and r is non-empty (d) r and s have the same number of tuples 2. where x is an integer (c) x ≠ 5 not (x = 5) (d) None of the above SECTION – B This section consists of TWENTY questions of FIVE marks each. s is guaranteed to be same as r. and more. ⊗) is not a group.z). Given relations r(w. Consider the following sequence: s1 : s2 =1 and s1 = 1 + mine {si −1 .com 2. the result of select distinct w. 3. Let S = {0. Prove by induction on a n that sn = . else only the first fifteen unscored answers will be considered. Percentile.x from r. score off the answer not to be evaluated.x) and s(y. All India Rank. For more details.gatementor. 4. ⊗) where G ⊂ S and G has 2 elements. Which of the following pairs is not equivalent? (a) x = 5 not (not (x = 5) (b) x = 5 x > 4 and x < 6.gateforum. 7} and ⊗ denote multiplication modulo 8.2007 conducted by GATE Forum in over 25 cities all over India. si − 2 } for i > n 2. Attempt ANY FIFTEEN questions. (b) Write 3 distinct groups (G. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.2000 www. 2. Given the following relation instance X Y Z 1 4 2 1 5 3 1 6 3 3 2 2 Which of the following functional dependencies are satisfied by the instance? (a) XY Z and Z Y (b) YZ X and Y Z (c) YZ X and X Z (d) XZ Y and Y X 2. The edge labels are of the form d. For more details. Two vertices are adjacent iff the symmetric difference of the corresponding sets has exactly 2 elements.s denotes the move from state qo to qo in which the input symbol 1 is read and pushed to the stack. What is the condition on the values of i and j? 8.1}. n} and G a graph with 2n vertices. …. A pushdown automaton (pda) is given in the following extended notation of finite state diagrams: q0 2.GATE CS . What is the degree of a vertex in G? (b) How many connected components does G have? 7. over {0. (b) Consider the grammar S aS Ab S ε A bA A ε Where S. of all strings that contain neither the substring 00 nor the substring 11.1} *. and more. x R denotes revese of x . visit www.gatementor.gateforum. s/1.gateforum. All India Rank. s / s ′ where d is the input symbol read and s. Join All India Mock GATE Classroom Test Series . (a) What is the number of multisets of size 4 that can be constructed from n distinct elements so that at least one element occurs exactly twice? (b) How many multisets can be consctructed from n distinct elements? 6.1.s/s The nodes denote the states while the edges denote the moves of the pda.s 1. Let S be a set of n elements {1. For example the edge labeled 1. j ≥ 0. This grammar generates strings of the form ai b j for some i. A multiset is an unordered collection of elements where elements may repeat any number of times.2000 www.com 5. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (a) Introduce two edges with appropriate labels in the above diagram so that the resulting pda accepts the language { x2 x R } x ∈ {0. 2.s/s q1 1.com Join discussion of this test paper at http://forum. a. each vertex corresponding to a distinct subset of S. interaction with IISc alumni in our online discussion forums. A are non-terminal symbols with S being the start symbol.. Percentile.2007 conducted by GATE Forum in over 25 cities all over India.s/1. s ′ are the stack contents before and after the move. Note: The R R symmetric difference of two sets R1 and R2 is defined as 1 ∪ 2 R2 R1 (a) Every vertex in G has the same degree. (a) Construct as minimal finite state machine that accepts the language.b are terminal symbols and ε is the empty string. by empty stack.com Think GATE Think GATE Forum . The size of a multiset is the number of elements in it counting repetitions. where i and j satisfy some condition. Do not draw any pictures. visit www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. …. With I1 as the least significant bit.AD0 T3 T6 T7 T8 30H A 50H T5 D T9 TA C B IO/ M (a) Write the contents of the boxes. …. C and D in hexadecimal in your answer sheet. interaction with IISc alumni in our online discussion forums. Label the input bits I1.com Join discussion of this test paper at http://forum. 11. All India Rank. Use 1 to signify truth. 10. R2. A. Percentile. one two-input gate and two NOT gates. T3 and T4. Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input): (a) Write the truth table for all bits. 00H SUB C ADD B DAA S2: JC S3 Join All India Mock GATE Classroom Test Series .2000 www.com (b) Describe a non-deterministic pda with three states in the above notation that { } accept the language 0n1m n ≤ m ≤ 2n by empty stack 9. I2.GATE CS . (b) Draw one circuit for each output bit using. Label the output bits R1.com Think GATE Think GATE Forum . and more. where registers B and C contain BCD values: S1: MVI A.2007 conducted by GATE Forum in over 25 cities all over India. With R1 as the least significant bit. two two-input AND gates. (b) Write the state of both ALE and RD pins at time units T1. T2.gateforum. For more details. B. Consider the following 8085 program segment.gatementor.gateforum. Consider the 8085 instruction IN 09H stored as follows: Memory Address Machine Code 3050 DA 3051 09 And the following incomplete timing diagram for the instruction: T1 T2 T4 30H A15-A8 AD7 . (c) How do you generate the signal that tells the peripheral to put the data on the bus? Answer by completing the following statement in your answer book: By combining signals ……………. 99H MVI D. altogether. Branch instructions are not overlapped. Join All India Mock GATE Classroom Test Series . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. 52*34+52**+ Show the contents of the stack. If the branch is not taken. calculate the average instruction execution time. A S4: ………… (a) For the two pairs (B = 44. Under ideal conditions. JZ S4 MVI D. A MVI A. Ignore the fact that some branch instructions may be conditional. (b) What.2007 conducted by GATE Forum in over 25 cities all over India. When 80% of all branch instructions are conditional branch instructions. C = 25) and (B = 33. For more details. C = 46) at S1. (b) The following postfix expression. An instruction pipeline has five stages where each stage takes 2 nanoseconds and all instructions use all five stages. the following instructions can be overlapped. (a) To implement a queue using the above stack implementation.com MOV E. an operation REVERSE.gateforum.gateforum. (i) Find the values in register A when control reaches S2. (ii) Find the values in registers D and E when control reaches S4. (i) After evaluating 5 2 * 3 4 + (ii) After evaluating 5 2 * 3 4 + 5 2 (iii) At the end of evaluation. the branch need not be taken. 99H SUB E MOV E. 13. is evaluated using a stack. in general. and more.gatementor. visit www.com Join discussion of this test paper at http://forum. FFH JMP S4 S3: INC A A DAA MOV E. (a) Calculate the average instruction execution time assuming that 20% of all instruction executed are branch instructions. the instruction after the branch is not fetched till the branch instruction is completed. show how to implement ENQUEUE using a single operation and DEQUEUE using a sequence of 3 operations. Percentile. containing single digit operands and arithmetic operators + and *.com Think GATE Think GATE Forum . interaction with IISc alumni in our online discussion forums. All India Rank. is the value of D and E as a function of B and C when control reaches S4. (b) If a branch instruction is a conditional branch instruction. which reverses the order of the elements on the stack. 12.2000 www. i.e.GATE CS . in addition to PUSH and POP. Suppose a stack implementation supports.. and 50% of the conditional branch instructions are such that the branch is taken. visit www. and a variable count. r. 6: if (m*q – n * p) 0 and (m*s – n * r) 0 then clash : = true.gateforum. is_set (i) will return false. } (a) Suppose we make the following sequence of calls: set (7).2000 www. Join All India Mock GATE Classroom Test Series . 7: if (m*q – n * p) 0 and (m*s – n * r) 0 then clash : = true. p[7]. 5: If (m*s – n * r) 0 then clash : = true. set(9). n.com Join discussion of this test paper at http://forum. that returns true if the line segment with n endpoints (p. p. set (3). and more. 15. 1: function clash (m. by writing the line m number and the content of each box in your answer book. q[2]. 4: if (m*q – n * p) 0 then clash : = true.q) above the line. q [count] = i.GATE CS . q. Consider the following procedures set and iset: set (i) { count = count + 1. After these quence of calls. below the line. p[3] and p[9] contain? (b) Complete the following statement “The first count elements of _______ contain values i such that set ( __________) has been called”.gatementor. initialized to 0. 2: begin 3: clash = false. m (a) If mq – np < 0.N] and q[1…….2007 conducted by GATE Forum in over 25 cities all over India. (c) Show that if set (i) has not been called for some i. Consider the line y = n x.com Think GATE Think GATE Forum . For more details. return true.s) intersects the line y = x. where n and m are positive integers.. then regardless of what p[i] contains. Percentile.N] both uninitialized that is. p[i] = count. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and what do q[1].q) and (r. Suppose you are given arrays p[1…. s: integer): Boolean. q[3]. then is the point (p. if (q[p[i]] ≠i) return false. what is the value of count. interaction with IISc alumni in our online discussion forums. All India Rank.gateforum. or on the line? (b) Complete the following function. } is_set(i) { if (p[i] ≤ 0 or p[i] > count) return false.com 14. 8: end. each location may contain an arbitrary value). visit www.m] with all elements initialized to 0. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. writeln(z) end. All India Rank. var x: integer.2000 www. begin Join All India Mock GATE Classroom Test Series . procedure Q [z:integer). procedure P (y:integer).gateforum.com 16. Assume you are also given an array f[0…. The array is to be sorted using swap operations (elements that are swapped need to be adjacent). program main. 18. fib(n) { if (n > M) error ().GATE CS . Write the box number and the corresponding contents in your answer book.2007 conducted by GATE Forum in over 25 cities all over India. begin z: z + x. For more details. A recursive program to compute Fibonacci numbers is shown below.. (a) What is the minimum number of swaps needed to sort such an array in the worst case? (b) Give an ordering of elements in the above array so that the minimum number of swaps needed to sort the array is maximum. and three occurre3nces of 2 in any order. and more. five occurrences of 1. Q(x). begin x: y + 2. writeln(x) end. Percentile. if ( ) _________________(1) return ____________(2) t = fib(n – 1) + fib (n – 2).com Think GATE Think GATE Forum . (b) What is the time complexity of the resulting program when computing fib(n)? 17. interaction with IISc alumni in our online discussion forums. An array contains four occurrences of 0.gateforum. var x: integer. Consider the following program is pseudo-Pascal syntax. __________(3) return t. } (a) Fill in the boxes with expressions/statements to make fib() store and reuse computed Fibonacci values. if ( n==0) return 1.gatementor. if (n ==1) return 1.com Join discussion of this test paper at http://forum. gateforum. val = F. and their contents in your answer book. i. 20. All India Rank. int R = 0.val = F. (a) Fill in the boxes below to get a solution for the readers-writers problem. val = T. val * T. Join All India Mock GATE Classroom Test Series .gatementor. mutex (initialized to 1) and busy waiting.val = E1. val =4} (a) Using this SDTS. (b) It is required to compute the total number of reductions performed to parse a given input.e.2 and 3).2007 conducted by GATE Forum in over 25 cities all over India. val} T F – T1 {T. visit www. If (W ==0) { R = R +1. Write the box numbers (1. when (a) The parameter passing mechanism is call-by-value and the scope rule is static scooping? (b) The parameter passing mechanism is call-by-reference and the scope rule is dynamic scooping? 19. Q(x). val} T F {T.gateforum.GATE CS . modify the SDTS given. using a single binary semphore. W = 0. construct a parse tree for the expression 4–2–4*2 and also compute its E. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.red. val} F 2 {F. and more. without changing the grammar.2000 www. val – T1. the number of reductions performed while reducing an input to E.val. interaction with IISc alumni in our online discussion forums. Percentile. val =2} F 4 {F.com Think GATE Think GATE Forum .com x:=5. For more details. What is the output of the program. val} E T {E. to find E. Consider the syntax directed translation scheme (SDTS) given in the following. writeln(x) end. Assume attribute evaluation with bottom-up parsing.com Join discussion of this test paper at http://forum. P(x). Reader ( ) { L1: wait (mutex). attributes are evaluated immediately after a reduction.. Using synthesized attributes only. E E1 * T {E. (a) Suppose you are given an empty B+-tree where each node (leaf and internal) can store up to 5 key values. we try to move a value to the left sibling.. Then what approximately is the average number of keys in each leaf level node. Join All India Mock GATE Classroom Test Series . 1. (i) In the normal case. 2. } Writer () { L2: wait(mutex). suppose a B+-tree node can hold a maximum of m keys. (b) Can the above solution lead to starvation of writers? 21. visit www. Percentile. and (ii) After all 10 insertions Do NOT show intermediate stages. (b) Suppose instead of splitting a node when it is full. (c) In general.. and (ii) With the insertion as in (b). in order. and you insert a long sequence of keys in increasing order.….….GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. and more.com Join discussion of this test paper at http://forum. 9 have been inserted. If there is no left sibling.com _______(1) } else { _______(2) goto L1. signal (mutex). signal (mutex).. All India Rank.2007 conducted by GATE Forum in over 25 cities all over India.gateforum. signal (mutex). For more details. as in (a) that each node can hold up to 5 keys.2. Show the tree pictorially (i) After 6 insertions. Show the tree after values.gateforum. Suppose values 1.com Think GATE Think GATE Forum . or the left sibling is full. Assume. 10 are inserted. into the tree. we split the node. If ( ) { ____(3) signal (mutex). goto L2./* do the read */ wait (mutex) R = R – 1./*do the write*/ wait(mutex) W = 0. interaction with IISc alumni in our online discussion forums.gatementor. } …. ….2000 www. } W=1. Assume there is at most one transaction per day on each account.gateforum. Consider a bank database with only one relation transaction (transno.com 22. date. acctno. and more.amount) for every pair of transactions T1. interaction with IISc alumni in our online discussion forums. visit www. For more details. amount) The amount attribute value is positive for deposits and negative for withdrawals.com Join discussion of this test paper at http://forum. Percentile.2000 www.com Think GATE Think GATE Forum .GATE CS . write a query to find for each account the minimum balance it ever reached (not including the 0 balance when the account is created). (acctno. All India Rank. T2.2007 conducted by GATE Forum in over 25 cities all over India. To simply your query.date. T2 such that T1 and T2 are transaction on the same account and the date of T2 is ≤ the date of T1. and each account has had atleast one transaction since it was created. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Join All India Mock GATE Classroom Test Series .gateforum. (a) Define an SQL view TP containing the information. break it up into 2 steps by defining an intermediate view V.gatementor. T1. (b) Using only the above view TP. R2 and R4 are not (c) R1 and R4 are equivalence relations.2007 conducted by GATE Forum in over 25 cities all over India. and more. Do not use the ORS for any rough work. R3 and R4 are not (b) R1 and R3 are equivalence relations. R2 and R3 are not (d) R1. For more details.b) iff |a – b| ≤ 2 over the set of natural numbers Which of the following statements is correct? (a) R1 and R2 are equivalence relations.3 Consider two well-formed formulas in prepositional logic F1: P ⇒ ¬P F2: (P⇒¬P)∨(¬P⇒P) Which of the following statements is correct? 1.com Think GATE Think GATE Forum . B. A. S2 is false (c) S1 is false. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. visit www.GATE CS . This question consists of TWENTY-FIVE sub-questions (1. For each of these sub-questions.25) of ONE mark each. C and D are provided. R2.2 (a) S1 and S2 are both true (b) S1 is true.com SECTION .gatementor. F2 is satisfiable (c) F1 is unsatisfiable.1 – 1. F2 is valid (b) F1 unsatisfiable. interaction with IISc alumni in our online discussion forums. You may use the answer book for any rough work. Do not darken more than one bubble for any sub-question. Which of the following statements is correct? 1. All India Rank.2001 www. S2 is true (d) S1 and S2 are both false Consider the following relations: R1 (a. Choose the most appropriate alternative and darken its bubble on the Objective Response Sheet (ORS) against the corresponding sub-question number using a soft HB pencil.b) iff (a+b) is odd over the set of integers R3 (a.com Join discussion of this test paper at http://forum.A 1.gateforum. if needed.gateforum. Percentile. R3 and R4 are all equivalence relations 1.1 Consider the following statements: S1: The sum of two singular n × n matrices may be non-singular S2: The sum of two n × n non-singular matrices may be singular.4 (a) F1 is satisfiable. F2 is valid (d) F1 and F2 are both satisfiable consider the following two statements: { S2: {0 } S1: 02n n ≥ 1 is a regular language m n m+ n 1 0 } m ≥ 1 and n ≥ 1 is a regular language Which of the following statements is correct? (a) Only S1 is correct (b) Only S2 is correct (c) Both S1 and S2 are correct (d) None of S1 and S2 is correct Join All India Mock GATE Classroom Test Series .b) iff a.b > 0 over the set of non-zero rational numbers R4 (a. four possible alternatives. 1.b) iff (a+b) is even over the set of integers R2 (a. 5 Which of the following statements s true? (a) If a language is context free it can always be accepted by a deterministic push-down automaton (b) The union of two context free languages is context free (c) The intersection of two context free languages is context free (d) The complement of a context free language is context free 1. visit www.com 1. Percentile.8 Which of the following statements is false? (a) Virtual memory implements the translation of a program’s address space into physical memory address space (b) Virtual memory allows each program to exceed the size of the primary memory (c) Virtual memory increases the degree of multiprogramming (d) Virtual memory reduces the context switching overhead 1.GATE CS .10 (b) RESET IN (c) HOLD (d) READY Suppose a processor does not have any stack pointer register.2001 www.9 A low memory can be connected to 8085 by using (a) INTER 1.gateforum. the maximum number of states in an equivalent minimized DFA is at least (a) N2 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.7 (b) 2N (c) 2N (d) N! More than one word are put in one cache block to (a) exploit the temporal locality of reference in a program (b) exploit the spatial locality of reference in a program (c) reduce the miss penalty (d) none of the above 1.2007 conducted by GATE Forum in over 25 cities all over India. interaction with IISc alumni in our online discussion forums.com Join discussion of this test paper at http://forum. For more details.gateforum. but no nested subroutine calls (c) Nested subroutine calls are possible. but interrupts are not (d) All sequences of subroutine calls and also interrupts are possible Join All India Mock GATE Classroom Test Series .6 Given an arbitary non-deterministic finite automaton (NFA) with N states. and more. Which of the following statements is true? (a) It cannot have subroutine call instruction (b) It can have subroutine call instruction.gatementor.com Think GATE Think GATE Forum . All India Rank. 14 Randomized quicksort is an extension of quicksort where the pivot is chosen randomly. which one of the following represents the minimal Sum-Of-Products of the map? wx yz (a) xy + y ′z 1. For the element stored at index i of the array (i≤n). the index of the parent is (a) i-1 (b) i 2 (c) i 2 (d) ( i + 1) 2 Join All India Mock GATE Classroom Test Series . visit www.gateforum. All India Rank.11 Given the following Karnaugh map. Percentile.gateforum.gatementor.GATE CS .com 1.15 (b) O(n log n) (c) O(n2) (d) O(n!) Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of the array. For more details.com Think GATE Think GATE Forum . In order to change the mode from privileged to non-privileged (a) a hardware interrupt is needed (b) a software interrupt is needed (c) a privileged instruction (which does not generate an interrupt) is needed (d) a non-privileged instruction (which does not generate an interrupt is needed 1.13 A CPU has two modes-privileged and non-privileged.12 00 01 11 10 00 0 X 0 X 01 X 1 X 1 11 0 X 1 0 10 0 1 X 0 (b) wx ′y ′ + xy + xz (c) w ′x + y ′z + xy (d) xz+y A processor needs software interrupt to (a) test the interrupt system of the processor (b) implement co-routines (c) obtain system services which need execution of privileged instructions (d) return from subroutine 1.2007 conducted by GATE Forum in over 25 cities all over India. What is the worst case complexity of sorting n numbers using randomized quicksort? (a) O(n) 1.2001 www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums. and more.com Join discussion of this test paper at http://forum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.20 1. r2.21 Consider a set of n tasks with known runtimes r1.22 Which of the following requires a device driver? (a) Register (b) Cache (c) Main memory (d) Disk Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum. interaction with IISc alumni in our online discussion forums.gatementor. Which of the following processor scheduling algorithms will result in the maximum throughput? (a) Round-Robin (b) Shortest-Job-First (c) Highest-Response-Ratio-Next (d) First-Come-First-Served Where does the swap space reside? (a) RAM (b) Disk (c) ROM (d) On-chip cache Consider a virtual memory system with FIFO page replacement policy. All India Rank.18 (a) f(n) = O(g(n) and g(n) ≠O(f(n)) (b) g(n) = O(f(n) and f(n) ≠O(g(n)) (c) f(n)≠O(g(n)) and g(n) ≠O(f(n)) (d) f(n)=O(g(n)) and g(n) =O(f(n)) The process of assigning load addresses to the various parts of the program and adjusting the code and date in the program to reflect the assigned addresses is called (a) Assembly (b) Parsing (c) Relocation (d) Symbol resolution Which of the following statements is false? (a) An unambiguous grammar has same leftmost and rightmost derivation (b) An LL(1) parser is a top-down parser (c) LALR is more powerful than SLR (d) An ambiguous grammar can never be LR(k) for any k 1.2001 www. visit www.com 1. Percentile.com Think GATE Think GATE Forum .gateforum.gateforum.GATE CS .19 1. For more details. rn to be run on a uniprocessor machine. For an arbitrary page access pattern. …. and more. increasing the number of page frames in main memory will (a) always decrease the number of page faults (b) always increase the number of page faults (c) sometimes increase the number of page faults (d) never affect the number of page faults 1. Which of the following statements is correct? 1.16 10 Let f ( n ) = n2 log n and g ( n ) = n (log n ) be two positive functions of n.17 1.2007 conducted by GATE Forum in over 25 cities all over India. Choose the most appropriate alternative and darken its bubble on the Objective Response Sheet (ORS) against the corresponding sub-question number using a soft HB pencil.2001 www.25) of TWO marks each. C such that A∩(B∪C) is finite. All India Rank.25 Let r and s be two relations over the relation schemes R and S respectively.Y).B.B. Percentile.GATE CS . B.com 1. For each of these sub-questions. You may use the answer book for any rough work.2007 conducted by GATE Forum in over 25 cities all over India.gatementor.1 How many 4-digit even numbers have all 4 digits distinct? (a) 2240 2. Then the decomposition of R into R1 (AB) and R2(CD) is (a) dependency preserving and lossless join (b) lossless join but not dependency preserving (c) dependency preserving but not lossless join (d) not dependency preserving and not lossless join 1. C and D are provided. Do not darken more than one bubble for any sub-question.1 – 2.gateforum. Which of the following is true about S1 and S2? (a) Only S1 is correct (b) Only S2 is correct (c) Both S1 and S2 are correct (d) None of S1 and S2 is correct Join All India Mock GATE Classroom Test Series . if needed. For more details.D) and functional dependencies A B and C D.C. Do not use the ORS for any rough work. interaction with IISc alumni in our online discussion forums.com Join discussion of this test paper at http://forum.gateforum. This question consists of TWENTY-FIVE sub-questions (2.2 (b) 2296 (c) 2620 (d) 4536 Consider the following statements: S1: There exists infinite sets A. A. 2. then the relational algebra expression σ A = a (r s) is always equal to (a) σ A = a (r) (c) σ A = a (r) (b) r s (d) None of the above 2.24 Suppose the adjacency relation of vertices in a graph is represented in a table Adj (X.com Think GATE Think GATE Forum . and more. visit www. and let A be an attribute in R.23 Consider a schema R(A. S2: There exists two irrational numbers x and y such that (x+y) is rational. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. four possible alternatives. Which of the following queries cannot be expressed by a relational algebra expression of constant length? (a) List of all vertices adjacent to a given vertex (b) List all vertices which have self loops (c) List all vertices which belong to cycles of less than three vertices (d) List all vertices reachable from a given vertex 1. w R is the reverse of w { } L3 = 02i i is an integer { 2 } L3 = 0i i is an integer Which of the languages are regular? 2. and more. Given a Turing machine M over the input alphabet Σ.GATE CS . and let E and F be subsets of A.gateforum.5 1 (b) 77 1 76 ∑ = {a.4 (a) Only S1 is correct (b) Only S2 is correct (c) Both S1 and S2 are correct (d) None of S1 and S2 is correct Seven (distinct) car accidents occurred in a week.com Think GATE Think GATE Forum . b} *.2001 www.gatementor. does the computation of M on w visit the state q? Which of the following statements about X is correct? (a) X is decidable (b) X is undecidable but partially decidable (c) X is undecidable and not even partially decidable (d) X is not a decision problem Join All India Mock GATE Classroom Test Series . For more details.6 (b) 14 (c) 15 (d) 48 Consider the following languages: { } L1 = ww w ∈ {a. S1:f(E∪F)=f(E) ∪f(F) S2:f(E∩F)=f(E) ∩f(F) Which of the following is true about S1 and S2? 2.7 (a) Only L1 and L2 (b) Only L2. All India Rank. interaction with IISc alumni in our online discussion forums. any state q of M And a word w ∈Σ*.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. b} accepting Consider a DFA over (c) 1 27 (d) 7 27 all strings which have number of a’s divisible by 6 and number of b’s divisible by 8. L3 and L4 (c) Only L3 and L4 (d) Only L3 Consider the following problem X.com Join discussion of this test paper at http://forum. visit www.3 Let f: A B be a function. b} * { } L2 = ww R w ∈ {a.2007 conducted by GATE Forum in over 25 cities all over India. What is the probability that they all occurred on the same day? (a) 2. Percentile. Consider the following statements about images. What is the minimum number of states that the DFA will have? (a) 8 2.com 2. All India Rank.gatementor.9 Which is the most appropriate match for the items in the first column with the items in the second column X. III) (Z. I) (c) (X. Writing re-locatable code Z. II) (b) (X.2001 www.gateforum. III) (Z. For more details. I) (Y.gateforum. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times 0. Indirect Addressing I. Array implementation Y.com 2. Passing array as parameter (a) (X. Base Register Addressing III. I) (d) (X. II) (Y.com Join discussion of this test paper at http://forum.8 Consider the following circuit with initial state Q0 = Q1 = 0. X D1 D0 Clock Q0 Y Q1 Clock C Consider the following timing diagrams of X and C.2007 conducted by GATE Forum in over 25 cities all over India. Indexed Addressing II. visit www. I) (Z. II) (Z. the clock period of C≥40 nanosecond.com Think GATE Think GATE Forum . II) Join All India Mock GATE Classroom Test Series . III) (Y. III) (Y. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile.GATE CS . Which one is the correct plot of Y? C X (a) (b) (c) (d) 2. interaction with IISc alumni in our online discussion forums. The state of the circuit is given by the value 4Q2 + 2Q1 + Q0 D0 Q0 D1 Q1 Q2 D2 LSB MSB Clock Which one of the following is the correct state sequence of the circuit? (a) 1.3.7. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.7.6.7.GATE CS .gateforum.2.2007 conducted by GATE Forum in over 25 cities all over India.11 (b) DBC (c) DE5 (d) 9E7 Consider the circuit shown below. For more details.6.2 (b) 1. Q1 = Q2 = 0.com Join discussion of this test paper at http://forum.5.6.3.4.2001 www.5.com Think GATE Think GATE Forum .4 (c) 1.com 2. and more. a 2:1 MUX 1 0 a g 2:1 MUX f b c b x1 c x2 Which of the following is true? 2.7.12 (a) f = x1′ + x2 (b) f = x1′ x2 + x1x2′ (c) f = x1x2 + x1′ x2′ (d) f = x1 + x2′ Consider the circuit given below with initial state Q0 =1.5.6. Percentile. All India Rank.5. visit www.2.2.gatementor.gateforum.4 Join All India Mock GATE Classroom Test Series .4 (d) 1.3. The output of a 2:1 Mux is given by the function ( ac ′ + bc ) .3. interaction with IISc alumni in our online discussion forums.10 The 2’s complement representation of ( −539 )10 is hexadecimal is (a) ABE 2. where = A or B. A2. The MUX is of size 8 × (2:1) and the DEMUX is of size 8 × (1:2). interaction with IISc alumni in our online discussion forums.GATE CS . visit www.v) (d) None of the above How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1 . which of the following statements is correct? (a) d(r.13 Consider the following data path of a simple non-pilelined CPU. The registers A.com 2. and more.gateforum. If u is visited before v during the breadth-first traversal. K vn } of n vertices? (a) 2. SP and MAR are 16-bit registers.u)<d(r. B. MDR.u)≤d(r.u)>d(r.2001 www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. SP can be decremented locally. Percentile. the bus and the ALU are 8-bit wide.14 2.16 (b) 3 n ( n − 1) 2 n ( n −1) (b) 2n (c) n! (d) 2 2 What is the minimum number of stacks of size n required to implement a queue of size n? (a) One (b) Two (c) Three (d) Four Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum.com Think GATE Think GATE Forum .v) (b) d(r. v2 .gateforum. A1.v) be the lengths of the shortest paths from r to u and v respectively in G. For more details.15 (c) 4 (d) 5 Consider an undirected unweighted graph G. A1 A2 B MUX 1:2 A dcr SP DEMUX 1:2 MAR MDR The CPU instruction “push r”.2007 conducted by GATE Forum in over 25 cities all over India. Let a breadth-first traversal of G be done starting from a node r. Each memory operation takes 2 CPU clock cycles and uses MAR (Memory Address Register) and MDR (Memory Date Register).v) (c) d(r. All India Rank. Let d(r.u) and d(r. has the specification M [SP] r SP SP – 1 How many CPU clock cycles are needed to execute the “push r” instruction? (a) 2 2. z=x+y+z.2007 conducted by GATE Forum in over 25 cities all over India. } func1(x. 7 (d) None of the above Consider the following three C functions: [P1] int*g(void) { intx=10. *px=10. y=3. *px=10. interaction with IISc alumni in our online discussion forums. return px. func1(y.gatementor.z) { y=y+4. } Join All India Mock GATE Classroom Test Series . return(&x). 3 (b) 31.com Think GATE Think GATE Forum . and more.GATE CS .com Join discussion of this test paper at http://forum. Percentile. print y.2001 www. } 2. } [P3] int*g(void) { int*px px =(int*)malloc (size of (int)). All India Rank. } [P2] int*g(void) { int*px.17 What is printed by the print statements in the program P1 assuming call by reference parameter passing? Program P1() { x=10.com 2.18 (a) 10. print x.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.y. return px.x).x. visit www. For more details.gateforum. 3 (c) 27. P2 and P3 Consider the following program Program P2 var n:int: procedure W(var x:int) begin x=x+1. end If the language has dynamic scooping and parameters are passed by reference. interaction with IISc alumni in our online discussion forums. visit www.gateforum. what is the approximate size of the page table? (a) 16 MB (b) 8 MB (c) 2 MB (d) 24 MB Join All India Mock GATE Classroom Test Series . what will be printed by the program? (a) 10 (b) 11 (c) 3 (d) None of the above 2. All India Rank. D. W(n).2007 conducted by GATE Forum in over 25 cities all over India.com Which of the above three functions are likely to cause problems with pointers? 2.20 2.gateforum. printx. For more details.com Join discussion of this test paper at http://forum. n=3.gatementor.19 (a) Only P3 (b) Only P1 and P3 (c) Only P1 and P2 (d) P1. Percentile.com Think GATE Think GATE Forum .2001 www. and more. end procedure D begin var n:int. If the page size is 4KB. End begin \\begin P2 n = 10.21 Which of the following does not interrupt a running process? (a) A device (b) Timer (c) Scheduler process (d) Power failure Consider a machine with 64 MB physical memory and a 32-bit virtual address space. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS . Enter critical section.com Think GATE Think GATE Forum .w) with z > x is deleted Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. then exit critical section Flag[i]=false. while (P) do no-op. Perform other non-critical section actions. C AD (d) A BCD Which of the following relational calculus expressions is not safe? (a) {t ∃u ∈ R (t A = u A ) ∧ ¬∃s ∈ R (b) {t ∀u ∈ R (u A = " x " ⇒ ∃s ∈ R (t A = s A ∧ s A = u A ))} (c) {t ¬ (t ∈ R )} (d) {t ∃u ∈ R (t A = u A ) ∧ ∃s ∈ R 1 2 1 (t A = s A )} 2 1 1 2 (t A = s A )} Consider a relation geq which represents “greater than or equal to”. B C.23 2. (x. create table geq ( Ib integer not null ub integer not null primary key 1b foreign key (ub) references geq on delete cascade ) Which of the following is possible if a tuple (x.gateforum.w) with z > y is deleted (b) A tuple (z. Which of the following does not have a lossless join.22 Consider Peterson’s algorithm for mutual exclusion between two concurrent processes i and j.y)∈ geq only if y≥x.com 2.2001 www. All India Rank. Until false. B CD (b) A B. visit www.com Join discussion of this test paper at http://forum. C D (c) AB C.GATE CS . interaction with IISc alumni in our online discussion forums. dependency preserving BCNF decomposition? (a) A B.y) is deleted? (a) A tuple (z.C. Percentile.24 2.B. repeat flag[i]=true. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. that is.D) is a relation. and more. the predicate P in the while loop should be 2.gateforum. perform actions. turn=j. For more details. The program executed by process is shown below.gatementor.25 (a) flag[j]=true and turn=i (b) flag[j]=true and turn=j (c) flag[i]=true and turn=j (d) flag[i]=true and turn=i R(A. For the program to guarantee mutual exclusion. Join All India Mock GATE Classroom Test Series . { } Give a deterministic PDA for the language L = ancb2n n ≥ 1 over the alphabet = ∑ = {a. give an induction proof to show that the following equation is true for all natural numbers m and n: sum(m+n)=sum(m)+sum(n)+mn 4.2007 conducted by GATE Forum in over 25 cities all over India. b} *.…. Any FIFTEEN out of these questions have to be answered on the Answer Book provided.3. b. 3.gateforum.gatementor. does M loop forever on w? You may assume that the halting problem of Turing machine is undecidable but partially decidable.com Think GATE Think GATE Forum .+n for all natural numbers n. c} . (b) Show that X is not even partially decidable. All India Rank. and more. Specify the acceptance state. Construct DFA’s for the following languages: { } L = {w w ∈ {a. where N ={0.b) = (2a + 1) 2b − 1.gateforum. (a) prove that powerset ( A ∩ B ) = powerset(A)∩powerset(B) (b) Let sum(n)=0+1+2+…. w has an odd number of a's and an odd nuber of b's} (a) L = w w ∈ {a. Consider the function h: N×N N so that h (a. (a) Show that X is undecidable. interaction with IISc alumni in our online discussion forums. Percentile.y) is prohibited SECTION B This section consists of TWENTY questions of FIVE marks each.w) with w < x is deleted (d) The deletion of (x. b} *. Let a decision problem X be defined as follows: X: Given a Turing machine M over Σ and nay word w ∈ Σ. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. (b) Prove that it is also a Subjection (onto) 5.2.com Join discussion of this test paper at http://forum. w has baab as a subsring (b) 6. (a) Prove that the function h is an injection (one-one). 7.com (c) A tuple (z.. visit www.GATE CS .} is the set of natural numbers.1.2001 www. For more details.. rotation speed 3000 rpm.2001 www.gateforum. The cache is organized as a 4-way set associative cache with cache block size of 16 bytes.1. The operating system initiates the transfer between the disk and the memory sector-wise. Excess 3 To BCD b8 b4 b2 b1 A sequential circuit takes an input stream of 0’s and 1’s and produces an output stream of 0’s and 1’s. DMA requests are always granted.com Join discussion of this test paper at http://forum. assume memory read-write time = 0. The read bits are formed into bytes in a serial-in-parallel-out buffer and each byte is then transferred to memory. Once the head has been placed on the right track.GATE CS . An example of input and output stream is shown below. data density 1 KB/sector. For more details. 2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. From then onward. Initially it replicates the input on its output until two consecutive 0’s are encountered on the input. For parts (c) and (d) below. the disk reads a sector in a single scan.com Think GATE Think GATE Forum . 4) its self-dual? Justify your answer. Percentile. 1000 tracks/surface. All India Rank. and more. whereupon the process repeats. Join All India Mock GATE Classroom Test Series . the DMA initialization and termination overhead is negligible compared to the total sector transfer time.gatementor. It reads bits from the sector while the head is passing over the sector. (a) Is the 3-variable function f = ∑ (0.4 microseconds. interrupt driven transfer has an interrupt overhead = 0. interaction with IISc alumni in our online discussion forums.gateforum.1 microsecond/byte. A CPU has 32-bit memory address and a 256 KB cache memory. e8 e4 e2 e1 11. The disk writing is exactly a complementary process. (b) Give a minimal product-of-sum form of the b output of the following excess-3 to BCD converter. it produces an output stream. visit www.com 8. (a) What is the number of sets in the cache? (b) What is the size (in bits) of the tag field per cache block? (c) What is the number and size of comparators required for tag matching? (d) How many address bits are required to find the byte offset within a cache block? (e) What is the total amount of extra memory (in bytes) required for the tag bits? 10. 16 sectors/track. (a) What is the total capacity of the disk? (b) What is the data transfer rate? (c) What is the percentage of time the CPU is required for this disk I/O for bytewise interrupts driven transfer? (d) What is the maximum percentage of time the CPU is held up for this disk I/O for cycle-stealing DMA transfer? 9. which is the bit-wise complement of input stream until it encounters two consecutive 1’s. Consider a disk with following specifications: 20 surface.2007 conducted by GATE Forum in over 25 cities all over India. abc(s+1). For more details. 12. and WB (Write Back). (b) Give the minimized sum-of-product expression for J and K inputs of one of its state flip-flops.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. /* r2 r3 – r4 */ 12: sub r4. 32. Join All India Mock GATE Classroom Test Series . Percentile.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. (a) Give the state transition diagram. 20. visit www. 15. } main() { abc(“123”) } (a) What will be the output of the program? (b) If abc(s) is called with a null-terminated string s of length n characters (not counting the null (‘\0’) character). (c) Can all hazards be avoided by forwarding in this case? 13. interaction with IISc alumni in our online discussion forums.com The input stream: 101100 01001011 0 11 The desired output: 101100 10110100 0 11 J-K master-slave flip-flops are to be used to design the circuit. 100(r1) /* M[r1+100] r2 */ 14: sub r3.gatementor. r3. (a) Insert the following keys one by one into a binary search tree in the order specified.2001 www. Consider the following C program: void abc(char*s) { if(s[0]==’\0’)return.com Join discussion of this test paper at http://forum. and more. how many characters will be printed by abc(s)? 14. (b) Identify the data hazards. r4. r2. r4. /* r4 r2 – r3 */ 13: sw r2.gateforum. 25.s[0]). Consider the execution of the following instruction sequence: 11: sub r2. r3. abc(s+1). EX (Execute). 9. r2. 12. Consider a 5-stage pipeline – IF (Instruction Fetch). /* r3 r4 – r2 */ (a) Show all data dependencies between the four instructions. 3. 1 Show the final binary search tree after the insertions. MEM (memory). ID (Instruction Decode and register read). printf(“%c”.gateforum. All (memory or register) reads take place in the second phase of a clock cycle and writes occur in the first phase of the clock cycle. All India Rank. n5.gateforum. } *Tree.n5.9). The production rules of the grammar are: E aA E (E) A +E A *E Aε (a) Compute the FIRST and FOLLOW sets for E and A.n4.2).com (b) Draw the binary search tree after deleting 15 from it. (n4.4)}.n4. } 15.(n2.y. S2: if(x>y) return _____________: S3: else return _____________. it (t ==NULL) return0. +.(n2.(n1. Consider the following grammar with terminal alphabet ∑ {a.(.n2.n5.gateforum. struct tnode *left. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.(n1.7). ). (b) How many distinct minimum spanning trees does this graph have? (c) Is the minimum among the edge weights of a minimum spanning tree unique overall possible minimum spanning trees of a graph? (d) Is the maximum among the edge weights of a minimum spanning tree unique over all possible minimum spanning trees of a graph? 16.gatementor.n3.n6.(n3.4). Percentile. All India Rank.8).n6} and edge set E={(n1. x=depth(t left).12).n6. (c) Complete the statements S1.n3.2001 www.GATE CS .3). For more details. *right. (a) List the edges of a minimum spanning tree of the graph.com Think GATE Think GATE Forum .(n4.n2.n4.com Join discussion of this test paper at http://forum.2007 conducted by GATE Forum in over 25 cities all over India. *} and start symbol E. S1: ____________. (b) Complete the LL(1) parse table for the grammar. and more. int depth(Tree t) { int x. visit www. Consider a weighted undirected graph with vertex set V = {n1. typedef struct tnode{ int key. The third value in each tuple represents the weight of the edge specified in the tuple. S2 and S3 in the following function so that the function computes the depth of a binary rooted at t. Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums. com Think GATE Think GATE Forum . Assume that you can call a function newlabel( ) that returns a distinct label for a statement. Use the operator ‘\\’ to concatenate two strings and the function gen(s) to generate a line containing the string s.com 17. The non-terminals S and S1 have an attribute code that represents generated code. Is the grammar ambiguous? 19.GATE CS . S6: Set R1 free. S7: Set R2 free. Q7: Set R1 free. The programs executed by the two processes are given below. S2: Set R1 busy. (a) Remove left-recursion from the following grammar: S Sa| Sb | a | b (b) Consider the following grammar: S aSbS| bSaS |ε Construct all possible parse trees for the string abab. S and S1 stand for statement.gatementor. Q2: Set R1 busy.gateforum. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Join discussion of this test paper at http://forum. Program for P2: Q1: While (R1 is busy) do no-op. visit www. R1 and R2 are free. Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. and the attribute varName contains the name of the variable in which the truth value is stored? The truth-value stored in the variable is 1 if E is true. 0 if E is false. All India Rank. Percentile. S3: While (R2 is busy) do no-op. Program for P1: S1: While (R1 is busy) do no-op. The syntax of the repeat-until statement is given by the following grammar S repeat S1 until E Where E stands for expressions. Two concurrent processes P1 and P2 want to use two resources R1 and R2 in a mutually exclusive manner. The attribute code represents generated code to evaluate the expression and store its truth value in a distinct variable. and more. S5: Use R1 and R2.gateforum. Q6: Set R2 free. For more details. Initially. Q4: Set R1 busy. Q5: Use R1 and R2. S4: Set R2 busy. 18. interaction with IISc alumni in our online discussion forums. The nonterminal E has two attributes. Q3: While (R1 is busy) do no-op.2001 www. Give a syntax-directed definition to generate three-address code for the repeatuntil statement. 50. (b) Can deadlock occur in the above program? If yes.2001 www. Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum. Write an SQL query to list the centr_code having an examinee of score greater than 80. For more details.σ. The number of sectors per track is 100. 7. after insertion of 30. name. 22. We wish to construct a B+ tree with fan-out (the number of pointers per node) equal to 3 for the following set of key values: 80. 90 Assume that the tree is initially empty and the values are added in the order given. interaction with IISc alumni in our online discussion forums. 70.gatementor. (a) Consider a set of disk requests to read data from tracks 32.2007 conducted by GATE Forum in over 25 cities all over India. Percentile. and the head is initially at track 25 moving up (towards larger track numbers).e. 5 and 10. (c) Suppose the relation appears (regno. score). visit www. (b) The key values 30 and 10 are now deleted from the tree in that order. the time to move the head between two successive tracks is 0. (c) Exchange the statements Q1 and Q3 and statements Q2 and Q4. what is the worst case time to complete all the requests? 21.. Is mutual exclusion guaranteed now? Can deadlock occur? 20. 45. both P1 and P2 use R1 or R2 at the same time). Show the tree after each deletion. what is the total seek time for servicing the requests? (b) Consider an initial set of 100 arbitrary disk requests and assume that no new disk requests arrive while servicing these requests. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.GATE CS .com (a) Is mutual exclusion guaranteed for R1 and R2? If not. 10. (b) Write an SQL query to list the regno of examinees who have a score greater than the average score. Intermediate trees need not be shown.gateforum. where regno is the primary key to score is a real number. Assuming that the elevator algorithm is used to schedule disk requests. All India Rank. centr_code) specifies the center where an examinee appears.2 millisecond. 30. show a possible interleaving of the statements of P1 and P2 leading to deadlock.×) to find the list of names which appear more than once in examinee. Consider a disk with the 100 tracks numbered from 0 to 99 rotating at 3000 rpm.com Think GATE Think GATE Forum . and more. (a) Write a relational algebra using (∏.gateforum. 100. show a possible interleaving of the statements of P1 and P2 such that mutual exclusion is violated (i. and after insertion of 90.ρ. Consider the relation examinee (regno. (a) Show the tree after insertion of 10. If the head is initially at track 0 and the elevator algorithm is used to schedule disk requests. (b) The set of all non-singular matrices forms a group under multiplication. the number of comparisons needed to search a singly linked list of length n for a given element is (a) log n 1. For each of these sub-questions. 1 1 The rank of the matrix is 0 0 (a) 4 1. Do not use the ORS for any rough work. All India Rank. T (1) = 1 is k +1 1.6 ( (d) 2 The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is (a) 2 1.4 (d) 0 The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree (a) 0 but not 1 1. Percentile.25) of ONE mark each.2007 conducted by GATE Forum in over 25 cities all over India. four possible alternatives.2 (b) 2 (b) 1 but not 0 ( ) (a) 2 k ) (3 (b) 2 −1 ) k (c) 3log2 k (d) 2log3 (b) 3 (c) 4 n (d) n − 2 + 2 2 In the worst case. B. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum.7 The language accepted by a Pushdown Automaton in which the stack is limited to 10 items is best described as (a) Context free (b) Regular (c) Deterministic Context free (d) Recursive Join All India Mock GATE Classroom Test Series .com SECTION A 1.3 (c) 1 (b) n 2 (c) log2n − 1 (d) n Which of the following is true? (a) The set of all rational negative numbers forms a group under multiplication. A.gateforum. For more details.1 – 1. 1. interaction with IISc alumni in our online discussion forums.com Think GATE Think GATE Forum . (c) The set of all matrices forms a group under multiplication. Do not darken more than one bubble for any sub-question. (d) Both B and C are true.gatementor.com Join discussion of this test paper at http://forum.1995 www. You may use the answer book (last few pages) for any rough work. C and D are provided. visit www. and more. Choose the most appropriate alternative and darken its bubble on the Objective Response Sheet (ORS) against the corresponding sub-question number using a soft HB pencil.GATE CS .1 This question consists of TWENTY-FIVE sub-questions (1.5 (c) 0 or 1 The solution to the recurrence equation T 2k = 3T 2k −1 + 1. 1. x.9 1.10 1.com Think GATE Think GATE Forum . and “” is implication) (a) (X∧¬Z)Y 1.11 (b) (X∧Y)¬Z (c) X(Y∧¬Z) (d) (XY)∧¬Z A device employing INTR line for device interrupt puts the CALL instruction on the data bus while (a) INTA is active (b) HOLD is active (c) READY is active (d) None of the above In 8085 which of the following modifies the program counter? (a) Only PCHL instruction (b) Only ADD instructions (c) Only JMP and CALL instructions (d) All instructions In serial data transmission.z) shown in Karnaugh-map below is wx 00 yz 1. interaction with IISc alumni in our online discussion forums.gatementor.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India.com Join discussion of this test paper at http://forum.13 01 11 10 00 0 1 1 0 01 x 0 0 1 11 x 0 0 1 10 0 1 1 x (a) xz + y ′z (b) xz ′ + zx ′ (c) x ′y + zx ′ (d) None of the above Which of the following is not a form of memory? (a) instruction cache (b) instruction register (c) instruction opcode (d) translation look-a-side buffer Join All India Mock GATE Classroom Test Series . “∧” is conjunction. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. visit www.12 Minimum sum of product expression for f(w. Percentile.gateforum.com 1.y. All India Rank. For more details. and more. is negation.1995 www.8 “If X then Y unless Z” is represented by which of the following formulas in prepositional logic? (“ ¬ “. every byte of data is padded with a ‘0’ in the beginning and one or two ‘1’s at the end of byte because (a) Receiver is to be synchronized for byte reception (b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits (c) Padded bits are useful in parity computation (d) None of the above 1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.18 The results returned by function under value-result and reference parameter passing conventions (a) Do not differ (b) Differ in the presence of loops (c) Differ in all cases (d) May differ in the presence of exception 1.gateforum. F.15 The 2’s complement representation of the decimal value –15 is (a) 1111 1. All India Rank. and more. For more details. (d) Recursion requires the activation record for the recursive function to be saved on a different stack before the recursive fraction can be called.gateforum.GATE CS .1 (b) is equivalent to the binary value 0.00111… (d) cannot be represented precisely in binary 1. is decomposed into BCNF.14 The decimal value 0. visit www.16 (b) 11111 (c) 111111 (d) 10001 Sign extension is a step in (a) floating point multiplication (b) signed 16 bit integer addition (c) arithmetic left shift (d) converting a signed integer from one size to another 1. interaction with IISc alumni in our online discussion forums. (c) The visibility of global variables depends on the actual function calling sequence.com Think GATE Think GATE Forum . The redundancy (arising out of functional dependencies) in the resulting set of relations is (a) Zero (b) More than zero but less than that of an equivalent 3NF decomposition (c) Proportional to the size of F+ (d) Indetermine Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. 1.gatementor.com 1.1995 www.19 Relation R with an associated set of functional dependencies. Percentile.com Join discussion of this test paper at http://forum.17 In the C language (a) At most one activation record exists between the current activation record and the activation record for the main (b) The number of activation records between the current activation record and the activation record fro the main depends on the actual function calling sequence.25 (a) is equivalent to the binary value 0.01 (c) is equivalent to the binary value 0. 25 Maximum number of edges in a n-node undirected graph without self loops is (a) n2 2.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor. Join All India Mock GATE Classroom Test Series . four possible alternatives. All India Rank.gateforum. (b) n ( n − 1) 2 (c) n .21 In 2’s complement addition. Choose the most appropriate alternative and darken its bubble on the Objective Response Sheet (ORS) against the corresponding sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. (d) Has been used most number of times.23 The optimal page replacement algorithm will select the page that (a) Has not been used for the longest time in the past. overflow (a) is flagged whenever there is carry from sign bit addition (b) cannot occur when a positive value is added to a negative value (c) is flagged when the carries from sign bit and previous bit match (d) None of the above 1. Do not use the ORS for any rough work.1995 www.com Join discussion of this test paper at http://forum. and more. B. A. (d) None of the above 1.1 – 2. For more details. (b) Will not be used for the longest time in the future. (c) Has been used least number of times.20 With regard to the expressive power of the formal relational query languages. C and D are provided. 1.com 1. interaction with IISc alumni in our online discussion forums. which of the following statements is true? (a) Relational algebra is more powerful than relational calculus (b) Relational algebra has the same power as relational calculus. For each of these sub-questions.1 (d) ( n + 1) ( n ) 2 This question consists of TWENTY-FIVE sub-questions (2.25) of TWO marks each.gateforum.24 In the absolute addressing mode (a) the operand is inside the instruction (b) the address of the operand is inside the instruction (c) the register containing the address of the operand is specified inside the instruction (d) the location of the operand is implicit 1. Percentile. (c) Relational algebra has the same power as safe relational calculus.2007 conducted by GATE Forum in over 25 cities all over India. visit www. You may use the answer book (last few pages) for any rough work.com Think GATE Think GATE Forum .22 Which of the following scheduling algorithms is non-preemptive? (a) Round Robin (b) First-In First-Out (c) Multilevel Queue Scheduling (d) Multilevel Queue Scheduling with Feedback 1. 2 ∑ (1.1 Consider the following logic circuit whose inputs are functions f1.com 2. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. f3 and output is f.3 (a) xyz ′ (b) xy+z (c) x+y (d) None of the above ( ) Let f(A. Percentile. 7) (d) None of the above Consider the following multiplexor where 10.10. y .y.y. y .1.5) . 11.com Think GATE Think GATE Forum . and f ( x.B) = A′ + B. All India Rank.y. f2.com Join discussion of this test paper at http://forum. f1(x.5) ∑ (0.GATE CS .y.y. and more. z ) = ∑ ( 6. f1 ( x.gateforum.1995 www. z ) = ∑ (1. 12. EN is the Enable input.z) implemented by the above circuit is 2.gatementor. Simplified expression for function f f ( x + y . z is (a) x ′ + z (b) xyz (c) xy ′ + z (d) None of the above Join All India Mock GATE Classroom Test Series . 4.2007 conducted by GATE Forum in over 25 cities all over India.z)=? Given that ∑ (0.11 respectively and f is the output of the multiplexor. interaction with IISc alumni in our online discussion forums. f ( x. 7 ) .5) (b) ∑ (6. y ) .gateforum. 3. 3.1.z) f3(x.z) f2(x. y .z)=? OUTPUT The function f(x.y. 10 11 12 13 A1 A0 EN 4 TO 1 multiplexor f(x.z) f(x.01.5) . 13 are four data input lines selected by two address line combinations A1A0 =00. z ) = 2 f3 is (a) (c) 2. visit www. For more details. 4. gateforum. interaction with IISc alumni in our online discussion forums. where an arc label is and x stands for 1-bit input and y stands y for 2-bit output 0/01 A 1/01 B 1/10 C 1/10 0/00 0/01 (a) Outputs the sum of the present and the previous bits of the input. Assuming that the main memory is byte-addressable and that the array is stored starting from memory address 0.8 Consider the following declaration of a two-dimensional array in C: char a[100][100]. All India Rank.6 The performance of a pipelined processor suffers if (a) the pipeline stages have different delays (b) consecutive instructions are dependent on each other (c) the pipeline stages share hardware resources (d) All of the above 2.4 2.com Think GATE Think GATE Forum .5 What are the states of the Auxillary Carry (AC) and Carry Flag (CY) after executing the following 8085 program? MVI H. the address of a [40][50] is (a) 4040 (b) 4050 (c) 5040 (d) 5050 Join All India Mock GATE Classroom Test Series .GATE CS .com Join discussion of this test paper at http://forum. (b) Outputs 01 whenever the input sequence contains 11 (c) Outputs 00 whenever the input sequence contains 10 (d) None of the above 2.2007 conducted by GATE Forum in over 25 cities all over India.7 Horizontal microprogramming (a) does not require use of signal decoders (b) results in larger sized microinstructions than vertical microprogramming (c) uses one bit for each control signal (d) all of the above 2. For more details.gatementor. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.1995 www. H ADD L (a) AC = 0 and CY =0 (b) AC = 1 and CY =1 (c) AC = 1 and CY =0 (d) AC = 0 and CY =1 The finite state machine described by the following state diagram with A as x starting state.com 2. 5DH MIV L. visit www. 6BH MOV A. Percentile.gateforum. 13 The smallest finite automaton 2 which accepts the language {x length of x is divisible by 3} has (a) 2 states 2. the number of nodes in the let sub tree is at least half and at most twice the number of nodes in the right sub tree. For more details. (b) The complement of a recursively enumerable language is recursively enumerable.. what is the expected number of comparisons made by the algorithm before it terminates? (a) n 2..gateforum.9 The number of leaf nodes in a rooted tree of n nodes. visit www.2007 conducted by GATE Forum in over 25 cities all over India. Assuming that x is present A. If A[i]=x then Stop else Goto 1.14 (b) 3 states (c) 4 states (d) 5 states Which of the following is true? (a) The complement of a recursive language is recursive. All India Rank.n] having n distinct values: 1. and more.com 2.gatementor. Is best described by (a) O(n) 2.12 (b) O(log n) (c) O(log log n) (d) O(1) A weight-balanced tree is a binary tree in which for each node.1 (c) 2n (d) n 2 The running time of the following algorithm Procedure A(n) If n<=2 return(1) else return (A( n )).GATE CS .11 (b) n . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. interaction with IISc alumni in our online discussion forums. Choose an i uniformly at random from l. (d) The complement of a context-free language is context-free Join All India Mock GATE Classroom Test Series . (c) The complement of a recursive language is either recursive or recursively enumerable.nl 2.com Think GATE Think GATE Forum . Percentile.1995 www.gateforum.com Join discussion of this test paper at http://forum. The maximum possible height (number of nodes on the path from the root to the furthest leaf) of such a tree on n nodes is best described by which of the following? (a) log2n (b) log 4 n (d) log3 n (c) log3n 3 2.10 n 2 (b) ( n − 1) 3 (c) ( n − 1) 2 (d) (2n + 1) 3 Consider the following algorithm for searching for a given number x in an unsorted array A[l. with each node having 0 or 3 children is: (a) 2. com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gatementor.com 2.15 2.GATE CS . Percentile.20 Dynamic linking can cause security concerns because (a) Security is dynamic (b) The path for searching dynamic libraries is not known till runtime (c) Linking is insecure (d) Cryptographic procedures are not available for dynamic linking 2. For more details. interaction with IISc alumni in our online discussion forums.gateforum.17 (b) X 3 = 3 1 16 (b) 1 8 (c) 7 8 (d) 15 16 The binary relation S = φ (empty set) on set A = {1.2. visit www.3} is (a) Neither reflexive nor symmetric (b) Symmetric and reflexive (c) Transitive and reflexive (d) Transitive and symmetric The C language is: (a) A context free language (b) A context sensitive language (c) A regular language (d) Parsable fully only by a Turing machine 2.1995 www. (C) If the execution of a program terminates. (B) If a program waits for certain events such as I/O. (a) A (b) A and B (c) A and C (d) A. another program is immediately scheduled for execution. All India Rank.21 Which combination of the following features will suffice to characterize an OS as a multi-programmed OS? (A) More than one program may be loaded into main memory at the same time for execution. and more. another program is immediately scheduled for execution.19 To evaluate an expression without any embedded function calls (a) One stack is enough (b) Two stacks are needed (c) As many stacks as the height of the expression tree are needed (d) A Turning machine is needed in the general case 2.2007 conducted by GATE Forum in over 25 cities all over India. The probability that at least one head and one tail turn up is (a) 2.18 (d) X 3 = 2 Four fair coins are tossed simultaneously. B and C Join All India Mock GATE Classroom Test Series .com Join discussion of this test paper at http://forum.16 X The Newton-Raphson iteration X n +1 = n 2 equation 3 can be used to solve the + (2 X n ) (a) X 2 = 3 (c) X 2 = 2 2.gateforum. com Think GATE Think GATE Forum .gateforum. the number of pointers per node) of the B+ tree? (a) 16 2. the number of blocks used for the index. Percentile. (c) the size of the blocks.22 In the index allocation scheme of blocks to a file.com Join discussion of this test paper at http://forum. To make a guaranteed identification. For more details. Given this scenario. visit www. (a) Dependency-preservation (b) Lossless-join (c) BCNF definition (d) 3NF definition From the following instance of a relation schema R(A. Assume that all student names are of length 8 bytes. G.e. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. and relation S is decomposed using another set of functional dependencies. One decomposition is definitely BCNF. but it is not known which is which.C). interaction with IISc alumni in our online discussion forums. and the size of the blocks.GATE CS .2007 conducted by GATE Forum in over 25 cities all over India. (d) None of the above 2. and index pointers are of size 4 bytes. (b) the number of blocks used for the index. and the size of the address of the blocks. the other is definitely. the maximum possible size of the file depends on (a) the size of the blocks. 3NF. and the size of the address of the blocks. All India Rank.B.com 2. we can conclude that: A B C 1 1 1 1 1 0 2 3 2 2 3 2 (a) A functionally determines B and B functionally determines C (b) A functionally determines B and B does not functionally determines C (c) B does not functionally determines C (d) A does not functionally determines B and B does not functionally determines C Join All India Mock GATE Classroom Test Series .23 A B+ . what would be the best choice of the degree (i.tree index is to be built on the Name attribute of the relation STUDENT. disk blocks are of size 512 bytes. F. which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available).gatementor.1995 www.24 2. and more.25 (b) 42 (c) 43 (d) 44 Relation R is decomposed using a set of functional dependencies. Consider the binary relation ‘⊆ (set inclusion)’ on (S). Join All India Mock GATE Classroom Test Series . (a) Obtain the eigen values of the matrix 1 0 A= 0 0 49 2 43 94 0 −2 104 0 0 −1 2 34 (b) Determine whether each of the following is a tautology.1995 www. Is it irreflexive? Add the minimum number of ordered pairs to S to make it an equivalence relation. “¬” in negation.GATE CS . 2. Let A be a set of n(>0) elements.⊆) 5.gatementor. Draw the logic circuit implementing the expression obtained.2.3}. interaction with IISc alumni in our online discussion forums. 3. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. z ) = xy ′ + yz ′ with only one complement operation and one or more AND/OR operations. Draw all binary trees having exactly three nodes labeled A. (a) Give the expression for Nr in terms of n. 7.com Think GATE Think GATE Forum . For more details.com SECTION B This section consists of TWENTY questions of FIVE marks each. (a) S = { 1.gateforum.b} and let (S) be the powerset of S. and more.com Join discussion of this test paper at http://forum. Any FIFTEEN out of these questions have to be answered on the Answer Book provided. and “↔” is biconditional (if and only if).1 is binary relation on set A = {1. (a) Express the function f ( x. (b) Let S = {a. B and C on which Preorder traversal gives the sequence C. Let Nr be the number of binary relations on A and let Nf be the number of functions from A to A. (c) Which is larger for all possible n. y . Percentile. All India Rank. 2 } . “∧” is conjunction. “→” is implication.A. Nr or Nf? 4. (i) A ↔ ( A ∨ A) (ii) ( A ∨ B) → B A ∧ (¬ ( A ∨ B ) (iii) 6. visit www. Draw the Hasse diagram corresponding to the lattice ((S). a contradiction. Give the modified S.B.gateforum. (b) Give the expression for Nf in terms of n. or neither (“∨” is disjunction. using a single NOT gate and one or more AND/OR gates.2007 conducted by GATE Forum in over 25 cities all over India. and more. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Consider the following circuit.1995 www. A= 110 011 111 101 000 000 000 000 B= 101 101 011 110 000 000 000 000 Clock No 1 2 3 4 5 6 7 8 (b) What does the circuit implement? Join All India Mock GATE Classroom Test Series . For more details.com Think GATE Think GATE Forum . visit www. R0. A REG R0 (6 – bit) b2 B a2 a1 b1 b0 CLOCK a0 0 EA REG R1 (6 – bit) b2 a2 a1 b1 EA REG R2 (5 – bit) b2 a2 EA z0 z1 z2 Z=z3 (a) For 8 clocks pulses on the CLOCK terminal and the inputs A. Percentile.com (b) Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that employs only 6 NAND gates each with 2-inputs.2007 conducted by GATE Forum in over 25 cities all over India. R1 and R2 are registers with loading clock shown. B and the full adders are as shown in the circuit. Assume Clock period is greater than the settling time of all circuits. The bits of input number A.com Join discussion of this test paper at http://forum. obtain the output Z (sequence of 4-bit values of Z).gateforum.gateforum. The registers are loaded with their input data with the falling edge of a clock pulse (signal CLOCK shown) and appears as shown. 8. interaction with IISc alumni in our online discussion forums. Assume initial contents of R0. The output is Z = z3z2z1z0. R1 and R2 as all zeros. A = a2a1a0 and B = b2b1b0 are three bit binary numbers input to the circuit. All India Rank.GATE CS . B as shown.gatementor. visit www. and more. 1 24 ? sign fraction exponent (a) It is required to represent the decimal value –7.com 9.GATE CS . starting with the last element and ending with the first element.2007 conducted by GATE Forum in over 25 cities all over India. char C) { if (………………………………….gateforum. interaction with IISc alumni in our online discussion forums. The sign bit is the most significant bit. printf(“Move disk %d from pole %c to pole %c\n”. an array is declared as float A[2048]. (b) If the program accesses the elements of this array one by one in reverse order i.gateforum.. how many data cache misses would occur? Justify your answer briefly. Join All India Mock GATE Classroom Test Series . Percentile. and the starting address of the array is 0×00000000. n.C). 10. Express your final answer in the hexadecimal. In a C program. Consider the following 32-bit floating-point representation scheme as shown in the formal below.e. (a) Which elements of the array conflict with element A[0] in the data cache? Justify your answer briefly. move (…………………………………. Derive the values of the various fields.) { move (………………………………….com Join discussion of this test paper at http://forum. a 24 bit fraction field (with the binary point being at the left end of the fraction bits). Each array element is 4 Bytes in size.). The following recursive function in C is a solution to the Towers of Hanoi problem. Void move (int n.1995 www. A. Fill in the dotted parts of the solution. with 16 being the base of exponentiation). For more details. All India Rank. 11. (b) What is the largest values that can be represented using this format? Express your answer as the nearest power of 10.com Think GATE Think GATE Forum . char B. A value is specified by 3 fields. a one bit sign field (with 0 for positive and 1 for negative values). with block (line) size of 16 Bytes. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. This program is run on a computer that has a direct mapped data cache of size 8 Kbytes. and a 7 bit exponent field (in excess-64 signed integer representation. char A.gatementor.5 as a normalized floating point number in the given format. Assume that the data cache is initially empty and that no other data or instruction accesses are to be considered.). GATE CS - 1995 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 12. Fill in the blanks in the following template of an algorithm to compute all pairs shortest path lengths in a directed graph G with n*n adjacency matrix A. A[i,j]equals if there is an edge in G from i to j, and 0 otherwise. Your aim in filling in the blanks is to ensure that the algorithm is correct. INITIALIZATION: For i = 1 … n {For j = 1 … n { if A[i,j]=0 then P[i,j] = _______ else P[i,j] =____;} ALGORITHM: For i = 1 …n { For j = 1 …n {For k = 1 …n {P[__,___]=min{_______,_______};} } } (a) Copy the complete line containing the blanks in the Initialization step and fill in the blanks. (b) Copy the complete line containing the blanks in the Algorithm step and fill in the blanks. (c) Fill in the blank: The running time of the Algorithm is O(____). 13. (a) In how many ways can a given positive integer n ≥ 2 be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for n = 3, the number of ways is 2, i.e., 1+2, 2+1. Give only the answer without any explanation. (b) In how many ways can a given positive integer n ≥ 3 be expressed as the sum of 3 positive integers (which are not necessarily distinct). For example, for n = 4, the number of ways is 3, i.e., 1+2+1, 2+1+1. Give only the answer without any explanation. (c) In how many ways can a given positive integer n ≥ k be expressed as the sum of k positive integers (which are not necessarily distinct)? Give only the answer without explanation. 14. The aim of the following question is to prove that the language {M | M is the code of a Turing Machine which, irrespective of the input, halts and outputs a 1}, is undecidable. This is to be done by reducing form the language M ′, x M ′ halts on x , which is known to be undecidable. In parts (a) and (b) { } describe the 2 main steps in the construction of M. in part (c) describe the key propery which relates the behaviour of M on its input w to the behaviour of M ′ on x. (a) On input w, what is the first step that M must make? (b) On input w, based on the outcome of the first step, what is the second step that M must make? (c) What key property relates the behaviour of M on w to the behaviour of M ′ on x? Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1995 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 15. A university placement center maintains a relational database of companies that interview students on campus and make job offers to those successful in the interview. The schema of the database is given below: COMPANY (cname, clocation) STUDENT (scrollno, sname, sdegree) INTERVIEW (cname, srollno, idate) OFFER (cname,srollno, osalary) The COMPANY relation gives the name and location of the company. The STUDENT relation gives the student’s roll number, name and the degree program for which the student is registered in the university. The INTERVIEW relation gives the date on which a students is interviewed by a company. The OFFER relation gives the salary offered to a student who is successful in a company’s interview. The key for each relation is indicated by the underlined attributes. (a) Write relational algebra expressions (using only the operator for the following queries: ,σ,π,∪,− ) (i) List the rollnumbers and names of those students who attended at least one interview but did not receive any job offer. (ii) List the rollnumbers and names of students who went for interviews and received job offers from every company with which they interviewed. (b) Write an SQL query to list, for each degree program in which more than five students were offered jobs, the name of the degree and the average offered salary of students in this degree program. 16. For relation R = (L, M, N , O, P), the following dependencies hold: M O NO P P L and L MN R is decomposed into R1 =(L, M, N , P) and R2 = (M, O). (a) Is the above decomposition a lossless-join decomposition? Explain. (b) Is the above decomposition dependency-preserving? If not, list all the dependencies that are not preserved. (c) What is the highest normal form satisfied by the above decomposition? 17. (a) The following table refers to search times for a key in B-trees and B+-trees. B+-tree B-tree Successful Search Unsuccessful search Successful Search Unsuccessful search X1 X2 X3 X4 A successful search means that the key exists in the database and unsuccessful means that it is not present in the database. Each of the entries X1, X2, X3 and X4 can have a value of either Constant or Variable. Constant means that the search time is the same, independent of the specific key value, where Variable means that it is dependent on the specific key value chosen for the search. Give the correct values for the entries X1, X2, X3 and X4 (for example X1 = Constant, X2= Constant, X3 = Constant, X4= Constant). Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1995 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com (b) Relation R(A,B) has the following view defined on it: CREATE VIEW V AS (SELECT R1.A,R2.B FROM R AS R1, R AS R2 WHERE R1.B=R2.A) (i) The current contents of relation R are shown below. What are the contents of the view V? A B 1 2 2 3 2 4 4 5 6 7 6 8 9 10 (ii) The tuples (2,11) and (11,6) are now inserted into R. What are the additional tupels that are inserted in V? 18. (a) Draw the process state transition diagram of an OS in which (i) each process is in one of the five states: created, ready, running, blocked (i.e. sleep or wait), or terminated, and (ii) only non-preemptive scheduling is used by the OS. Label the transitions appropriately. (b) The functionality of atomic TEST-AND-SET assembly language instruction is given by the following C function. int TEST-AND-SET (int *x) { int y; A1:y=*x; A2:*x=1; A3:return y; } (i) Complete the following C functions for implementing code for entering and leaving critical sections based on the above TEST-AND-SET instruction. int mutex=0; void enter-cs() { while (…………………………………); } Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1995 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com void leave-cs() { …………………………………..; } (ii) Is the above solution to the critical section problem deadlock free and starvation-free? (iii) For the above solution, show by an example that mutual exclusion is not ensured if TEST-AND-SET instruction is not atomic. 19. A computer system uses 32-bit virtual address, and 32-bit physical address. The physical memory is byte addressable, and the page size is 4 kbytes. It is decided to use two level page tables to translate from virtual address to physical address. Equal number of bits should be used for indexing first level and second level page table, and the size of each page table entry is 4 bytes. (a) Give a diagram showing how a virtual address would be translated to a physical address. (b) What is the number of page table entries that can be contained in each page? (c) How many bits are available for storing protection and other information in each page table entry? 20. The following solution to the single producer single consumer problem uses semaphores for synchronization. #define BUFFSIZE 100 buffer buf[BUFFSIZE]; int first=last=0; semaphore b_full=0; semaphore b_empty=BUFFSIZE; void producer() { while (1) { produce an item; p1: …………………..; put the item into buff (first); first=(first+1)%BUFFSIZE; p2: …………………..; } } void consumer() { Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 1995 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com while (1) { c1:…………………….. take the item from buf[last]; last=(last+1)%BUFFSIZE; c2: ……………………..; consume the item; } } (a) Complete the dotted part of the above solution. (b) Using another semaphore variable, insert one line statement each immediately after p1, immediately before p2, immediately after c1, and immediately before c2 so that the program works correctly for multiple procedures and consumers. 21. We require a four state automaton to recognize the regular expression ( a b ) * abb. (a) Give an NFA for this purpose. (b) Give a DFA for this purpose. 22. (a) Construct all the parse trees corresponding to i + j * k for the grammar E E+E E E*E E id (b) In this grammar, what is the precedence of the two operators * and +? (c) If only one parse tree is desired for any string in the same language, what changes are to be made so that the resulting LALR(1) grammar is nonambiguous? Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 2003 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com Q.1 — Q.30 carry one mark each. 1. Consider the following C function. float f,(float x, int y) { float p, s; int i; for (s=1,p=1,i=1; i<y; i++) { p *= x/i; s+=p; } return s; } For large values of y, the return value of the function f best approximates (A) X y 2. (B) ex (C) ln(1+x) (D) X x III. B[1] IV. B[2][3] Assume the following C variable declaration int * A[10], B[10][10]; Of the following expressions I. A[2] II. A[2][3] which will not give compile-time errors if used as left hand sides of assignment statements in a C program? 3. (A) I,II, and IV only (B) II, III, and IV only (C) II and IV only (D) IV only Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1 , the 2 values of P(A|B) and P(B|A) respectively are (A) 4. 1 1 , 4 2 1 1 , 2 4 (C) 1 ,1 2 (D) 1, 1 2 Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A? (A) 2 5. (B) (B) 30 (C) 56 (D) 256 n couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is 2n (A) * 2n n (B) 3n (C) ( 2n ) ! 2 n 2n (D) n Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 2003 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 6. Let T(n) be the number of different binary search trees on n distinct elements. n Then T(n)= ∑ T ( k − 1) T ( x ) , where x is k =1 (A) n – k + 1 7. (B) n – k (C) n – k – 1 (D) n – k – 2 Consider the set Σ* of all strings over the alphabet Σ = {0, 1}. Σ* with the concatenation operator for strings (A) does not form a group (B) forms a non-commutative group (C) does not have a right identity element (D) forms a group if the empty string is removed from Σ* 8. 9. Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between (A) k and n (B) k – 1 and k + 1 (C) k – 1 and n – 1 (D) k + 1 and n – k Assuming all numbers are in 2’s complement representation, which of the following numbers is divisible by 11111011? (A) 11100111 10. (B) 11100100 (C) 11010111 (D) 11011011 For a pipelined CPU with a single ALU, consider the following situations I. The j + 1-st instruction uses the result of the j-th instruction as an operand II. The execution of a conditional jump instruction III. The j-th and j + 1-st instructions require the ALU at the same time Which of the above can cause a hazard? (A) I and II only 11. (C) III only (D) All the three Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is (A) Θ (1) 12. (B) II and III only (B) Θ (log n) (C) Θ (n) (D) Θ (n2) Ram and Shyam have been asked to show that a certain problem Π is NPcomplete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions? (A) Π is NP-hard but not NP-complete (B) Π is in NP, but is not NP-complete (C) Π is NP-complete (D) Π is neither NP-hard, nor in NP Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 2003 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 13. Nobody knows yet if P = NP. Consider the language L defined as follows. ( 0 + 1) * if P = NP L= φ otherwise Which of the following statements is true? (A) L is recursive (B) L is recursively enumerable but not recursive (C) L is not recursively enumerable (D) Whether L is recursive or not will be known after we find out if P = NP 14. 15. The regular expression 0*(10*)* denotes the same set as (A) (1*0)*1* (B) 0+(0+10)* (C) (0+1)*10(0+1)* (D) None of the above If the strings of a language L can be effectively enumerated in lexicographic (i.e., alphabetic) order, which of the following statements is true? (A) L is necessarily finite (B) L is regular but not necessarily finite (C) L is context free but not necessarily regular (D) L is recursive but not necessarily context free 16. Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar? (A) Removing left recursion alone (B) Factoring the grammar alone (C) Removing left recursion and factoring the grammar (D) None of the above 17. 18. Assume that the SLR parser for a grammar G has n1 states and the LALR parser for G has n2 states. The relationship between n1 and n2 is (A) n1 is necessarily less than n2 (B) n1 is necessarily equal to n2 (C) n1 is necessarily greater than n2 (D) None of the above In a bottom-up evaluation of a syntax directed definition, inherited attributes can (A) always be evaluated (B) be evaluated only if the definition is L-attributed (C) be evaluated only if the definition has synthesized attributes (D) never be evaluated Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum GATE CS - 2003 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 19. 20. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree? (A) 7 5 1 0 3 2 4 6 8 9 (B) 0 2 4 3 1 6 5 9 8 7 (C) 0 1 2 3 4 5 6 7 8 9 (D) 9 8 6 4 2 3 0 1 5 7 Consider the following three claims I. (n + k)m = Θ(nm) where k and m are constants II. 2n+1 = O(2n) III. 22n+1 = O(2n) Which of these claims are correct? (A) I and II 21. (B) I and III (C) II and III (D) I, II, and III III a b f h g e IV a f g h b e Consider the following graph Among the following sequences I abeghf II abfehg Which are depth first traversals of the above graph? 22. (A) I, II and IV only (B) I and IV only (C) II, III and IV only (D) I, III and IV only The usual Θ(n2) implementation of Insertion Sort to sort an array uses linear search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will (A) remain Θ(n2) (B) become Θ(n (log n)2) (C) become Θ(n log n) (D) become Θ(n) Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum 2003 www. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. For more details. Using a larger block size in a fixed block size file system leads to (A) better disk throughput but poorer disk space utilization (B) better disk throughput and better disk space utilization (C) poorer disk throughput but better disk space utilization (D) poorer disk throughput and poorer disk space utilization 26.com Think GATE Think GATE Forum . All India Rank. Which of the following assertions is FALSE about the Internet Protocol (IP)? (A) It is possible for a computer to have multiple IP addresses (B) IP packets from the same source to the same destination can take different routes in the network (C) IP ensures that a packet is discarded if it is unable to reach its destination within a given number of hops (D) The packet source cannot set the route of an outgoing packets. In a system with 32 bit virtual addresses and 1KB page size. use of one-level page tables for virtual to physical address translation is not practical because of (A) the large amount of internal fragmentation (B) the large amount of external fragmentation (C) the large memory overhead in maintaining page tables (D) the large computation overhead in the translation process 27.com Join discussion of this test paper at http://forum.GATE CS . Which of the following functionalities must be implemented by a transport protocol over and above the network protocol? (A) Recovery from packet losses (B) Detection of duplicate packets (C) Packet delivery in the correct order (D) End to end connectivity Join All India Mock GATE Classroom Test Series . interaction with IISc alumni in our online discussion forums. values do not have any types (C) In dynamically typed languages. and more. each variable in a program has a fixed type (B) In un-typed languages.gatementor. Percentile. the route is determined only by the routing tables in the routers on the way 28. variables have no types (D) In all statically typed languages. the 7th smallest element can be found in time (A) Θ(n log n) 24. (B) Θ(n) (C) Θ(log n) (D) Θ(1) Which of the following statements is FALSE? (A) In statically typed languages. each variable in a program is associated with values of only a single type during the execution of the program 25.2007 conducted by GATE Forum in over 25 cities all over India.com 23.gateforum. In a heap with n elements with the smallest element at the root. visit www. . Which of the following is a valid first order formula? (Here α and β are first order formulae with x as their only free variable) (A) ((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α⇒β] (B) (∀x)[α] ⇒ (∃x)[α ∧ β] (C) ((∀x)[α ∨ β] ⇒ (∃x)[α] ⇒ (∀x)[α] (D) (∀x)[α ⇒ β] ⇒ ((∀x)[α] ⇒ (∀x)[β]) Join All India Mock GATE Classroom Test Series . 31-90 carry two marks each. an from r1. Which of the following statements CANNOT be true? (A) P(x) = True for all x ∈ S such that x ≠ b (B) P(x) = False for all x ∈ S such that x ≠ a and x ≠ c (C) P(x) = False for all x ∈ S such that b ≤ x and x ≠ c (D) P(x) = False for all x ∈ S such that a ≤ x and b ≤ x 32.2007 conducted by GATE Forum in over 25 cities all over India.K an a1 . All India Rank. 31. Percentile. . Which of the following scenarios may lead to an irrecoverable error in a database system? (A) A transaction writes a data item after it is read by an uncommitted transaction (B) A transaction reads a data item after it is read by an uncommitted transaction (C) A transaction reads a data item after it is written by a committed transaction (D) A transaction reads a data item after it is written by an uncommitted transaction 30. Consider the following SQL query select distinct a1. a2 . Let P: S {True.K an a1 . a2 .com Join discussion of this test paper at http://forum.. r2. . P(b) = False and P(x) ⇒ P(y) for all x. and a maximum element c. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. False} be a predicate defined on S. and more. Let (S. where ⇒ stands for logical implication.com Think GATE Think GATE Forum .K an a1 . For more details.K an r2 … rm) Q. y ∈ S satisfying x≤y.gateforum.com 29.gatementor. interaction with IISc alumni in our online discussion forums. this query is equivalent to which of the following relational algebra expressions? (A) (B) (C) (D) Π σ ρ ( r1 × r2 × K × rm ) Π σ ρ (r1 Π σ ρ ( r1 ∪ r2 ∪ K ∪ rm ) Π σ ρ ( r1 ∩ r2 ∩ K ∩ rm ) a1 .gateforum.GATE CS ...2003 www. a2 . a2 .. rm where P For an arbitrary predicate P. Suppose that P(a) = True. ≤) be a partial order with two minimal elements a and b. visit www. a2.. (A) m (21m-39)+4 6 (B) m (4m2-3m+5) 6 (C) m (3m2. (B) 24 (C) 30 (D) 60 Let f : A B be an injective (one-to-one) function. Which of the following statements is true? 34.2003 www. visit www.com 33. for all subsets C of A. Define g : 2A 2B as: g(C) = {f(x) | x ∈ C}.gateforum.gateforum.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. All India Rank. (A) I1 satisfies α. Define h : 2B 2A as: h(D) = {x | x ∈ A. for all subsets D of B. 35. interaction with IISc alumni in our online discussion forums. I1 does not (C) Neither I2 nor I1 satisfies α (D) Both I1 and 12 satisfy α m identical balls are to be placed in n distinct bags.com Think GATE Think GATE Forum . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Join discussion of this test paper at http://forum.GATE CS . Which of the following statements is always true? (A) g(h(D)) ⊆ D (B) g(h(D)) ⊇ D (C) g(h(D)) ∩ D = φ (D) g(h(D)) ∩ (B—D) ≠ φ Join All India Mock GATE Classroom Test Series . You are given that m ≥ kn. Consider the following formula _ and its two interpretations I1 and I2 α: (∀x)[Px ⇔ (∀y)[Qxy ⇔ ¬Qyy]] ⇒ (∀x)[¬Px] I1: Domain: the set of natural numbers Px ≡ ‘x is a prime number’ Qxy ≡ ‘y divides x’ I2: same as I1 except that Px = ‘x is a composite number’. and more. Percentile. For more details. In how many ways can the balls be placed in the bags if each bag must contain at least k balls? m − k (A) n −1 m − kn + n − 1 (B) n −1 m − 1 (C) n − k m − kn + n + k − 2 (D) n−k Consider the following recurrence relation T(1) = 1 T(n + 1) = T(n)+ n + 1 for all n≥1 The value of T(m2) for m ≥1 is 36. f(x) ∈ D}. where k is a natural number ≥1. I2 does not (B) I2 satisfies α.5 -11m+20)-5 2 (D) m 5 (5m3 -34m2 +137m-104)+ 6 6 How many perfect matching are there in a complete graph of 6 vertices? (A) 15 37. does this system of equations have infinitely many solutions? (A) 0 (B) 1 (C) 2 (D) infinitely many Join All India Mock GATE Classroom Test Series . c} with binary operators + and × defined as follows. For a non-empty sequence<sj.gateforum. g(e) = 11. c. g(b) = 5. min-degree of G cannot be v ∈V (A) 3 41. Therefore.2007 conducted by GATE Forum in over 25 cities all over India. an. (B) 1 (C) 2 (D) 3 Let Σ = {a. Percentile. (B) 283858 (C) 293959 (D) 210510710 A graph G = (V. a + c = c. For how many values of α.. y) that satisfy the equations) is (A) 0 39. The min-degree of G is defined as { } min degree (ν ) .. c + a = a. Given the following set of equations: (a × x) + (a × y) = c (b × x) + (c × y) = c The number of solution(s) (i. b. visit www. Consider the set {a.. where each ai ∈Σ. b. define f(s) = Π ni =1Pi ( i ) . Let pi denote the i-th prime number (p1 = 2). (B) 4 (C) 5 (D) 6 Consider the following system of linear equations 2 1 −4 4 3 −12 1 2 −8 x α y = 5 z 7 Notice that the second and the third columns of the coefficient matrix are linearly dependent.. h..GATE CS . interaction with IISc alumni in our online discussion forums.com Think GATE Think GATE Forum . For more details.. g a For a non-empty string s=a1 . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. of a non-empty sequence of strings? (A) 273757 40.sn>of strings from Σ+. f s define h ( 〈 si K sn 〉 ) = Π ni =1Pi ( i ) Which of the following numbers is the encoding. g(c) = 7.gatementor.e. c × b = c and b × c = a. d. and more. e} be an alphabet. We define an encoding scheme as follows: g(a) = 3.2003 www. g(d) = 9.com 38.com Join discussion of this test paper at http://forum. pair(s) (x.E) satisfies |E|≤3|V|-6. All India Rank.. For example. (A) 1. and mantissa fields respectively.3 respectively The following is a scheme for floating point number representation using 16 bits.3.6 respectively (D) 1. and 1.3. If we use the Newton-Raphson method to find the roots of f(x) =0 using x0. exponent.2007 conducted by GATE Forum in over 25 cities all over India.3. 0. interaction with IISc alumni in our online discussion forums.6. Bit Position 15 14 …… 9 8 …… 0 s e m Sign Exponent Mantissa Let s. The circuit outputs 00 until one of the following conditions holds. Join All India Mock GATE Classroom Test Series . the output at the k-th and all subsequent clock ticks is 10. the roots obtained would be 43. All India Rank. Then the floating point number represented is: ( −1)s 1 + m × 2−9 2e − 31 . 1. if the exponent ≠ 111111 0.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Think GATE Think GATE Forum . visit www.3. and 1.6 respectively (B) 0. In this case. For more details.2003 www. and m be the numbers represented in binary in the sign. 0. (B) 2-9 (C) 222 (D) 231 A 1-input.com 42. Percentile. x1.gateforum. 0. and 0.com Join discussion of this test paper at http://forum.6. e.gateforum. • zk – nk=2.6. 2-output synchronous sequential circuit behaves as follows: Let zk.3 respectively (C) 1. and x2 respectively as initial guesses. nk denote the number of 0’s and 1’s respectively in initial k bits of the input (zk+nk=k). and more. and 0. A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale). otherwise ( ) What is the maximum difference between two successive real numbers representable in this system? (A) 2-40 44.6.gatementor. denote addition and subtraction respectively)? 47. visit www. 10) (D) (11. the output at the k-th and all subsequent clock ticks is 01.com Think GATE Think GATE Forum . which of the following operations can be performed by suitably setting the control lines K and C0 only (+ and .2007 conducted by GATE Forum in over 25 cities all over India. All India Rank. What are the minimum possible literal counts of the product-of-sum and sum-ofproduct representations respectively of the function given by the following Karnaugh map? Here.com Join discussion of this test paper at http://forum.gateforum.GATE CS . interaction with IISc alumni in our online discussion forums. the literal count of (xy + xz’) is 4. but not A .gateforum.com nk – zk = 2. and A + 1 Consider the following circuit composed of XOR gates and non-inverting buffers. The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. Percentile. but not A – B or A + 1 (D) A + B. and A + 1. (B) (9. X denotes “don’t care” (A) (11.2003 www. For more details. (A) A + B. If the operands are in 2’s complement representation. and A . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. but not A + 1 (B) A + B.B. In this case.gatementor. and more.B. 9) 46. Join All India Mock GATE Classroom Test Series . What is the minimum number of states required in the state transition graph of the above circuit? (A) 5 (B) 6 (C) 7 (D) 8 • 45.B (C) A + B. 13) (C) (9. For example. 11) Consider the ALU shown below. and A . #1 . B0 MOV C. #1 .gateforum. interaction with IISc alumni in our online discussion forums. jump to X if zero flag is set SUB C.a1 and a0 respectively. left rotate A through carry flag by one bit (D) ADD A. BB+1 JMP Z . B. All India Rank. #1 . jump to Y if carry flag is set JMP Z . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. If the initial value of register A is A0 the value of register B after the program execution will be (A) the number of 0 bits in A0 (B) the number of 1 bits in A0 (C) A0 (D) 8 Which of the following instructions when inserted at location X will ensure that the value of register A after program execution is the same as its initial value? (A) RRC A. #0 . if the initial values of A and the carry flag are a7.. no operation (C) LRC A. right rotate A through carry by one bit.com The non-inverting buffers have delays δ1 = 2 ns and δ 2 = 4 ns as shown in the figure. how many transition(s) (change of logic levels) occur(s) at B during the interval from 0 to 10 ns? (A) 1 (B) 2 (C) 3 (D) 4 The following information pertains to 48-49: Consider the following assembly language program for a hypothetical processor A. #1 Join All India Mock GATE Classroom Test Series . Thus: . compare C with 0 JZ X . Percentile. #1 (B) NOP .com Join discussion of this test paper at http://forum. instruction will be c0a7.2007 conducted by GATE Forum in over 25 cities all over India.gatementor. If the following waveform is applied at input A.GATE CS . Z: Y: MOV B. and C are 8 bit registers.2003 www. The meanings of various instructions are shown as comments. CC-1 RRC A. and more. Both XOR gates and all wires have zero delay. C8 CMP C. For more details. JC Y . #0 .gateforum. their values after the execution of this ..com Think GATE Think GATE Forum . visit www. Assume that all gate inputs. 49. #1 . outputs and wires are stable at logic level 0 at time 0. jump to Z X: 48. c0 respectively. #8 .a0 and . jump to Z ADD B. R.com Think GATE Think GATE Forum . 1.GATE CS . Let S denote the set of seven bit binary strings in which the first. 1}. Percentile. Consider two languages L1 and L2.2003 www.b}. Which of the following CANNOT be true? (A) L1 ∈ P and L2 is finite (B) L1 ∈ NP and L2 ∈ P (C) L1 is undecidable and L2 is decidable (D) L1 is recursively enumerable and L2 is recursive 53.com Join discussion of this test paper at http://forum. of which q0 is the starting state. The transition function of M is described in the following table. Let f: Σ Σ be a polynomial time computable bijection such that (∀x)[x∈ L1 iff f(x) ∈ L2]. then it writes 1 on the same tape square.com 50. The symbol B is the blank symbol used to indicate end of an input string. The tape alphabet of M is {0. visit www. each on the alphabet Σ. interaction with IISc alumni in our online discussion forums. Consider the following deterministic finite state automaton M. The table is interpreted as illustrated below. R) in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current tape square. B} and its input alphabet is {0. All India Rank.gatementor. For more details. Further. 1. A single tape Turing Machine M has two states q0 and q1. moves its tape head one position to the right and transitions to state q1. and the last bits are 1. (B) 5 (C) 7 (D) 8 Let G = ({S}.2007 conducted by GATE Forum in over 25 cities all over India. y ∈ L(G) such that xy∉ L(G) (C) There is a deterministic pushdown automaton that accepts L(G) (D) We can find a deterministic finite state automaton that accepts L(G) 52.{a.S) be a context free grammar where the rule set R is S aSb|SS|ε Which of the following statements is true? (A) G is not ambiguous (B) There exist x. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. The number of strings in S that are accepted by M is (A) 1 51.gateforum. The entry (q1. Join All India Mock GATE Classroom Test Series . the fourth. let f-1 be also polynomial time computable. and more.gateforum. w. (B) L1 = {0. Which of the following statements is true? (A) L1 = {0. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. is a string. Let the language accepted by M be L. but L is not (B) L is recursively enumerable.com Which of the following statements is true about M? (A) M does not halt on any string in (0+1)+ (B) M does not halt on any string in (00+1)* (C) M halts on all strings ending in a 0 (D) M halts on all strings ending in a 1 54. w. second component. but L is not (C) Both L and L are recursive (D) Neither L nor L is recursively enumerable 55. 0> | M halts on w} L1 = {<M. visit www. i> is a triplet. i. whose first component.1}* (C) L1 ⊆ L (D) L1 = L Consider the grammar shown below S i E t S S′ | a S ′ e S |ε Eb Join All India Mock GATE Classroom Test Series . Let L = L0∪L1.com Join discussion of this test paper at http://forum.2007 conducted by GATE Forum in over 25 cities all over India. Percentile. All India Rank. M. and third component.com Think GATE Think GATE Forum .GATE CS . is an encoding of a Turing Machine. 1> | M does not halt on w} Here <M. Which of the following is true? (A) L is recursively enumerable.1}* . w.gatementor. and more. is a bit. Let L1 be the language accepted by the NFA M1 obtained by changing the accepting state of M to a non-accepting state and by changing the non-accepting states of M to accepting states.L 56. Consider the NFA M shown below.gateforum.2003 www. interaction with IISc alumni in our online discussion forums. For more details.gateforum. w. Define languages L0 and L1 as follows: L0 = {<M. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. All India Rank. (A) LL(1) (B) SLR(1) but not LL(1) (C) LALR(1) but not SLR(1) (D) LR(l) but not LALR(1) Consider the translation scheme shown below. and more. S id : = E {gen(id. S ′ ε} and { S ′ ε} Consider the grammar shown below. gen is a function that generates the output code. gen(t = E1.place = E. of this grammar.$] respectively are 57.place = t. X = t3 A program consists of two modules executed sequentially. The probability density function of the overall time taken to execute the program is given by t (A) f1 ( t ) + f2 ( t ) (B) ∫f 1 ( x ) f2 ( x ) dx 0 Join All India Mock GATE Classroom Test Series . M. (A) { S ′ e S} and{ S ′ ε} (B) { S ′ e S}and { } (C) { S ′ ε} and { S ′ ε} (D) { S ′ e S.2007 conducted by GATE Forum in over 25 cities all over India. t2 = Z. t2 = t1 + Z. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. and newtemp is a function that returns the name of a new temporary variable on every call. (B) 9 5 + 2 + (C) 9 5 2 + + (D) + + 9 5 2 Consider the syntax directed definition shown below. this translation scheme will print (A) 9 + 5 + 2 59. (A) X = Y + Z (B) t1 = Y + Z.val represents the corresponding integer value.place. X = t2 (D) t1 = Y.). the 3-address code sequence generated by this definition is 60. the entries M[ S ′ . Percentile.val).com In the predictive parse table.gatementor. interaction with IISc alumni in our online discussion forums.} E id {E.GATE CS . For the statement ‘X : = Y + Z’.place.2003 www.place + E2. SCC C cC|d This grammar is 58.com Think GATE Think GATE Forum . E.gateforum. t3 = t1 + t2. STR R + T {print(’+’).} Here.} Here num is a token that represents an integer and num.gateforum.place = id.).com Join discussion of this test paper at http://forum.place. For more details.e] and M[ S ′ .} R|ε T num {print(num. X = t1 (C) t1 = Y. visit www. Assume that ti’s are the temporary variable names generated by newtemp.} E E1 + E2 {t = newtemp( ). For an input string ‘9 + 5 + 2’. Assume that Push and Pop operations take X seconds each. For m ≥1. an. n ( n − 1) 2 n ( n − 1) 4 (C) n ( n + 1) 4 (D) 2n[log2n] What would be the worst case time complexity of the Insertion Sort algorithm. and Y seconds elapse between the end of one such stack operation and the start of the next operation. f2(t)} 0 The following information pertains to 61-62: In a permutation a1 . and more. where n is the number of elements in the set.gateforum.com Think GATE Think GATE Forum . I. n with at most n inversions? (A) Θ(n2) 63. of n distinct integers. All India Rank.gatementor. Insertion of an element if it is not already present in the set Which of the following data structures can be used for this purpose? (A) A heap can be used but not a balanced binary search tree (B) A balanced binary search tree can be used but not a heap (C) Both balanced binary search tree and heap can be used (D) Neither balanced binary search tree nor heap can be used 64.. interaction with IISc alumni in our online discussion forums. . suppose we push the first n natural numbers in sequence. 61. .5) (D) Θ(n) A data structure is required for storing a set of integers such that each of the following operations can be done in O(log n) time. what is the expected number of inversions in a randomly chosen permutation of 1. Let S be a stack of size n ≥1. visit www.X (D) Y + 2X Join All India Mock GATE Classroom Test Series . (B) (B) Θ(n log n) (C) Θ(n1. and then perform n pop operations. .com Join discussion of this test paper at http://forum. The average stack-life of an element of this stack is (A) n(X + Y) (B) 3Y + 2X (C) n(X + Y) ..GATE CS . aj) such that i < j and ai > aj. Starting with the empty stack. For more details. Percentile.gateforum. . If all permutations are equally likely. n? (A) 62.2007 conducted by GATE Forum in over 25 cities all over India.2003 www. define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S.com t (C) ∫f 1 ( x ) f2 ( t − x ) dx (D) max{f1(t). Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. if the inputs are restricted to permutations of 1. an inversion is a pair (ai. Deletion of the smallest element II. .com Join discussion of this test paper at http://forum.com 65. All India Rank.2003 www.com Think GATE Think GATE Forum . Percentile.2007 conducted by GATE Forum in over 25 cities all over India.GATE CS . and more.gatementor. interaction with IISc alumni in our online discussion forums. visit www. Consider the following 2-3-4 tree (i. B-tree with a minimum degree of two) in which each data item is a letter.gateforum. What is the result of inserting G in the above tree? (A) (B) (C) (D) None of the above Join All India Mock GATE Classroom Test Series . For more details.e. The usual alphabetical ordering of letters is used in constructing the tree. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. com Join discussion of this test paper at http://forum. (B) 31 (C) 38 (D) 41 The following are the starting and ending times of activities A. Which of the following can always be inferred from the path costs computed? (A) The number of edges in the shortest paths from v1 to all vertices of G (B) G1 is connected (C) V1 forms a clique in G (D) G1 is a tree 68.5) 67. interaction with IISc alumni in our online discussion forums. 0 if e ∈ E1 1 otherwise ω (e) = A single-source shortest path algorithm is executed on the weighted graph (V. xs denotes the starting time and xe denotes the ending time of activity X. E.E) be an undirected graph with a subgraph G1 = (V1.gatementor.E. Here. What is the weight of a minimum spanning tree of the following graph? (A) 29 69.2003 www. Let G = (V. For more details. The complexity of computing the cube root of n (n is represented in binary notation) is (A) O(n) but not O(n0. D. The cube root of a natural number n is defined as the largest natural number m such that m3≤n.com 66. but not O((log log n)0.gateforum. E1). F. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. B. G and H respectively in chronological order: “as bs cs ae ds ce es fs be de gs ee fe hs ge he”.5.gateforum. and more. C. visit www.w) with an arbitrary vertex v1 of V1 as the source. Weights are assigned to edges of G as follows. All India Rank.com Think GATE Think GATE Forum .2007 conducted by GATE Forum in over 25 cities all over India.5) (B) O(n0. An activity Join All India Mock GATE Classroom Test Series . Percentile.5) but not O((log n)k) for any constant k > 0 (C) O((log n)k) for some constant k > 0. but not O((log log n)m) for any constant m > 0 (D) O((log log n)k) for some constant k > 0.GATE CS . We need to schedule the activities in a set of rooms available to us. y) ∧ C(y)] ⇒ A(x)] ∧ (∃x)[B(x. All India Rank.x)] (D) (∀x) [(∀y) [B(x. For more details. .k] contains the longest path length from j to k (D) If there exists a path from j to k.k ) ∈ E A j. (B) 4 (C) 5 (D) 6 Let G = (V.E) be a directed graph with n vertices.. y). C(y) B(x. interaction with IISc alumni in our online discussion forums. What is the minimum number of rooms required? (A) 3 70.k] = max(A[j.y) ∧ C(y)] ⇒ A(x)] ∧ ¬(∃x)[B(x.k} edges 71. vk+1) ∈ E for all k in i through j .k]).gatementor.1.gateforum.x)] (B) (∀x) [(∀y) [B(x.y) ∧ C(y)] ⇒ A(x)] ∧ ¬(∃x)[B(x. then G has a Hamiltonian cycle (C) If there exists a path from j to k. Consider the following logic program P A(x) B(x. for i = 1 to n for j = 1 to n for k = 1 to n A[j. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. .i] + A[i.com can be scheduled in a room only if the room is reserved for the activity for its entire duration.gateforum. A[j. Percentile.x)] 72.j] ≥ n . Derive clause (P ∨ Q) from clauses (P ∨ R).com Think GATE Think GATE Forum .k] ≤ n (B) If A[j. A path from vi to vj in G is a sequence of vertices (vi.GATE CS . Let A be an n x n array initialized as follows..y) ∧ C(y)] ⇒ A(x)] ∨ ¬(∃x)[B(x. 1 if ( j. and more. Which of the following statements is necessarily true for all j and k after termination of the above algorithm? (A) A[j.2003 www. The following resolution rule is used in logic programming.x)] (C) (∀x) [(∃y) [B(x. A[j.1. vj) such that (vk. A simple path is a path in which no vertex appears more than once.k].com Join discussion of this test paper at http://forum. (Q ∨ ¬R) Which of the following statements related to this rule is FALSE? (A) ((P ∨ R) ^ (Q ∨ ¬R)) ⇒ (P ∨ Q) is logically valid (B) (P ∨ Q) ⇒ ((P ∨ R) ∧ (Q ∨ ¬R)) is logically valid (C) (P ∨ Q) is satisfiable if and only if (P ∨ R) ∧ (Q ∨ ¬R) is satisfiable (D) (P ∨ Q) ⇒ FALSE if and only if both P and Q are unsatisfiable Join All India Mock GATE Classroom Test Series .x) Which of the following first order sentences is equivalent to P? (A) (∀x) [(∃y) [B(x. k = 0 otherwise Consider the following algorithm. every simple path from j to k contains at most A[j. visit www.2007 conducted by GATE Forum in over 25 cities all over India. vi+1. j = 5.gatementor. interaction with IISc alumni in our online discussion forums.f(1). i = 200. the values printed by the above program are (A) 115.2007 conducted by GATE Forum in over 25 cities all over India. print(x + 10).2003 www. Class P { Class Q subclass of P { void f(int i) { void f(int i) { print(i). 220 75. If the programming language uses static scoping and call by need parameter passing mechanism.com Join discussion of this test paper at http://forum.f(1). 220 (C) 25.GATE CS . Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. the values printed by the above program are (A) 115.gateforum. 220 (B) 25. Here ((P)y) denotes a typecast of y to P. (C) 25. print(2*i). ((P)y).com The following information pertains to 73-74: The following program fragment is written in a programming language that allows global variables and does not allow nested declarations of functions. Percentile.com Think GATE Think GATE Forum . void P(x) { int i = 10. visit www. All India Rank. (B) 25. though the syntax is similar. 105 If the programming language uses dynamic scoping and call by name parameter passing mechanism. z. 15 (D) 115. For more details. and more. j = 20.gateforum. The language should not be assumed to be either Java or C++.f(1). The output produced by executing the above program fragment will be (A) 1 2 1 (B) 2 1 1 (C) 2 1 2 (D) 2 2 2 Join All India Mock GATE Classroom Test Series . x. Pz = new Q(). 15 (D) 115. 105 Consider the following class definitions in a hypothetical Object Oriented language that supports inheritance and uses dynamic binding. print (x). 220 74. global int i = 100. } main() {P(i + j).} 73. } } } } Now consider the following program fragment: Px = new Q() Qy = new Q(). GATE CS . and TLB access time is also 1 ns. with a hit rate of 96%. Page tables for both levels are stored in the main memory. A uni-processor computer system only has two processes. Main memory access time is 10 ns. (B) 2 ns (C) 3 ns (D) 4 ns Suppose a process has only the following pages in its virtual address space: two contiguous code pages starting at virtual address 0×00000000. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. The amount of memory required for storing the page tables of this process is (A) 8 KB (B) 12 KB (C) 16 KB (D) 20 KB Join All India Mock GATE Classroom Test Series . and a stack page starting at virtual address 0×FFFFF000.gateforum. The I/O of both processes can proceed in parallel. visit www.5 ns) (A) 1. The TLB caches recently used virtual page numbers and the corresponding physical page numbers. Assuming that no page faults occur. the 10 most significant bits of the virtual address are used as index into the first level page table while the next 10 bits are used as index into the second level page table. 78.2003 www.com Think GATE Think GATE Forum . the average time taken to access a virtual address is approximately (to the nearest 0. Assume that the page table entries in both levels of page tables are 4 bytes wide. Virtual and physical addresses are both 32 bits wide. two contiguous data pages starting at virtual address 0×00400000.com 76. Both the processes were created at nearly the same time. For more details.78-79: A processor uses 2-level page tables for virtual to physical address translation. the processor has a translation look-aside buffer (TLB).gateforum. Which of the following is NOT an advantage of using shared. For virtual to physical address translation.5 ns 79. All India Rank. The processor also has a physically addressed cache with a hit rate of 90%. Which of the following scheduling strategies will result in the least CPU utilization (over a long period of time) for this system? (A) First come first served scheduling (B) Shortest remaining time first scheduling (C) Static priority scheduling with different priorities for the two processes (D) Round robin scheduling with a time quantum of 5 ms The following information pertains to Q. both of which alternate 10 ms CPU bursts with 90 ms I/O bursts.com Join discussion of this test paper at http://forum. dynamically linked libraries as opposed to using statically linked libraries? (A) Smaller sizes of executable files (B) Lesser overall page fault rate in the system (C) Faster program startup (D) Existing programs need not be re-linked to take advantage of newer versions of libraries 77. and more. interaction with IISc alumni in our online discussion forums. Percentile. Further. cache access time is 1 ns.gatementor. The memory is byte addressable. The 12 least significant bits of the virtual address are used as offset within the page.2007 conducted by GATE Forum in over 25 cities all over India. X. A and B are using the sliding window protocol for flow control.87 and 191.255. V(S) at X.203.87. Which of the following pairs of IP addresses could belong to this network? (A) 172. The code for the processes P and Q is shown below. 84. V(S) at Z.GATE CS .35. What is the minimum packet size that can be used on this network? (A) 50 bytes (B) 100 bytes (C) 200 bytes (D) None of the above Host A is sending data to host B over a full duplex link. S and T initially 1 (B) P(S) at W. The subnet mask for a particular network is 255. V(T) at Z. Y. Process P: Process Q: while (1) { while (1) { W: Y: print ‘0’. and more. P(T) at Y. All India Rank. print ‘1’.com Think GATE Think GATE Forum . S and T initially 1 82. Percentile.35.31. V(S) at Z. V(S) at Z.161. P(T) at Y.2003 www. S and T initially 1 (B) P(S) at W.88.8.233 (B) 10. interaction with IISc alumni in our online discussion forums. V(T) at X. P(T) at Y. P(S) at Y.43 and 128. 83.57. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. P(T) at Z.gatementor. S and T initially 1 (C) P(S) at W. X: Z: } } Synchronization statements can be inserted only at points W. Which of the following will ensure that the output string never contains a substring of the form 01n0 or 10n1 where n is odd? (A) P(S) at W. V(T) at X. and Z 80. P(T) at Y. P(S) at Y. and T initially 0 81. V(S) at X.8. The Join All India Mock GATE Classroom Test Series .gateforum.29.com The following information pertains to Q.56. print ‘1’. P(T) at Y. Which of the following will always lead to an output staring with ‘001100110011’? (A) P(S) at W.2 and 10.55 A 2km long broadcast LAN has 107 bps bandwidth and uses CSMA/CD.31. S initially 1 (D) V(S) at W.0. S initially 1. For more details.4 (C) 191. V(T) at Z. V(T) at Z. V(T) at X. V(S) at Z.2007 conducted by GATE Forum in over 25 cities all over India. S and T initially 1 (D) P(S) at W.62 and 172. P(T) at Y. print ‘0’. and T initially 0 (C) P(S) at W. The signal travels along the wire at 2×108 m/s. V(S) at X.31.234.com Join discussion of this test paper at http://forum.129. S initially 1.80-81: Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T.28. Data packets (sent only from A to B) are all 1000 bytes long and the transmission time for such a packet is 50 µs Acknowledgement packets (sent only from B to A) are very small and require negligible transmission time. V(T) at X. The send and receive window sizes are 5 packets each. visit www.88 (D) 128. V(S) at X.gateforum. Course_name.00 × 106 bps Consider the following functional dependencies in a database. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.gateforum. and more. Instructor) Grades: (Roll_number. Age) is (A) in second normal form but not in third normal form (B) in third normal form but not in BCNF (C) in BCNF 86. Students: (Roll_number. Name. Date_of_Birth Age Age Eligibility Name Roll_number Roll_number Name Course_number Course_name Course_number Instructor (Roll_number.69 × 106 bps (B) 11.gateforum.com Think GATE Think GATE Forum .com propagation delay over the link is 200 µs. (A) 7. All India Rank.Instructor = Korth and Courses. Name.GATE CS .Course_number = Grades. For more details. Courses.com Join discussion of this test paper at http://forum. Course_number) Grade The relation (Roll_number. visit www. Roll_number = Grades.Roll_number and Courses.gatementor.2003 www. Grades where Students. interaction with IISc alumni in our online discussion forums. Date_of_birth.grade = A Which of the following sets is computed by the above query? (A) Names of students who have got an A grade in all courses taught by Korth (B) Names of students who have got an A grade in all courses (C) Names of students who have got an A grade in at least one of the courses taught by Korth (D) None of the above Join All India Mock GATE Classroom Test Series .2007 conducted by GATE Forum in over 25 cities all over India. Percentile. What is the maximum achievable throughput in this communication? 85.33 × 106 bps (D) 15. Date_of_birth) Courses: (Course number.11 × 106 bps (C) 12. Grade) select distinct Name from Students. (D) in none of the above Consider the set of relations shown below and the SQL query that follows.Course_number and Grades. Course_number. The variable n is initialized to an integer ≥3.2007 conducted by GATE Forum in over 25 cities all over India. Percentile. for (k=2. for (j=3. k++) for (j=k+1. All India Rank.com Think GATE Think GATE Forum . T2. (∃i)[m=i2]} (C) {m|m ≤ n.gateforum.gatementor. and more. k <= n. In the diagram. k. j++) if (!A[j]) printf(”%d ”.j).GATE CS .gateforum. j <= n. and the following execution schedule of transactions T1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus.com Join discussion of this test paper at http://forum.com 87. D2. For more details. and T3. and TwoLog_n is initialized to the value of 2 * log2 ( n ) for (k=3.2003 www. T3 (C) The schedule is serializable as T3. k++) A[k] = 0. Consider three data items D1. j. T1 (D) The schedule is not serializable 88. Which of the following statements is correct? (A) The schedule is serializable as T2. T1. j <= n. interaction with IISc alumni in our online discussion forums. k <= TwoLog_n. and A is an array of integers. T2. R(D) and W(D) denote the actions reading and writing the data item D respectively. The set of numbers printed by this program fragment is (A) {m|m ≤ n. and D3. In the following C program fragment. n and TwoLog_n are integer variables. T3. (∃i)[m=i!]} (B) {m|m ≤ n. visit www. j++) A[j] = A[j] || (j%k). T1 (B) The schedule is serializable as T2. m is prime} (D) {} Join All India Mock GATE Classroom Test Series . the function f returns 1 if and only if (A) the list is empty or has exactly one element (B) the elements in the list are sorted in non-decreasing order of data value (C) the elements in the list are sorted in non-increasing order of data value (D) not all elements in the list have the same data value Join All India Mock GATE Classroom Test Series . print(x).2007 conducted by GATE Forum in over 25 cities all over India. }. int f(struct item *p) { return ((p == NULL) || (p ->next == NULL) || ((p->data <= p -> next -> data) && f(p-> next))).gateforum. P(&x) print(x).GATE CS . Q(x). } void P(int *y) { int x = *y+2.com Think GATE Think GATE Forum . struct item { int data.h> #define print(x) printf(”%d “.2003 www. #include <stdio. and more. interaction with IISc alumni in our online discussion forums. Consider the C program shown below.com Join discussion of this test paper at http://forum. (B) 22 12 11 (C) 14 6 6 (D) 7 6 6 Consider the function f defined below. visit www. void Q(int z) { z += x. All India Rank. } main(void) { x = 5.com 89.gateforum. struct item * next. *y = x-1. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. } The output of this program is (A) 12 7 6 90. Percentile. } For a given linked list p. print(z). For more details. x) int x.gatementor. 20 Carry One Mark Each 1. Page 1 of 29 .com Q. ∀i. Let W = X × Y and E be the set of all subsets of W.gateforum.ECTest ID: 00 All India Mock GATE Test Series www. How many context switches are © All rights reserved by GATE Forum Educational Services Pvt. The minimum number of multiplications needed to evaluate p on an input x is: (A) 3 (B) 4 (C) 6 (D) 9 2. 9} under multiplication modulo 10 is not a group. Which one of them is false? (A) It is not closed (B) 2 does not have an inverse (C) 3 does not have an inverse (D) 8 does not have an inverse 4. Then R is: (A) Neither a Partial Order nor an Equivalence Relation (B) A Partial Order but not a Total Order (C) A Total Order (D) An Equivalence Relation 5. 8. Let X.3. y ) R ( u. y and z respectively.2. v ) if x < u and y > v.gateforum.com. 7. No part of this booklet may be reproduced or utilized in any form without the written permission. Consider the polynomial p ( x ) = a0 + a1 x + a2 x 2 + a3 x 2 .5.Z be sets of sizes x. 2 and 6. respectively. 6. 20 and 30 time units and arrive at times 0. Ltd. Discuss this questions paper at www. Consider three CPU-intensive processes. For which one of the following reasons does Internet Protocol (IP) use the timeto-live (TTL) field in the IP datagram header? (A) Ensure packets reach destination within that time (B) Discard packets that reach later than that time (C) Prevent packets from looping indefinitely (D) Limit the time for which a packet gets queued in intermediate routers. The set {1. where ai ≠ 0. A relation R is defined on ordered pairs of integers as follows: ( x.Y.1 – Q. The number of functions from Z to E is: (A) Z 2 xy (B) Z × 2 xy (C) Z 2 x +y (D) 2 xyz 3. which require 10. Given below are four plausible reasons. E Given the items above.gateforum. which two of them will appear in the same set in the canonical sets-of-items for the grammar? (A) (i) and (ii) (B) (ii) and (iii) (C) (i) and (iii) (D) None of the above 8. Consider the following grammar. + E (iii) E → F + .E (ii) E → F .com needed if the operating system implements a shortest remaining time first scheduling algorithm? Do not count the context switches at time zero and at the end. (A) 1 (B) 2 (C) 3 (D) 4 7.gateforum. (i) S → S * . No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www. Which one of the following circuits (using clocked D flip-flops) will delay the phase of f by 180°? (A) f D Q D Q D Q clk (B) f D Q clk © All rights reserved by GATE Forum Educational Services Pvt. S → S*E S→E E →F +E E →F F → id Consider the following LR ( 0 ) items corresponding to the grammar above. Ltd. You are given a free running clock with a duty cycle of 50% and a digital waveform f which changes only at the negative edge of the clock.com. Page 2 of 29 .ECTest ID: 00 All India Mock GATE Test Series www. Page 3 of 29 . Consider a weighted complete graph G on the vertex set {ν 1 .com (C) f D Q D Q D Q clk (D) f D Q clk 9.gateforum.ν 2 .com.ν j ) is 2 i . the smallest element can be found in time (A) O ( n ) (B) O (log n ) (C) O (loglog n ) (D) O (1) 11. No part of this booklet may be reproduced or utilized in any form without the written permission.ECTest ID: 00 All India Mock GATE Test Series www. Discuss this questions paper at www.j .. In a binary max heap containing n numbers. The weight of a minimum spanning tree of G is: (A) n − 1 (B) 2n − 2 n (C) 2 (D) n2 12. Which one of the following is a legal program counter (all values in decimal)? (A) 400 (B) 500 (C) 600 (D) 700 10...ν n } such that the weight of the edge (ν i .. the data structure to be used is: (A) Queue © All rights reserved by GATE Forum Educational Services Pvt. To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time. Ltd.gateforum.. A program starts at address 300 (in decimal). A CPU has 24-bit instructions. i > 0. Page 4 of 29 . Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the following is true? (A) val ( j ) = θ (log n ) (B) val ( j ) = θ ( n) (C) val ( j ) = θ ( n ) (D) val ( j ) = θ ( n log n ) 16. i /= 2.ECTest ID: 00 All India Mock GATE Test Series www. Discuss this questions paper at www. Ltd. is stored in X[2i] and the right child.gateforum. if any. No part of this booklet may be reproduced or utilized in any form without the written permission. the left child. j +=i) . in X[2i+1]. Let S be an NP-complete problem and Q and R be two other problems not known to be in NP.gateforum. if any. the root is stored at X[1]. j = 0. Which one of the following statements is true? (A) R is NP-complete (B) R is NP-hard (C) Q is NP-complete (D) Q is NP-hard © All rights reserved by GATE Forum Educational Services Pvt. Indexing of X starts at 1 instead of 0. To be able to store any binary tree on n vertices the minimum size of X should be (A) log2 n (B) n (C) 2n + 1 (D) 2n − 1 14.com.com (B) Stack (C) Heap (D) B-Tree 13. Let val ( j ) denote the value stored in the variable j after termination of the for loop. j and n are integer variables. A scheme for storing binary trees in an array X is as follows. For a node stored at X[i]. for (i = n. Which one of the following in place sorting algorithms needs the minimum number of swaps? (A) Quick sort (B) Insertion sort (C) Selection sort (D) Heap sort 15. Consider the following C-program fragment in which i. We are given a set X = { x1 .... An element in an array X is called a leader if it is greater than all elements to the right of it in X.. The best algorithm to find all leaders in an array (A) Solves it in linear time using a left to right pass of the array (B) Solves it in linear time using a right to left pass of the array (C) Solves it using divide and conquer in time θ ( n log n ) ( ) (D) Solves it in time θ n2 18.gateforum. m ≥ 0} . that transfer 2000 to a mortgage payment and then apply a 5% interest.com. and { L3 = 0n+ m 1n+ m0n + m (A) L1 only (B) L3 only (C) L1 and L2 (D) L2 and L3 20.xn } where xi = 2i. T1 start 2. Discuss this questions paper at www. A sample S ⊆ X is drawn by selecting each xi independently with probability pi = 1 . Which of these languages are NOT context free? Let L1 = 0n + m1n 0m n. T2 B old=10000 new=10500 7. T2 start 6. When the system is restarted. T1 commit 5. T2 commit Suppose the database system crashes just before log record 7 is written. m ≥ 0 . m ≥ 0 . Consider the following log sequence of two transactions on a bank account. which one statement is true of the recovery procedure? (A) We must redo log record 6 to set B to 10500 (B) We must undo log record 6 to set B to 10000 and then redo log records 2 and 3 © All rights reserved by GATE Forum Educational Services Pvt..ECTest ID: 00 All India Mock GATE Test Series www. with initial balance 12000.. L2 = 0n + m1n + m 0m n. { } { } n.gateforum. T1 M old=0 new=2000 4. The expected value of the 2 smallest number in sample S is: (A) 1 n (B) 2 (C) n (D) n 19.com 17. 1. Ltd. Page 5 of 29 . No part of this booklet may be reproduced or utilized in any form without the written permission. T1 B old=1200 new=10000 3. Suppose there are two n × 1 vectors. n} and two arbitrary subsets A ⊆ N and B ⊆ N.com (C) We need not redo log records 2 and 3 because transaction T1 has committed (D) We can apply redo and undo operations in arbitrary order because they are idempotent. Q. 2.gateforum. For each element in a set of size 2n. 1 2n n 1 2 Let E. Given a set of elements N = {1. Let X = ( E I F ) − ( F I G ) and Y = ( E − ( E I G ) ) − ( E − F ) .gateforum. Page 6 of 29 . Which one of the following is true? (A) X ⊂ Y (B) X ⊃ Y (C) X = Y (D) X − Y ≠ ∅ and Y − X ≠ ∅ 23. F and G be finite sets. and Fu = b. u and ν such that u ≠ ν . b is an n × 1 real vector.75 Carry Two Marks Each 21.. Which one of the following statements is false? (A) Determinant of F is zero (B) There are an infinite number of solutions to Fx = b (C) There is an x ≠ 0 such that Fx = 0 (D) F must have two identical rows 24.ECTest ID: 00 All India Mock GATE Test Series www. The probability that exactly n elements are chosen is: 2n n (A) n 4 2n n (B) n 2 (C) (D) 22. Ltd. Discuss this questions paper at www. an unbiased coin is tossed. where min ( S ) is the smallest integer in the set of © All rights reserved by GATE Forum Educational Services Pvt..... F is an n × n real matrix.com. Fν = b. An element is chosen if the corresponding coin toss were head. No part of this booklet may be reproduced or utilized in any form without the written permission.21 – Q. how many of the n ! permutations π from N to N satisfy min (π ( A ) ) = min (π ( B ) ) . The 2n coin tosses are independent.. ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com integers S, and π ( S ) is the set of integers obtained by applying permutation π to each element of S ? (A) (n − AUB) A B (B) (A + B 2 (C) n ! )n 2 AIB AUB (D) A I B 25. 2 2 n AUB Let S = {1, 2, 3,........, m} , m > 3. Let X1......X n be subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f ( i ) is the number of sets X j that contain the element i. That is f ( i ) = {j i ∈ X } . j m Then ∑ f ( i ) is: i =1 (A) 3m (B) 3n (C) 2m + 1 (D) 2n + 1 26. Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. (A) ∀x ( tiger ( x ) ∧ lion ( x ) ) → {(hungry ( x ) ∨ threatened ( x )) → attacks ( x )} (B) ∀x ( tiger ( x ) ∨ lion ( x ) ) → {(hungry ( x ) ∨ threatened ( x ) ) ∧ attacks ( x )} { } (C) ∀x ( tiger ( x ) ∨ lion ( x ) ) → attacks ( x ) → (hungry ( x ) ∨ threatened ( x ) ) (D) ∀x ( tiger ( x ) ∨ lion ( x ) ) → 27. {(hungry ( x ) ∨ threatened ( x )) → attacks ( x )} Consider the following propositional statements: ) (( A → C ) ∧ (B → C )) P2 : ( ( A ∨ B ) → C ) ) ≡ ( ( A → C ) ∨ ( B → C ) ) P1 : ( ( A ∧ B ) → C ) ≡ Which one of the following is true? (A) P1 is a tautology, but not P2 (B) P2 is a tautology, but not P1 (C) P1 and P2 are both tautologies (D) Both P1 and P2 are not tautologies © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 7 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com 28. A logical binary relation , is defined as follows: A B A B True True True True False True False True False False False True Let ~ be the unary negation (NOT) operator, with higher precedence then Which one of the following is equivalent to A ∧ B ? (A) (~ A (B) ~ ( A 29. B) ~ B) (C) ~ (~ A ~ B) (D) ~ (~ A B) If . s is a string over ( 0 + 1) * then let n0 ( s ) denote the number of 0’s in s and n1 ( s ) the number of 1’s in s. Which one of the following languages is not regular? (A) L = {s ∈ ( 0 + 1) * n0 ( s ) is a 3-digit prime} { } (B) L = s ∈ ( 0 + 1) * for every prefix s′ of s, n0 ( s′ ) − n1 ( s′ ) ≤ 2 { } (C) L = s ∈ ( 0 + 1) * n0 ( s ) − n1 ( s ) ≤ 4 (D) L = {s ∈ ( 0 + 1) * n0 ( s ) mod 7 = n1 ( s ) mod 5 = 0} 30. For S ∈ ( 0 + 1) * let d ( s ) denote the decimal value of s (e.g. d (101) = 5 ). Let L = {s ∈ ( 0 + 1) * d ( s ) mod5 = 2 and d ( s ) mod7 ≠ 4} Which one of the following statements is true? (A) L is recursively enumerable, but not recursive (B) L is recursive, but not context-free (C) L is context-free, but not regular (D) L is regular 31. Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V , E ) with V divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true? © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 8 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com (A) Both DHAM3 and SHAM3 are NP-hard (B) SHAM3 is NP-hard, but DHAM3 is not (C) DHAM3 is NP-hard, but SHAM3 is not (D) Neither DHAM3 nor SHAM3 is NP-hard 32. Consider the following statements about the context free grammar G = {S → SS, S → ab, S → ba, S →∈} I. G is ambiguous II. G produces all strings with equal number of a’s and b’s III. G can be accepted by a deterministic PDA. Which combination below expresses all the true statements about G? (A) I only (B) I and III only (C) II and III only (D) I, II and III 33. Let L1 be a regular language, L2 be a deterministic context-free language and L3 a recursively enumerable, but not recursive, language. Which one of the following statements is false? (A) L1 I L2 is a deterministic CFL (B) L3 I L1 is recursive (C) L1 U L2 is context free (D) L1 I L2 I L3 is recursively enumerable 34. Consider the regular language L = (111 + 11111) * . The minimum number of states in any DFA accepting this languages is: (A) 3 (B) 5 (C) 8 (D) 9 35. x 0 MUX 1 y z 0 MUX f 1 x y © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 9 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com Consider the circuit above. Which one of the following options correctly represents f ( x, y , z ) ? (A) x z + xy + yz (B) x z + xy + yz (C) xz + xy + yz (D) xz + xy + yz 36. Given two three bit numbers a2 a1 a0 and b2 b1b0 and c, the carry in, the function that represents the carry generate function when these two numbers are added is: (A) a2 b2 + a2 a1b1 + a2 a1a0 b0 + a2 a0 b1b0 + a1b2 b1 + a1 a0 b2 b0 + a0 b2 b1 b0 (B) a2 b2 + a2 b1b0 + a2 a1b1b0 + a1 a0 b2 b1 + a1a0 b2 + a1a0 b2 b0 + a2 a0 b1 b0 (C) a2 + b2 + ( a2 ⊕ b2 ) ( a1 + b1 + ( a1 ⊕ b1 ) ( a0 + b0 ) ) (D) a2 b2 + a2 a1b1 + a2 a1a0 b0 + a2 a0 b1b0 + a1 b2 b1 + a1 a0 b2 b0 + a0 b2 b1 b0 37. Consider the circuit in the diagram. The ⊕ operator represents Ex-OR. The D flipflops are initialized to zeroes (cleared). q2 Q D clk q1 Q D q0 clk Q D data clk clock The following data: 100110000 is supplied to the “data” terminal in nine clock cycles. After that the values of q2q1q0 are: (A) 000 (B) 001 (C) 010 (D) 101 38. Consider a Boolean function f (w, x, y , z ) . suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = w1 , x1 , y1 , z1 and i2 = w2 , x2 , y2 , z2 , we would like the function to remain true as the input i1 to i2 ( i1 and i2 differ in exactly one bit position) , without changes becoming from false © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 10 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com momentarily. Let f (w, x, y , z ) = ∑ (5, 7,11,12,13,15) . Which of the following cube covers of f will ensure that the required property is satisfied? (A) wxz, wxy , xyz, xyz, wyz (B) wxy , wxz, wyz (C) wxyz, xz, wxyz (D) wzy , wyz, wxz, wxz, xyz, xyz 39. We consider the addition of two 2’s complement numbers bn −1bn −2....b0 and an −1an −2....a0 . A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by cn −1cn −2....c0 and the carry-out by cout . Which one of the following options correctly identifies the overflow condition? ( (A) cout an −1 ⊕ bn −1 ) (B) an −1bn −1 cn −1 + an −1bn −1cn −1 (C) cout ⊕ cn −1 (D) an −1 ⊕ bn −1 ⊕ cn −1 40. Consider numbers represented in 4-bit gray code. Let h3 h2 h1h0 be the gray code representation of a number ( n + 1) (modulo 16 ) value n and let g3 g2 g1 g0 be the gray code of of the number. Which one of the following functions is correct? (A) g0 ( h3 h2 h1h0 ) = (B) g1 (C) g2 (D) g3 41. ∑ (1, 2, 3, 6,10,13,14,15) ( h h h h ) = ∑ ( 4, 9,10,11,12,13,14,15) ( h h h h ) = ∑ (2, 4,5, 6, 7,12,13,15) ( h h h h ) = ∑ ( 0,1, 6, 7,10,11,12,13) 3 2 1 0 3 2 1 0 3 2 1 0 A CPU has a cache with block size 64 bytes. The main memory has k banks, each bank being c bytes wide. Consecutive c − byte chunks are mapped on consecutive banks with wrap-around. All the k banks can be accessed in parallel, but two accesses to the same bank must be serialized. A cache block access may involve multiple iterations of parallel bank accesses depending on the amount of data obtained by accessing all the k banks in parallel. Each iteration requires k decoding the bank numbers to be accessed in parallel and this takes ns. The 2 latency of one bank access is 80 ns. If c = 2 and k = 24, the latency of retrieving a cache block starting at address zero from main memory is: (A) 92 ns (B) 104 ns (C) 172 ns © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 11 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com (D) 184 ns 42. A CPU has a five-stage pipeline and runs at 1 GHz frequency. Instruction fetch happens in the first stage of the pipeline. A conditional branch instruction computes the target address and evaluates the condition in the third stage of the pipeline. The processor stops fetching new instructions following a conditional branch until the branch outcome is known. A program executes 109 instructions out of which 20% are conditional branches. If each instruction takes one cycle to complete on average, the total execution time of the program is: (A) 1.0 second (B) 1.2 seconds (C) 1.4 seconds (D) 1.6 seconds 43. Consider a new instruction named branch-on-bit-set (mnemonic bbs). The instruction “bbs reg, pos, label” jumps to label if bit in position pos of register operand reg is one. A register is 32 bits wide and the bits are numbered 0 to 31, bit in position 0 being the least significant. Consider the following emulation of this instruction on a processor that does not have bbs implemented. temp ← reg & mask Branch to label if temp is non-zero. The variable temp is a temporary register. For correct emulation, the variable mask must be generated by (A) mask ← 0 × 1 pos (B) mask ← 0 × ffffffff pos (C) mask ← pos (D) mask ← 0 × f 44. Station A uses 32 byte packets to transmit messages to Station B using a sliding window protocol. The round trip delay between A and B is 80 milliseconds and the bottleneck bandwidth on the path between A and B is 128 kbps. What is the optimal window size that A should use? (A) 20 (B) 40 (C) 160 (D) 320 45. Two computers C1 and C2 are configured as follows. C1 has IP address 203.197.2.53 and netmask 255.255.128.0. C2 has IP address 203.197.75.201 and netmask 255.255.192.0. which one of the following statements is true? © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 12 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com (A) C1 and C2 both assume they are on the same network (B) C2 assumes C1 is on same network, but C1 assumes C2 is on a different network (C) C1 assumes C2 is on same network, but C2 assumes C1 is on a different network (D) C1 and C2 both assume they are on different networks. 46. Station A needs to send a message consisting of 9 packets to Station B using a sliding window (window size 3) and go-back-n error control strategy. All packets are ready and immediately available for transmission. If every 5th packet that A transmits gets lost (but no acks from B ever get lost), then what is the number of packets that A will transmit for sending the message to B? (A) 12 (B) 14 (C) 16 (D) 18 47. Consider the following graph: 2 b 1 a d 4 1 2 3 3 f 5 6 c 4 e 7 Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal’s algorithm? (A) ( a − b) , (d − f ) , ( b − f ) , (d − c ) , (d − e ) (B) ( a − b) , (d − f ) , (d − c ) , ( b − f ) , (d − e ) (C) (d − f ) , ( a − b ) , (d − c ) , ( b − f ) , (d − e ) (D) (d − f ) , ( a − b ) , ( b − f ) , (d − e ) , (d − c ) © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 13 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com 48. Let T be a depth first search tree in an undirected graph G. Vertices u and ν are leaves of this tree T . The degrees of both u and ν in G are at least 2. which one of the following statements is true? (A) There must exist a vertex w adjacent to both u and ν in G (B) There must exist a vertex w whose removal disconnects u and ν in G (C) There must exist a cycle in G containing u and ν (D) There must exist a cycle in G containing u and all its neighbours in G. 49. An implementation of a queue Q, using two stacks S1 and S2, is given below: void insert (Q, x) { push (S1, x); } void delete (Q) { if (stack-empty(S2)) then if (stack-empty(S1)) then { print(“Q is empty”); return; } else while (!(stack-empty(S1))){ x=pop(S1); push(S2,x); } x=pop(S2); } Let n insert and m ( ≤ n ) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n ? (A) n + m ≤ x < 2n and 2m ≤ y ≤ n + m (B) n + m ≤ x < 2n and 2m ≤ y ≤ 2n (C) 2m ≤ x < 2n and 2m ≤ y ≤ n + m (D) 2m ≤ x < 2n and 2m ≤ y ≤ 2n 50. A set X can be represented by an array x n as follows: if i ∈ X 1 x i = 0 otherwise Consider the following algorithm in which x, y and z are Boolean arrays of size n: algorithm zzz(x[ ], y[ ], z [ ] ) { int i; © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 14 of 29 ECTest ID: 00 All India Mock GATE Test Series www.gateforum.com for(i=0;i<n;++i) z[i] = (x[i] ∧ ~y[i]) ∨ (~x[i] ∧ y[i]) } The set Z computed by the algorithm is: 51. (A) (X U Y ) (B) (X I Y ) (C) ( X − Y ) I (Y − X) (D) ( X − Y ) U (Y − X) Consider the following recurrence: ( ) T ( n ) = 2T n + 1, T (1) = 1 Which one of the following is true? (A) T ( n ) = θ (loglog n ) (B) T ( n ) = θ (log n ) (C) T ( n ) = θ ( n) (D) T ( n ) = θ ( n ) 52. The median of n elements can be found in O ( n ) time. Which one of the following is correct about the complexity of quick sort, in which median is selected as pivot? (A) θ ( n ) (B) θ ( n log n ) ( ) θ (n ) (C) θ n2 (D) 53. 3 Consider the following C-function in which a n and b m are two sorted integer arrays and c n + m be another integer array. void xyz(int a[], int b [], int c []){ int i,j,k; i=j=k=0; while ((i<n) && (j<m)) if (a[i] < b[j]) c[k++] = a[i++]; else c[k++] = b[j++]; } © All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this questions paper at www.gateforum.com. Page 15 of 29 gateforum. int j) { { int x = a[i+2]. No part of this booklet may be reproduced or utilized in any form without the written permission.. Page 16 of 29 . work2 will compute the same output and have the same effect on program state as work1 S2: All the transformations applied to work1 to get work2 will always improve the performance (i. an and b1 . Ltd...e. bn where each number is 0 or 1. k = m + i − 1.. a[j] = x+1. Given two arrays of numbers a1 .. for any program state and input arguments. int i. int i. a[j] = t2+1. int t1 = i+2. the fastest algorithm to find the largest span ( i.com Which of the following condition(s) hold(s) after the termination of the while loop? (i) j < m.5 (C) Takes Θ ( n ) time and space (D) Takes O 55. int t2 = a[t1]..gateforum. and b m − 1 ≤ a i if j = m (A) only (i) (B) only (ii) (C) either (i) or (ii) but not both (D) neither (i) nor (ii) 54.com.. return a[i+2] – 3. or report that there is not such span. j ) such that ai + ai +1 + . k = n + j − 1. } S1: The transformation form work1 to work2 is valid.. Discuss this questions paper at www.. + bj .. ( n ) time only if the sum of the 2n elements is an even number Consider these two functions and two statements S1 and S2 about them. int work1(int *a. and a n − 1 < b j if i = n (ii) i < n.. int j) int work2(int *a. + aj = bi + bi +1 + . ( ) O (n ) (A) Takes O 3n (B) Takes 3 ( ) and Ω ( n ) time in the key comparison model and Ω 2n time if hashing is permitted 2. i.e reduce CPU time) of work2 compared to work1 (A) S1 is false and S2 is false (B) S1 is false and S2 is true (C) S1 is true and S2 is false (D) S1 is true and S2 is true © All rights reserved by GATE Forum Educational Services Pvt.ECTest ID: 00 All India Mock GATE Test Series www.. } return t2 – 3.. *px. subroutine swap(ix.ECTest ID: 00 All India Mock GATE Test Series www. Consider this C code to swap two integers and these five statements: the code void swap (int *px. initialize it to 13. int *py) { *px = *px . Page 17 of 29 . ib end S1: The compiler will generate code to allocate a temporary nameless cell. *px = *py .*py.com 56. Consider the following code written in a pass-by-reference language like FORTRAN and these statements about the code. } S1: will generate a compilation error S2: may generate a segmentation fault at runtime depending on the arguments passed S3: correctly implements the swap procedure for all input pointers referring to integers stored in memory locations accessible to the process © All rights reserved by GATE Forum Educational Services Pvt. 1b+5) print *. *py = *px + *py. ia.iy) it = ix L1 : ix = iy L2 : iy = it end ia = 3 ib = 8 call swap (ia. Ltd.gateforum.com. Discuss this questions paper at www.gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission. and pass the address of the cell swap S2: On execution the code will generate a runtime error on line L1 S3: On execution the code will generate a runtime error on line L2 S4: The program will print 13 and 8 S5: The program will print 13 and -2 Exactly the following set of statement(s) is correct: (A) S1 and S2 (B) S1 and S4 (C) S3 (D) S1 and S5 57. M S.} Here id is a token that represents an integer and id.ECTest ID: 00 All India Mock GATE Test Series www. i++) { for (j=0. Ltd. S → ER R → *E {print ('*') . No part of this booklet may be reproduced or utilized in any form without the written permission. © All rights reserved by GATE Forum Educational Services Pvt. Consider the following C code segment. Discuss this questions paper at www. y += (7 + 4*j).value represents the corresponding integer value.com. j++) { if (i%2) { x += (4*j + 5*i). (A) S1 (B) S2 and S3 (C) S2 and S4 (D) S2 and S5 58.value ) . Consider the following grammar: S → FR R → *S ε F → id In the predictive parser table. j<n. For an input ' 2 * 3 + 4 '. $ respectively.com S4: implements the swap procedure correctly for some but not all valid input pointers S5: may add or subtract integers and pointers.} R ε E → F + E {print ('+') . for (i – 0.gateforum. this translation scheme prints (A) 2 * 3 + 4 (B) 2 * +3 4 (C) 2 3 * 4 + (D) 2 3 4+* 60. (A) {S → FR} and {R → ε } (B) {S → FR} and (C) {S → FR} and {R → *S} (D) {F M. 59.} F F → ( S ) id {print (id.gateforum. of the grammar the entries {} → id} and {R → ε } Consider the following translation scheme. Page 18 of 29 . i<n. id and M R. void P (binary_semaphore *s) { unsigned y. unsigned *x = &(s->value).gateforum. A CPU generates 32-bit virtual addresses.gateforum. Discuss this questions paper at www. } Which one of the following is true? (A) The implementation may not work if context switching is disabled in P (B) Instead of using fetch-and –set. The atomic fetch-and-set x. } while (y). a pair of normal load/store can be used (C) The implementation of V is wrong (D) The code does not implement a binary semaphore 62. Which one of the following is true? (A) Efficient implementation of multi-user support is no longer possible © All rights reserved by GATE Forum Educational Services Pvt. The processor has a translation look-aside buffer (TLB) which can hold a total of 128 page table entries and is 4-way set associative. The page size is 4 KB. y. the operating system designers decide to get rid of the virtual memory entirely. The minimum size of the TLB tag is: (A) 11 bits (B) 13 bits (C) 15 bits (D) 20 bits 63. A computer system supports 32-bit virtual addresses as well as 32-bit physical addresses. } void V (binary_semaphore *s) { S->value = 0. No part of this booklet may be reproduced or utilized in any form without the written permission. do { fetch-and-set x. Ltd. Page 19 of 29 . Since the virtual address space is of the same size as the physical address space. y instruction unconditionally sets the memory location x to 1 and fetches the old value of x n y without allowing any intervening access to the memory location x.com.ECTest ID: 00 All India Mock GATE Test Series www. consider the following implementation of P and V functions on a binary semaphore S.com } } } Which one of the following is false? (A) The code contains loop invariant computation (B) There is scope of common sub-expression elimination in this code (C) There is scope of strength reduction in this code (D) There is scope of dead code elimination in this code 61. Consider the longest remaining time first (LRTF) scheduling algorithm. 2 respectively) with compute time bursts 2.4% 66. Consider three processes. currently.q y k (C) max ( x p . 20 and 30 units.com. process i has placed a request for an additional y i instances while holding the xi instances it already has. Consider the following snapshot of a system running n processes. all arriving at time zero. Consider the relation account (customer. Process i is holding xi instances of a resource R. ties are © All rights reserved by GATE Forum Educational Services Pvt. for all i.gateforum. xq ) > 1 67. Discuss this questions paper at www. There are exactly two processes p and q such that y p = yq = 0.6% (C) 30. and the last 10% of time doing I/O again. The average turn around time is: (A) 13 units (B) 14 units (C) 15 units (D) 16 units 65. xq ) > 1 (D) min ( x p . We would like to rank customers according to decreasing balance. all instances of R are occupied. 1. the next 70% of time doing computation. Further. Consider three processes (process id 0. with total execution time of 10. The operating system uses a shortest remaining compute time first scheduling algorithm and schedules a new process either when the running process gets blocked on I/O or when the running process finishes its compute burst. Assume that all I/O operations can be overlapped as much as possible. 4 and 8 time units.q y k (B) x p + xq ≥ mink ≠ p. In LRTF ties are broken by giving priority to the process with the lowest process id. The customer with the largest balance gets rank 1.gateforum. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock? (A) min ( x p .com (B) The processor cache organization can be made more efficient now (C) Hardware support for memory management is no longer needed (D) CPU scheduling can be made more efficient now 64. Page 20 of 29 . respectively.0% (D) 89. All processes arrive at time zero. xq ) < maxk ≠ p. Ltd. For what percentage of time does the CPU remain idle? (A) 0% (B) 10. No part of this booklet may be reproduced or utilized in any form without the written permission. 1 ≤ i ≤ n. Each process spends the first 20% of execution time doing I/O.ECTest ID: 00 All India Mock GATE Test Series www. balance) where customer is a primary key and there are no null values. Neither Query1 nor Query2 is a correct implementation of the specification 5.balance group by A. Ltd.customer) Query2: from account A. account B where A.ECTest ID: 00 All India Mock GATE Test Series www.balance group by A.student = paid.com.balance <=B. No part of this booklet may be reproduced or utilized in any form without the written permission. paid P where E.customer. Both Query1 and Query2 are correct implementation of the specification 3. account B where A.student Query4:select student from paid where exists (select * from enrolled where enrolled. course) in which (student. and the relation paid (student. course) is the primary key.com not broke but ranks are skipped: if exactly two customers have the largest balance they each get rank 1 and rank 2 is not assigned. Discuss this questions paper at www. Given the following four queries: Query1:select student from enrolled where student in (select student from paid) Query2:select student from paid where student in (select student from enrolled) Query3:select E. Assigning rank with a pure relational query takes less time than scanning in decreasing balance order assigning ranks using ODBC.customer) Query1: from account A. amount) where student is the primary key.gateforum. count(B. Which two of the above statements are correct? (A) 2 and 5 (B) 1 and 3 (C) 1 and 4 (D) 3 and 5 68. Assume no null values and no foreign keys or integrity constraints. Query1 is a correct implementation of the specification but Query2 is not 4. 1+count(B.customer. select A. Query1 will produce the same row set as Query2 for some but not all databases.student) Which one of the following statements is correct? (A) All queries return identical row sets for any database (B) Query2 and Query4 return identical row sets for all databases but there exist databases for which Query1 and Query2 return different row sets.customer select A.student from enrolled E. 1. 2.gateforum.balance < B.customer Consider these statements about Query1 and Query2. Consider the relation enrolled (student.student = P. (C) There exist databases for which Query3 returns strictly fewer rows than Query2 © All rights reserved by GATE Forum Educational Services Pvt. Page 21 of 29 . 7000.com. Consider the relation enrolled (student.ECTest ID: 00 All India Mock GATE Test Series www. 69. amount) where student is the primary key. No part of this booklet may be reproduced or utilized in any form without the written permission. Page 22 of 29 . Assume no null values and no foreign keys or integrity constraints. Plan 1 executes faster than Plan 2 for all databases (D) For x = 9000. 70. select amount > x paid enrolled Probe index on student Sequential scan Indexed nested loop join Indexed nested loop join Project on course Select on amount > x Project on course A disk seek takes 4ms.gateforum. Ltd. Plan I executes slower than Plan 2 for all databases. 8000. The following functional dependencies are given: AB → CD. and the relation paid (student. C → G. DE → F .com (D) There exist databases for which Query4 will encounter an integrity violation at runtime. disk data transfer bandwidth is 300 MB/s and checking a tuple to see if amount is greater than x takes 10µs. Assume that amounts 6000. Which of the following statements is correct? (A) Plan 1 and Plan 2 will not output identical row sets for all databases (B) A course may be listed more than once in the output of Plan 1 for some databases (C) For x = 5000. Which one of the following options is false? (A) {CF } (B) {BG} (C) { AF } (D) { AB} + = { ACDEFG} + = { ABCDG} + = { ACDEFG} + = { ABCDFG} © All rights reserved by GATE Forum Educational Services Pvt. course) is the primary key. Plan 2 on right) to “list all courses taken by students who have paid more than x” enrolled Probe index on student paid Sequential scan. G → A. AF → D.gateforum. Consider these query plans (Plan 1 on left. course) in which (student. Discuss this questions paper at www. 9000 and 10000 were each paid by 20% of the students. F → E . 3 ns (C) 1. 71.com Common Data Questions: Common Data for Questions 71. Page 23 of 29 . 75: Consider two cache organizations: The first one is 32 KB 2-way set associative with 32byte block size.7 ns 75. for n ≥ 6 . The hit latency of the set associative organization is h1 while that of the direct mapped one is h2.com. Discuss this questions paper at www. The number of connected components in G is: (A) n (B) n + 2 (C) 2n 2 (D) 2n n Common Data for Questions 74. The value of h1 is: (A) 2. 72.ECTest ID: 00 All India Mock GATE Test Series www. The size of an address is 32 bits in both cases. The second one is of the same size but direct mapped. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. The value of h2 is: (A) 2. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. A 2-to-1 multiplexer has a latency of 0.8 ns (D) 1.gateforum.6 ns while a kbit comparator has a latency of k 10 ns. 73: The 2n vertices of a graph G corresponds to all subsets of a set of size n. 74.4 ns (B) 2. The maximum degree of a vertex in G is: n 2 n 2 (A) 2 2 (B) 2n−2 (C) 2n −3 × 3 (D) 2n−1 73. The number of vertices of degree zero in G is: (A) 1 (B) n (C) n + 1 (D) 2n 72.4 ns © All rights reserved by GATE Forum Educational Services Pvt.gateforum. Which one of the following is the sequence of items in the array representing the resultant heap? (A) 10. No part of this booklet may be reproduced or utilized in any form without the written permission. each process in the set arrives at the barrier and waits for all others to arrive and then all processes leave the barrier. Let the number of processes in the set be three and S be a binary semaphore with the usual P and V functions. 2. The nodes from the second level of the tree from left to right are stored from a[4] location onward. 3. 3.e. 6. 3 (D) 10. 3. 10 and 4 are inserted. Which one of the following is a valid sequence of elements in an array representing 3-ary max heap? (A) 1. nodes in the next level.76 to Q85 Carry Two Marks Each Statement for Linked Answer Questions 76 & 77: A 3-ary max heap is like a binary max heap. 2.3 ns (C) 1. 5. 1. 76. 6. 1 (C) 10. 9. Ltd.gateforum. 6. 5 Statement for Linked Answer Questions 78 & 79: Barrier is a synchronization construct where a set of processes synchronizes globally i. 7.com. 1 (D) 9. Suppose the elements 7. 7. 4. 8. 3. 4. Consider the following C implementation of a barrier with line numbers shown on left. 2. in that order.gateforum. 4. from left to right. 6. 6. 2.8 ns (D) 1. 6. is stored from a[1] to a[3].7 ns Linked Answer Questions: Q. 1 77. 5. 3. 7. 9 (B) 9.76. a[0]. A 3-ary heap can be represented by an array as follows: The root is stored in the first location. 8. 3. 9. 9. 9. Q. 5 (C) 9. 8. 1. 2. 5. 1. 5. into the valid 3ary max heap found in the above question. 6.com (B) 2. 8. void barrier (void) { © All rights reserved by GATE Forum Educational Services Pvt. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property. 5. but instead of 2 children. 7. nodes have 3 children. 8. Discuss this questions paper at www. 8. 5. 8. 4 (B) 10.ECTest ID: 00 All India Mock GATE Test Series www. Page 24 of 29 . 3. 6. 1. 8. 9: process_left = 0.com.ECTest ID: 00 All India Mock GATE Test Series www. In a concurrent program all the three processes call the barrier function when they need to synchronize globally. Which one of the following is true? (A) The barrier implementation is wrong due to the use of binary semaphore S (B) The barrier implementation may lead to a deadlock if two barrier in invocations are used in immediate succession. 79. 6: process_left++. 10: } 11: V(S). j<512. i<512. Consider the following two C code segments.gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission.gateforum. 2: process_arrived++. Suppose A is a twodimensional array of size 512×512 with elements that occupy 8-bytes each. (C) Context switch is disabled at the beginning of the barrier and re-enabled at the end. j++) { x +=A[i] [j]. 5: P(S). 4: while (process_arrived !=3). Which one of the following rectifies the problem in the implementation? (A) Lines 6 to 10 are simply replaced by process_arrived-(B) At the beginning of the barrier the first process to enter the barrier waits until process_arrived becomes zero before proceeding to execute P(S). Discuss this questions paper at www. The above implementation of barrier is incorrect. (D) The variable process_left is made private instead of shared Statement for Linked Answer Questions 80 & 81: A CPU has a 32 KB direct mapped cache with 128-byte block size.com 1: P(S). } The variables process_arrived and process_left are shared among all processes and are initialized to zero. (C) Lines 6 to 10 need not be inside a critical section (D) The barrier implementation is correct if there are only two processes instead of three. 3. Page 25 of 29 . P1: for (i=0. 78. } } © All rights reserved by GATE Forum Educational Services Pvt. 7: if (process_left==3) { 8: process_arrived = 0. P1 and P2. Ltd. i++) { for (j=0. V(S). } } P1 and P2 are executed independently with the same initial state. Port conflicts are always resolved in favour of the port with the lower index value. the root sends out (one or more) data units to enable the setting up of the spanning tree of shortest paths from the root bridge to each bridge. j. First. Discuss this questions paper at www. x are in registers. 80. When there is a possibility of multiple bridges forwarding to the same LAN (but not through the root port). the array A is not in the cache and i. i<512.ECTest ID: 00 All India Mock GATE Test Series www. Next. Page 26 of 29 . In order to avoid packets looping through circuits in the graph.gateforum. the root bridge is identified as the bridge with the least serial number. the bridges organize themselves in a spanning tree.com. © All rights reserved by GATE Forum Educational Services Pvt. the one with the lowest serial number is preferred.gateforum. The value of the ratio M1 is: M2 (A) 0 (B) 1 16 (C) 1 8 (D) 16 Statement for Linked Answer Questions 82 & 83: Consider the diagram shown below where a number of LANs are connected by (transparent) bridges. ties are broken as follows: bridges closest to the root get preference and between such bridges. j<512.com P2: for (i=0. Let the number of cache misses experienced by P1 be M1 and that for P2 be M2. Each bridge identifies a port (the root port) through which it will forward frames to the root bridge. The value of M1 is: (A) 0 (B) 2048 (C) 16384 (D) 262144 81. i++) { for (j=0. No part of this booklet may be reproduced or utilized in any form without the written permission. namely. Ltd. j++) { x +=A[j] [i]. B3. Which of the following options represents the correct forwarding table on B3? (A) (B) Hosts Port H1. Ltd. B4 (C) B1. B4 (D) B1.gateforum. B3. B2 83. B2 (B) B1. B2.com B1 H1 1 H2 2 H4 H3 2 3 4 B5 1 B3 3 4 1 H6 H5 H7 2 1 H9 82. H9. B5. B5. Page 27 of 29 .gateforum. 2 2 H8 1 B4 B2 3 3 H10 H11 H12 For the given connection of LANs by bridges. Discuss this questions paper at www. B5.ECTest ID: 00 All India Mock GATE Test Series www. Let host H1 send out a broadcast ping packet. B4. Consider the correct spanning tree for the previous question. B3. H4 3 H5. H6. No part of this booklet may be reproduced or utilized in any form without the written permission. B5. B2. H10 1 © All rights reserved by GATE Forum Educational Services Pvt. which one of the following choices represents the depth first traversal of the spanning tree of bridges? (A) B1.com. B4. H2. B3. H3. H7. (D) S → A C CB S → A C CB C → aC b ∈ C → aC b ∈ A → aA ∈ A → aA a B → Bb ∈ B → Bb b In the correct grammar above. H8.gateforum. H12 4 H7. { } Which one of the following grammars generates the language L = ai b j i ≠ j ? (B) S → aS Sb a b (A) S → A C CB C → aC b a b A → aA ∈ B → Bb ∈ (C) 85.H11. H4 3 H5. H6 1 H7.Hosts Port ECTest ID: 00 All India Mock GATE H1. Discuss this questions paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission. H11. H10 1 H5. H11. Page 28 of 29 . H8. H9. H10. H9. H11. H10 1 H1. H3. H4 3 H1. m ) + 2 (B) l + m + 2 (C) l + m + 3 (D) max ( l . H4 3 H5. Ltd. H2 4 H7. H6. H8.com 4 H7.Test H2 Series www.com. H8. what is the length of the derivation (number of steps starring from S) to generate the string al bm with l ≠ m ? (A) max ( l .H12 2 (D) Hosts Port Hosts Port H3. H12 2 (C) H3. H2. m ) + 3 © All rights reserved by GATE Forum Educational Services Pvt.gateforum. H9. H12 2 Statement for Linked Answer Questions 84 & 85: 84. gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission.ECTest ID: 00 All India Mock GATE Test Series www.com. Ltd. Discuss this questions paper at www. Page 29 of 29 .gateforum.com © All rights reserved by GATE Forum Educational Services Pvt. (B) n2 and n n (B) 2n (C) 22 2 (D) 2n Let G be the non-planar graph with the minimum possible number of edges. Page 1 of 19 . 2 1 5 4 6 3 Which of the following is NOT a topological ordering? (A) 1 2 3 4 5 6 6.1 – Q. shown below. 4. 3. 6} . (D) Equivalence problem for FSAs.gateforum. 5. The number of ordered pairs in the largest and the smallest equivalence relations on S are: (A) n and n 3. (C) Both P and Q are true.gateforum. (A) P is true and Q is false. Let S be a set of n elements. 2. f ( x ) is continuous for all real values of x Q.20 Carry One Mark Each 1. Ltd.5. (C) Finiteness problem for FSAs.com Q. No part of this booklet may be reproduced or utilized in any form without the written permission. © All rights reserved by GATE Forum Educational Services Pvt. (B) 1 3 2 4 5 6 (C) 1 3 2 4 6 5 (D) 3 2 4 1 6 5 Which of the following problems is undecidable? (A) Membership problem for CFGs. Discuss this questions paper at www. (B) P is false and Q is true. (B) Ambiguity problem for CFGs. Consider the following two statements about the function f ( x ) = x : P. f ( x ) is differentiable for all real values of x Which of the following is TRUE? 2. Then G has (A) 9 edges and 5 vertices (B) 9 edges and 6 vertices (C) 10 edges and 5 vertices (D) 10 edges and 6 vertices Consider the DAG with V = {1. (C) n2 and 0 (D) n and 1 What is the maximum number of different Boolean functions involving n Boolean variables? (A) n2 4. (D) Both P and Q are false.CS GATE Paper 2007 www.com. 512 bytes of data are stored in a bit serial manner in a sector. (D) Infinite union of finite sets is regular. (D) 9. 28 bits (C) 512 Mbyte. 7. How many 3-to-8 line decoders with an enable input are needed to construct a 6to-64 line decoder without using any other logic gates? (A) 7 9. 20 bits (D) 64 Gbyte. x . (B) 8 (C) 9 (D) 10 Consider the following Boolean function of four variables: f (w. The capacity of the disk pack and the number of bits required to specify a particular sector in the disk are respectively: (A) 2h − 1 13. (A) independent of one variables. (B) Every finite subset of a non-regular set is regular. The number of bits in the TAG. 6 (B) 5 (C) 4 (D) 3 Which of the following sorting algorithms has the lowest worst-case complexity? (A) Merge sort (B) Bubble sort (C) Quick sort (D) Selection sort © All rights reserved by GATE Forum Educational Services Pvt. No part of this booklet may be reproduced or utilized in any form without the written permission. 5. z ) = ∑ (1. 8.gateforum. 28 bits The height of a binary tree is the maximum number of edges in any root to leaf path.CS GATE Paper 2007 7. Ltd.gateforum. LINE and WORD fields are respectively: (A) 9. 5. (B) 7. 128 tracks per surface and 256 sectors per track. (D) dependent on all the variables. Consider a 4-way set associative cache consisting of 128 lines with a line size of 64 words. The maximum number of nodes in a binary tree of height h is: (B) 2h−1 − 1 (C) 2h+1 − 1 (D) 2h+1 The maximum number of binary trees that can be formed with three unlabeled nodes is: (A) 1 14. 6. The CPU generates a 20-bit address of a word in main memory.3. 4.com Which of the following is TRUE? (A) Every subset of a regular set is regular. 6 (A) 256 Mbyte. www. 5 11.14) The function is: 10. y . (C) independent of three variables. Discuss this questions paper at www. (B) independent of two variables. 19 bits (B) 256 Mbyte. Page 2 of 19 . 12. 9.com. (C) The union of two non-regular sets is not regular. 6. 8 Consider a disk pack with 16 surfaces.12.11. (C) 7. com. (D) None of the above Which one of the following uses UDP as the transport protocol? (A) HTTP (B) Telnet (C) DNS (D) SMTP © All rights reserved by GATE Forum Educational Services Pvt. Group I 17.1 Q . The number of comparisons made in the execution of the loop for any n > 0 is: (A) log2 n + 1 16. (D) Blocking one kernel level thread blocks all related threads. (C) Same as the baud rate.1 (D) P . In Ethernet when Manchester encoding is used. j = 1.gateforum. Which one of the following statements is FALSE? (A) Context switch time is longer for kernel level threads than for user level threads. 20.com Consider the following segment of C-code: int j. www. Match entries in Group 1 to entries in Group 2.3 Q . Discuss this questions paper at www. Page 3 of 19 . (C) An LR(k) parser.CS GATE Paper 2007 15.gateforum.1 (B) P . Ltd. (D) An LALR(k) parser. n. the bit rate is: (A) Half the baud rate.3 (C) P . (B) User level threads do not need any hardware support. 18. Which one of the following is a top-down parser? (A) Recursive descent parser.2 Q . (C) Related kernel level threads can be scheduled on different processors in a multi-processor system.3 R . (D) log2 n + 1 (C) log2 n Group II (P) Gang Scheduling (1) Guaranteed Scheduling (Q) Rate Monotonic Scheduling (2) Real-time Scheduling (R) Fair Share Scheduling (3) Thread Scheduling (A) P .2 Consider the following statements about user level threads and kernel level threads. (B) Twice the baud rate. (B) n Group 1 contains some CPU scheduling algorithms and Group 2 contains some applications.1 Q . while (j <=n) j = j*2. No part of this booklet may be reproduced or utilized in any form without the written permission.2 R .3 R . 19.2 R . (B) Operator precedence parser. 3 . -2. (C) The complement of a cycle on 25 vertices. Let Connected(x) be a predicate which denotes that x is connected. Ltd. π 4 = a. Discuss this questions paper at www. (B) A complete graph on 90 vertices. b. d .gateforum. where I is the 4 × 4 identity matrix? I A (A) -5 26.20. b. (D) None of the above 24. Consider the following 4 partitions π 1 . Which of the following is an A I eigenvalue of . 23. 1 10 (B) -7 (C) 2 (D) 1 Consider the set S = {a. π 3 .CS GATE Paper 2007 www. (B) 3 (C) 4 (D) 5 Let Graph(x) be a predicate which denotes that x is a graph. The poset diagram for ( S ′. What is the probability that 2 appears at an earlier position than any other even number in the selected permutation? (A) 25.gateforum. 4. Suppose we uniformly and randomly select a permutation from the 20! Permutations of 1. π 3 = abc. π 4 } defined as follows: π i p π j if and only if π i refines π j . 1 2 (B) (C) 9! 20! (D) None of these Let A be a 4 × 4 matrix with eigenvalues -5..21 – Q. 1. No part of this booklet may be reproduced or utilized in any form without the written permission. π 4 on { } { } { } { } S : π 1 = abcd . π 3 . 2. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”? (A) ¬∀x ( Graph ( x ) ⇒ Connected ( x ) ) (B) ∃x ( Graph ( x ) ∧ ¬Connected ( x ) ) (C) ¬∀x ( ¬Graph ( x ) ∨ Connected ( x ) ) (D) ∀x ( Graph ( x ) ⇒ ¬Connected ( x ) ) Which of the following graphs has an Eulerian circuit? (A) Any k-regular graph where k is an even number. π 2 = ab. Let p be the partial order on the set of partitions S ′ = {π 1 . p ) is: (A) π1 (B) π1 π2 π3 π4 π2 π4 π3 © All rights reserved by GATE Forum Educational Services Pvt. d . π 2 .. c. How many different non-isomorphic Abelian groups of order 4 are there? (A) 2 22.com Q. d} . Page 4 of 19 .75 Carry Two Marks Each 21. cd .com. c. π 2 .…. CS GATE Paper 2007 www. Page 5 of 19 . −1 T therefore is not a basis of X. Discuss this questions paper at www.5 29.com.1} . 0.6 finite automaton (D) 1. 1. 0.gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission. Consider the set of (column) vectors defined by { T X = x ∈ R3 x1 + x2 + x3 = 0. 2} is: (A) not recursive (B) is recursive and is a deterministic CFL. −1 } is a linearly independent set. but it does not span X and T .4 accepting the language } L = w w ∈ {0. (C) is a regular language. (C) X is not a subspace of R3 (D) None of the above 28. −1. Ltd. x2 . respectively * has (A) 15 states 30.5 obtained from the Newton-Raphson 2 8 xn method. number of 0s and 1s in w are divisible by 3 and 5. The series converges to (A) 1. (D) is not a deterministic CFL but a CFL. Which of the following is } is a basis for the subspace X. A minimum { (B) state 2 deterministic (C) 1. © All rights reserved by GATE Forum Educational Services Pvt. 0 T (A) T (B) }. 1. .com π1 (C) (D) π2 π1 π2 π3 π3 π4 π4 27. 0 {1. Consider the series xn +1 = xn 9 + . x0 = 0. where x T = x1 . x3 TRUE? {1. −1.gateforum.1. (B) 11 states { (C) 10 states (D) 9 states } The language L = 0i 21i i ≥ 0 over the alphabet {0. Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables.1} } (B) + R + R Which of the following expressions are NOT equivalent to f ? (P) x ′y ′z ′ + w ′xy ′ + wy ′z + xz (Q) w ′y ′z ′ + wx ′y ′ + xz (R) w ′y ′z ′ + wx ′y ′ + xyz + xy ′z (S) x ′y ′z ′ + wx ′y ′ + w ′y (A) P only 33. x.gateforum. www. Ltd. Consider a two-level logic implementation of the look-ahead carry generator. Which of the following languages is regular? {ww w ∈ {0. Let Z = X * Y . Q. 35. (C) Only P and R are valid. 9. Assume that all Pi and Gi are available for the carry generator circuit and that the AND and OR gates can have any number of inputs. Q and R. where C0 is the input carry.1} } + R (A) + R 32. w ∈ {0. The number of AND gates and OR gates needed to implement the look-ahead carry generator for a 4-bit adder with S3 . w ∈ {0. w ∈ {0.com Let f (w. S2 . {ww x x. R are valid. Discuss this questions paper at www. Consider the following expressions P.com.5. the carry generate function Gi and the carry propagate function Pi for inputs Ai and Bi are given by: Pi = Ai ⊕ Bi and Gi = Ai Bi The expressions for the sum bit Si and the carry bit Ci +1 of the look-ahead carry adder are given by: Si = Pi ⊕ Ci and Ci +1 = Gi + Pi Ci . (B) Only Q and R are valid. Page 6 of 19 . No part of this booklet may be reproduced or utilized in any form without the written permission. 3 (B) 10. (A) Only P and Q are valid. (B) Q and S (C) R and S (D) S only Define the connective * for the Boolean variables X and Y as: X * Y = XY + X ′Y ′. 4. What is the minimum size of the multiplexer needed? (A) 2n line to 1 line (B) 2n +1 line to 1 line (C) 2n −1 line to 1 line (D) 2n − 2 line to 1 line In a look-ahead carry generator. 5 © All rights reserved by GATE Forum Educational Services Pvt.gateforum. 4 (C) 6. 7.1} } (C) {wxw x.13.15) . (D) All P.CS GATE Paper 2007 31. S0 and C4 as its outputs are respectively: (A) 6. 4 (D) 10.1} } (D) { xww x. y . 8. S1 . z ) = ∑ (0. πP : X = Y * Z Q :Y = X * Z R : X *Y * Z = 1 Which of the following is TRUE? 34. 4. then it cycles through the following sequence: 37. What is the number of clock cycles taken to complete the following sequence of instructions? ADD R2. 3. 2. If the counter starts at 0.com The control signal functions of a 4-bit binary counter are given below (where X is “don’t care”): Clear Clock Load Count Function 1 X X X Clear to 0 0 X 0 0 No change 0 ↑ 1 X Load input 0 ↑ 0 1 Count next The counter is connected as follows: A4 A3 A2 A1 Count=1 Clear 4-bit counter Load=0 Clock Inputs 0 0 1 1 Assume that the counter and gate delays are negligible. 3. R0 R2 R1 + R0 MUL R4.gateforum. The number of clock cycles for the EX stage depends on the instruction. Ltd. 1. No part of this booklet may be reproduced or utilized in any form without the written permission. ID and WB stages take one clock cycle each to complete the operation. 2. R2 R4 R3 * R2 SUB R6. Page 7 of 19 . R3. 5 (C) 0. Operand forwarding is used in the pipelined processor. R5. 4 (D) 0. 3. R4 R6 R5 − R4 © All rights reserved by GATE Forum Educational Services Pvt. The ADD and SUB instructions need 1 clock cycle and the MUL instruction needs 3 clock cycles in the EX stage. 1. (A) 0. Discuss this questions paper at www.CS GATE Paper 2007 36.com. 4 (B) 0. www. 3. R1.gateforum. 5 Consider a pipelined processor with the following four stages: IF: Instruction Fetch ID: Instruction Decode and Operand Fetch EX: Execute WB: Write Back The IF. 4. −. (A) 8. −. 3. −. 8. 41.gateforum. if (n <= 0) return 1.com. if (n > 3) {r = n. 2 (D) 1. 42. Ltd. −. by (A) Dijkstra’s algorithm starting from S. 3 (C) 1. (B) 5. −. return f(n-2)+2. 3 (D) 1. (B) 8 www. −. The top two elements of the stack after the first * is evaluated are: (A) 6. undirected connected graph. in terms of time complexity. 1 39.com (C) 10 (D) 14 The following postfix expression with single digit operands is evaluated using a stack: 823 ∧ /23*+51*- Note that ∧ is the exponentiation operator. −. −. 8. which of the following is the contents of the table when the sequence 1. (B) e d b g f c a (C) e d b f g c a (D) d e f g b c a Consider a hash table of size seven. −. Page 8 of 19 . and a hash function (3x + 4 ) mod7. 10. −. 3 In an unweighted. Consider the following C function: int f(int n) {static int r = 0. with starting index zero. 10. respectively The postorder traversal of the binary tree is: (A) d e b f g c a 40. −. } return f(n-1)+r. Assuming the hash table is initially empty. } What is the value of f (5 ) ? (A) 5 (B) 7 (C) 9 (D) 18 © All rights reserved by GATE Forum Educational Services Pvt. −. (B) Warshall’s algorithm (C) Performing a DFS starting from S. −. No part of this booklet may be reproduced or utilized in any form without the written permission. 8. 7 (C) 3.CS GATE Paper 2007 (A) 7 38. 10 (B) 1. 5 The inorder and preorder traversal of a binary tree are d b e a f c g and a b d e c f g. Discuss this questions paper at www. −. (D) Performing a BFS starting from S. 10 is inserted into the table using closed hashing? Note that − denotes an empty location in the table.gateforum. the shortest path from a node S to every other node is computed most efficiently. −. −. com. Discuss this questions paper at www. int GetValue (struct CellNode *ptr) { int value = 0. Page 9 of 19 . int gcd(n.gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission. what is the value of n? (A) 3 44.com (B) 4 (C) 5 (D) 6 In the following C function. } ( ) (A) Θ n2 46. return gcd(m. int element. www. (B) Ω ( n ) (C) Θ (log2 log2 n ) (D) Θ ( n) What is the time complexity of the following recursive function: int DoSomething (int n) { if (n <= 2) return 1. (B) Θ ( n log2 n ) (C) Θ (log2 n ) (D) Θ (log2 log2 n ) Consider the following C program segment where CellNode represents a node in a binary tree: struct CellNode { struct CellNOde *leftChild. else value = value + GetValue(ptr->leftChild) © All rights reserved by GATE Forum Educational Services Pvt. Ltd. if (ptr != NULL) { if ((ptr->leftChild == NULL) && (ptr->rightChild == NULL)) value = 1.CS GATE Paper 2007 43.n). struct CellNode *rightChild. n = n%m. else return (DoSomething (floor(sqrt(n))) + n). let n ≥ m. If L = 41.m) { if (n%m ==0) return m. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. }. A complete n-ary tree is a tree in which each node has n children or no children.gateforum. } How many recursive calls are made by this function? (A) Θ (log2 n ) 45. and I = 10. Let w be the minimum weight among all edge weights in an undirected connected graph.CS GATE Paper 2007 www. © All rights reserved by GATE Forum Educational Services Pvt. (C) At least n log2 n comparisons are needed. the number of comparisons performed is: (A) Θ (log2 n ) 48.com + GetValue(ptr->rightChild). } The value returned by GetValue when a pointer to the root of a binary tree is passed as its argument is: (A) the number of nodes in the tree (B) the number of internal nodes in the tree (C) the number of leaf nodes in the tree (D) the height of the tree 47. Ltd. Discuss this questions paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission. there is a truth assignment for which at least half the clauses evaluate to true.gateforum. at most one-fourth of the clauses evaluate to true. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element. (D) None of the above. (D) None of the above. where n is an even number. The maximum as well as the minimum of these n numbers needs to be determined. all edges have the same weight. where the Max Heap is represented by an array. (D) e is present in every minimum spanning tree.com.5n − 2 comparisons are needed. for some constant c. An array of n numbers is given. (C) There is a formula such that for each truth assignment. then in the cycle formed by adding e to T. are needed. Let e be a specific edge of weight w . Which of the following is FALSE? (A) There is a minimum spanning tree containing e. Page 10 of 19 . Which of the following is TRUE about the number of comparisons needed? (A) At least 2n − c comparisons. (B) At most 1. (B) Θ (log2 log2 n ) (C) Θ ( n ) (D) Θ ( n log2 n ) Which of the following is TRUE about formulae in Conjunctive Normal Form? (A) For any formula. (B) For any formula. (C) Every minimum spanning tree has an edge of weight w . 49. 50. (B) If e is not in a minimum spanning tree T. there is a truth assignment for which all the clauses evaluate to true. } return(value). Consider the process of inserting an element into a Max Heap.gateforum. CS GATE Paper 2007 51. with S as the start symbol.com Consider the following C code segment: int IsPrime(n) { int i. S1} . b. Consider ( n) and T ( n ) = Ω ( n ) and T ( n ) = Ω the grammar with (B) T ( n ) = O ( n) and T ( n ) = Ω (1) (D) None of the above non-terminals N = {S. Ltd.gateforum. t . Consider the following two statements: P: Every regular grammar is LL(1) Q: Every regular set has a LR(1) grammar Which of the following is TRUE? 54. i.Moves the content of memory location m to register Ri .Performs val OP Ri and stores the result in Ri . (A) Both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) Both P and Q are false In a simplified computer the instructions are: OP R j .com. and OP is either ADD or SUB. MOV m.Performs R j OP Ri and stores the result in register Ri . MOV Ri . (A) it is left recursive (B) it is right recursive (C) it is ambiguous (D) it is not context-free. The computer has only to registers. } Let T ( n ) denote the number of times the for loop is executed by the program on input n. C . Ri .i++) if(n%i == 0) {printf(“Not Prime\n”). for(i=2. Consider the following basic block: © All rights reserved by GATE Forum Educational Services Pvt.} return 1. Page 11 of 19 . and the following set of rules: S → iCtSS1 a S1 → eS ε C →b The grammar is NOT LL(1) because: 53.gateforum. e} .n. return 0. No part of this booklet may be reproduced or utilized in any form without the written permission. val denotes the content of memory location m. www. Which of the following is TRUE? (A) T ( n ) = O ( n) (C) T ( n ) = O ( n ) 52. terminals T = {a.i<=sqrt(n). Ri . Discuss this questions paper at www. m . OP m.Moves the content of register Ri to memory location m.Ri . (C) P is false. Which of these processes will finish LAST? © All rights reserved by GATE Forum Educational Services Pvt. Discuss this questions paper at www. Consider the following scenario. 57. and the column request denotes the number of units of each resource type requested by a process in order to complete execution. but Q is true (D) Both P and Q are false. Page 12 of 19 . The final value of the computation should be in memory. (B) 15 (C) 40 (D) 55 A virtual memory system uses First In First Out (FIFO) page replacement policy and allocates a fixed number of frames to a process. where the column alloc denotes the number of units of each resource type allocated to each process. What is the minimum number of MOV instructions in the code generated for this basic block? (A) 2 55. There are 5 units of each resource type. Y and Z. A single processor system has three resource types X. but Q is not the reason for P.gateforum. Which one of the following is TRUE? (A) Both P and Q are true. No part of this booklet may be reproduced or utilized in any form without the written permission. (B) 3 (C) 5 (D) 6 An operating system uses Shortest Remaining Time first (SRT) process scheduling algorithm. Ltd. Q: Some programs do not exhibit locality of reference.gateforum. Consider the arrival times and execution times for the following processes: Process Execution time Arrival time P1 20 0 P2 25 15 P3 10 30 P4 15 45 What is the total waiting time for process P2? (A) 5 56. and Q is the reason for P (B) Both P and Q are true.com.com t1 = a + b t2 = c + d t3 = e − t2 t4 = t1 − t3 Assume that all operands are initially in memory.CS GATE Paper 2007 www. Consider the following statements: P: Increasing the number of page frames allocated to a process sometimes increases the page fault rate. which are shared by three processes. Consider the following synchronization construct used by the processes: /* P1 */ while (true) { wants1 = true. Discuss this questions paper at www. but ensures mutual exclusion. What does the following relational algebra expression represent? Π courseId (( Π studId (σ sex ="female" ( studInfo ) ) × ΠcourseId ( enroll) ) − enroll) (A) Courses in which all the female students are enrolled. 59. The relation enroll(studId.gateforum. (B) It does not ensure bounded waiting. /* Critical Section */ wants1=false. P1 and P2. /* Critical Section */ Wants2=false. (D) It does not prevent deadlocks. name. while (wants1==true). since the system is in a deadlock. while (wants2==true).com. need to access a critical section of code. Two processes. (D) None of the above © All rights reserved by GATE Forum Educational Services Pvt.com alloc (A) P0 request X Y Z X Y Z P0 1 2 1 1 0 3 P1 2 0 1 0 1 2 P2 2 2 1 1 2 0 (B) P1 (C) P2 (D) None of the above.gateforum. sex). (B) Courses in which a proper subset of female students are enrolled. Ltd.CS GATE Paper 2007 www. which are initialized to false. Information about a collection of students is given by the relation studinfo(studId. Page 13 of 19 . Assume that every course is taken by at least one male and at least one female student. No part of this booklet may be reproduced or utilized in any form without the written permission. courseId) gives which student has enrolled for (or taken) what course(s). (C) It requires that processes enter the critical section in strict alternation. } /* Remainder section */ Here. wants1 and wants2 are shared variables. Which one of the following statements is TRUE about the above construct? (A) It does not ensure mutual exclusion. 58. (C) Courses in which only male students are enrolled. } /* Remainder section */ /* P2 */ while (true) { wants2 = true. empId From employee e Where e.com Consider the relation employee(name.department = “5”) (A) Q1 is the correct query (B) Q2 is the correct query (C) Both Q1 and Q2 produce the same answer. 63. the value field is 9 bytes long and a block pointer is 6 bytes long. Assuming that department 5 has more than one employee. supervisorName) with name as the key. sex. Consider the table employee(empId. (D) A prime attribute can be transitively dependent on a key in a BCNF relation.gateforum.empId From employee e Where not exists (Select * From employee s where s. Discuss this questions paper at www. Which one of the following statements if FALSE? (A) Any relation with two attributes is in BCNF (B) A relation in which every key has only one attribute is in 2NF (C) A prime attribute can be transitively dependent on a key in a 3 NF relation. and we want to find the employees who get higher salary than anyone in the department 5.sex = "male" } (A) Names of employees with a male supervisor. Page 14 of 19 . department.gateforum. 61.salary) Q2 : Select e. name. (C) Names of employees with no immediate female subordinates. data record pointer is 7 bytes long. data record pointer) pairs it can hold. Q2 below. (B) Names of employees with no immediate male subordinates. www.CS GATE Paper 2007 60.supervisorName ≠ e. The order of a leaf node in a B + − tree is the maximum number of (value. (D) Names of employees with a female supervisor. What does the following Tuple Relational Calculus query produce? {e.salary >=e.name employee ( e) ∧} ( ∀x ) ¬employee ( x ) ∨ x. No part of this booklet may be reproduced or utilized in any form without the written permission. what is the order of the leaf node? (A) 63 (B) 64 (C) 67 (D) 68 © All rights reserved by GATE Forum Educational Services Pvt. which one of the statements is TRUE for any arbitrary employee table? Q1 : Select e. Given that the block size is 1K bytes.name ∨ x. Ltd.salary > Any (Select distinct salary From employee s Where s. supervisorName gives the name of the supervisor of the employee under consideration. salary) and the two queries Q1 .com.department = “5” and s. (D) Neither Q1 nor Q2 is the correct query 62. (D) 64 subnets and 1024 hosts.com. (B) 200 metres of cable. 68. Let R bits/second be the channel capacity. The 1-bit delay in this network is equivalent to: (A) 500 metres of cable. (C) S1 is not conflict serializable and S2 is conflict serializable. Ltd. r2 ( X ) . r1 (Y ) . There are n stations in a slotted LAN. Each station attempts to transmit with a probability p in each time slot. the minimum number of bits for the sequence number field in a frame for maximum utilization.gateforum. r2 (Y ) .CS GATE Paper 2007 64. The message 11001001 is to be transmitted using the CRC polynomial x 3 + 1 to protect it from errors. n −1 (B) (1 − p )n −1 (C) p (1 − p ) n −1 (D) 1 − (1 − p ) n −1 In a token ring network the transmission speed is 107 bps and the propagation speed is 200 metres/µs. 65. r1 (Y ) . No part of this booklet may be reproduced or utilized in any form without the written permission. 69. What is the maximum number of subnets and the maximum number of hosts in each subnet? (A) 62 subnets and 262142 hosts. (B) S1 is conflict serializable and S2 is not conflict serializable. 67.w1 ( X ) (A) Both S1 and S2 are conflict serializable.gateforum. Assuming that processing delay is negligible. Page 15 of 19 . The message that should be transmitted is: (A) 11001001000 (B) 11001001011 (C) 11001010 (D) 110010010011 The distance between two stations M and N is L kilometers. (D) 50 metres of cable.com Consider the following schedules involving two transactions. when the sliding window protocol is used. All frames are K bits long. is: 2LtR + 2K (A) log2 K 2LtR (B) log2 K 2LtR + K (C) log2 K 2LtR + K (D) log2 2K © All rights reserved by GATE Forum Educational Services Pvt. (D) Both S1 and S2 are not conflict serializable. Which one of the following statements is TRUE? S1 : r1 ( X ) . Discuss this questions paper at www. www.w1 ( X ) S2 : r1 ( X ) . r2 ( X ) . The address of a class B host is to be split into subnets with a 6-bit subnet number.w2 (Y ) .w2 (Y ) . r2 (Y ) . What is the probability that ONLY one station transmits in a given time slot? (A) np (1 − p ) 66. (B) 64 subnets and 262142 hosts. (C) 62 subnets and 1022 hosts. The propagation delay per kilometer is t seconds. (C) 20 metres of cable. CS GATE Paper 2007 70.5 (B) P .4 R .1 Q . (B) 11 (C) 20 (D) 21 Assume that the memory is word addressable.3 Common Data Questions Common Data for Questions 71. 73: Consider the following program segment. No part of this booklet may be reproduced or utilized in any form without the written permission.2 S .2 S .1 R .2 Q . Discuss this questions paper at www. Page 16 of 19 . (3000) R1 m[3000] 2 MOV R2.4 R . The content of each of the memory locations from 2000 to 2010 is 100. 72. Ltd. Instruction LOOP: Operation Instruction size (no. The number of memory references for accessing the data in executing the program completely is: (A) 10 72.gateforum. After the execution of this program.com.4 R .2 Q . R1 R2 R1 + R2 1 MOV (R3).com Match the following: (P) SMTP (1) Application layer (Q) BGP (2) Transport layer (R) TCP (3) Data link layer (S) PPP (4) Network layer (5) Physical layer (A) P . the content of memory location 2010 is: (A) 100 (B) 101 (C) 102 (D) 110 © All rights reserved by GATE Forum Educational Services Pvt.3 (C) P .of words) MOV R1.1 Q . R2 and R3 are the general purpose registers.5 (D) P . Here R1. Assume that the memory is word addressable. 71. (R3) R2 M[R3] 1 ADD R2. R2 M[R3] R2 1 INC R3 R3 R3 + 1 1 DEC R1 R1 R1 – 1 1 BNZ LOOP Branch on not zero 2 Stop 1 HALT Assume that the content of memory location 3000 is 10 and the content of the register R3 is 2000. The program is loaded from the memory location 1000.3 S . www.1 S .gateforum. All the numbers are in decimal. . 1110. 2 4 8 16 32 32 Which of the following is the Huffman code for the letter a. . 001. 110. 11110. 001. www.com. f have probabilities 76. 0001. d. Discuss this questions paper at www.1875 (C) 2. . 010. 011.CS GATE Paper 2007 73. d.76 to Q. 1 1 1 1 1 1 . (B) ( a + b )* (C) b* a ( a + b ) * (D) b* ab* ab* The minimum state automaton equivalent to the above FSA has the following number of states (A) 1 (B) 2 (C) 3 (D) 4 Linked Answer Questions: Q. 10. c. c.9375 Statement for Linked Answer Questions 78 & 79: Consider the CFG with {S. 001. 10. If an interrupt occurs during the execution of the instruction “INC R3”. 0000 (D) 110. The language accepted by this automaton is given by the regular expression (A) b* ab* ab* ab* 75. b.gateforum. e. {a. respectively. . Ltd.com Assume that the memory is byte addressable and the word size is 32 bits. 000.25 (D) 1. e. 01. A.76? (A) 3 (B) 2. Page 17 of 19 . No part of this booklet may be reproduced or utilized in any form without the written permission. 111 77. 75: Consider the following Finite State Automaton: q3 a b b q0 q1 b a q2 b a a 74. 000 (C) 11. S as the start symbol and the following set of production rules: © All rights reserved by GATE Forum Educational Services Pvt.gateforum.85 Carry Two Marks Each Statement for Linked Answer Questions 76 & 77: Suppose the letters a. 100. B} as the non-terminal alphabet. 10. 11111 (B) 11. f? (A) 0. What is the average length of the correct answer to Q. . 010. what return address will be pushed on to the stack? (A) 1005 (B) 1020 (C) 1024 (D) 1040 Common Data for Questions 74. b. b} as the terminal alphabet. 1. 6. The complete array is accessed twice. Assume that the contents of the data cache do not change in between the two accesses.com. 4.78. 3. For the above reference string. how many more page faults occur with LRU than with the optimal page replacement policy? (A) 0 (B) 1 (C) 2 (D) 3 © All rights reserved by GATE Forum Educational Services Pvt. If optimal page replacement policy is used. How many data cache misses will occur in total? (A) 48 81. A 50 × 50 two-dimensional array of bytes is stored in the main memory starting from memory location 1100H. 3. 7. 2. Discuss this questions paper at www. 1 82. Ltd.gateforum.com (B) aabbbb (C) aabbab (D) abbbba For the correct answer strings to Q. Assume that none of the pages of the process are available in the memory initially.CS GATE Paper 2007 S B B B 78. www. Assume that a direct mapped data cache consisting of 32 lines of 64 bytes each is used in the system. (B) 50 (C) 56 (D) 59 Which of the following lines of the data cache will be replaced by new blocks in accessing the array for the second time? (A) line 4 to line 11 (B) line 4 to line 12 (C) line 0 to line 7 (D) line 0 to line 8 Statement for Linked Answer Questions 82 & 83: A process has been allocated 3 page frames. (B) 8 (C) 9 (D) 10 Least Recently Used (LRU) page replacement policy is a practical approximation to optimal page replacement. No part of this booklet may be reproduced or utilized in any form without the written permission. Assume that the data cache is initially empty.gateforum. how many derivation trees are there? (A) 1 (B) 2 (C) 3 (D) 4 Statement for Linked Answer Questions 80 & 81: Consider a machine with a byte addressable main memory of 216 bytes. → aB →b → bS → aBB S → bA A→a A → aS S → bAA Which of the following strings is generated by the grammar? (A) aaaabb 79. how many page faults occur for the above reference string? (A) 7 83. 80. The process makes the following sequence of page references (reference string): 1. 5. Page 18 of 19 . 84.gateforum.gateforum. i. j ) or ( i.10) starting from the initial position (0..e.4) to (5. How many distinct paths are there for the robot to reach the point (10. Discuss this questions paper at www.CS GATE Paper 2007 www. No part of this booklet may be reproduced or utilized in any form without the written permission.4). j ) then it can move to either ( i + 1. Ltd. 85. Page 19 of 19 .10) starting from (0. With this constraint.0)? 20 (A) 10 (B) 220 (C) 210 (D) None of the above Suppose that the robot is not allowed to traverse the line segment from (4.com Statement for Linked Answer Questions 84 & 85: Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right. if it is at ( i.0)? (A) 29 (B) 219 8 11 (C) × 4 5 20 8 11 (D) − × 10 4 5 © All rights reserved by GATE Forum Educational Services Pvt. how many distinct paths are there for the robot to reach (10.com. j + 1) . R are subsets c (P ∩ Q ∩ R ) ∪ P ∩ Q ∩ R ∪ Qc ∪ R c is ( (A) Qc ∪ R c 3. lim x →∞ x − sin x equals x + cos x (A) 1 2. then (D) U The following system of equations x1 + x2 + 2x3 = 1 x1 + 2x2 + 3x3 = 2 x1 + 4x2 + αx3 = 4 has a unique solution. X denotes a don’t care term. No part of this booklet may be reproduced or utilized in any form without the written permission.d + a. The only possible value(s) for α is/are 4.gateforum. What is the minimal form of the function represented by the Karnaugh map? ab cd (A) b. 5.1 – Q. If P.d 6.d + a.b. 00 01 00 1 01 X 11 X 10 1 11 10 1 1 1 X (B) a.CS GATE Paper 2008 www. Q. Discuss this questions paper at www. 1 or -1 (D) any real number In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to (A) The normalized value 2-127 (B) The normalized value 2-126 (C) The normalized value +0 (D) The special value +0 In the Karnaugh map shown below.com.b.d (C) b.20 Carry One Mark Each 1. (A) 0 (B) either 0 or 1 (C) one of 0.gateforum.d Let r denote number system radix. The only value(s) of r that satisfy the equation 121r = 11r is / are (A) decimal 10 (B) decimal 11 (C) decimal 10 and 11 (D) any value >2 © All rights reserved by GATE Forum Educational Services Pvt.d + a.b + b.d + a.b + b.d (D) a. Page 1 of 20 .com Q. (C) ∞ (B) -1 ) of (B) P ∪ Qc ∪ R c the (D) −∞ universal (C) P c ∪ Qc ∪ R c set U. Ltd. Page 2 of 20 . No part of this booklet may be reproduced or utilized in any form without the written permission. but accepted by a Turing machine 10.gateforum. (B) Σ m ( 4.15 ) then f2 is (A) Σ m ( 4. Which of the following are decidable? I. 7. Whether a given grammar is context-free (A) I and II 11. 8 ) } Which of the following is true for the language ap p is a prime ? (A) It is not accepted by a Turing Machine (B) It is regular but not context-free (C) It is context-free but not regular (D) It is neither regular nor context-free. (B) I and IV (C) II and III (D)II and IV Which of the following describes a handle (as applicable to LR-parsing) appropriately? (A) It is the position in a sentential form where the next shift or reduce operation will occur (B) It is non-terminal whose production will be used for reduction in the next step (C) It is a production that may be used for reduction in a future step along with a position in the sentential form where the next shift or reduce operation will occur (D) It is the production p that will be used for reduction in the next step along with a position in the sentential form where the right hand side of the production may be found © All rights reserved by GATE Forum Educational Services Pvt. 6.com (B) Θ (m) (C) Θ (m + n) (D) Θ (mn) Given f1. 8 ) { (D) Σ m ( 4. Whether two push-down automata accept the same language IV.15) f f3 f = Σm (1. www. Whether a given context-free language is regular III. Whether the intersection of two regular languages is infinite II.5.CS GATE Paper 2008 7. 8 ) (C) Σ m ( 6. Ltd. 6.com. 8 ) f3 = Σm (1. f3 and f in canonical sum of products form (in decimal) for the circuit f1 f2 f1 = Σm ( 4. 6 ) 9. The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity (A) Θ (n) 8. 6. 6.gateforum. 8. Discuss this questions paper at www. 17. 14.CS GATE Paper 2008 12. If L and L are recursively enumerable then L is (A) regular (B) context-free (C) context-sensitive (D) recursive What is the maximum size of data that the application layer can pass on to the TCP layer below? (A) Any size (B) 216 bytes-size of TCP header (C) 216 bytes (D) 1500 bytes Which of the following tuple relational calculus expression(s) is/are equivalent to ∀t ∈ r (P ( t ) ) ? I. z = 5 (D) x = 5. y = 3. Page 3 of 20 . www.gateforum. z = 5 © All rights reserved by GATE Forum Educational Services Pvt. ¬∃t ∈ r ( ¬P ( t ) ) IV. y = 4. 15. Ltd. z = 3 (C) x = 6.gateforum. (B) bind (C) listen (D) connect Which combination of the integer variables x. z = 2 (B) x = 6. No part of this booklet may be reproduced or utilized in any form without the written permission. y and z makes the variable a get the value 4 in the following expression? a = (x > y) ? ((x > z) ? x : z) : ((y > z) ? y : z) (A) x = 3. ¬∃t ∈ r (P ( t ) ) II. y = 5. Discuss this questions paper at www. y = 4.com. ∃t ∉ r (P ( t ) ) III.com Some code optimizations are carried out on the intermediate code because (A) They enhance the portability of the compiler to other target processors (B) Program analysis is more accurate on intermediate code than on machine code (C) The information from dataflow analysis cannot otherwise be used for optimization (D) The information from the front end cannot otherwise be used for optimization 13. 16. ∃t ∉ r ( ¬P ( t ) ) (A) I only (B) II only (C) III only (D) III and IV only A clustering index is defined on the fields which are of type (A) non-key and ordering (B) non-key and non-ordering (C) key and ordering (D) key and non-ordering Which of the following system calls results in the sending of SYN packets? (A) socket 18. where k is a positive integer. No part of this booklet may be reproduced or utilized in any form without the written permission. (B) 1000 The Newton-Raphson iteration xn+1 = (C) 100e (D) 100 1 R xn + can be used to compute the 2 xn (A) square of R (B) reciprocal of R (C) square root of R (D) logarithm of R Which of the following statements is true for every planar graph on n vertices? (A) The graph is connected (B) The graph is Eulerian (C) The graph has a vertex-cover of size at most 3n/4 (D) The graph has an independent set of size at least n/3 24. Ltd.CS GATE Paper 2008 19.gateforum.com The Breadth First Search algorithm has been implemented using the queue data structure. Then 1≤i≤2k i even (B) P = Q + K (C) P = Q (D) P = Q + 2K © All rights reserved by GATE Forum Educational Services Pvt.com. O N (B) NQMPOR P (C) QMNPRO (D) QMNPOR The data blocks of a very large file in the Unix file system are allocated using (A) contiguous allocation (B) linked allocation (C) indexed allocation (D) an extension of indexed allocation Q. 23. Page 4 of 20 .75 Carry Two Marks Each 21. www. The minimum number of equal length subintervals needed to approximate 2 1 x −6 ∫1 xe dx to an accuracy of at least 3 × 10 u sin g the trapezoidal rule is (A) 1000e 22.gateforum. Discuss this questions paper at www. Let P = ∑ i and Q = 1≤i≤ 2k i odd (A) P = Q − K ∑ i.21 – Q. One possible order of visiting the nodes of the following graph is M Q R (A) MNOPQR 20. y ) ) (C) ∀x ∃y ( fsa ( x ) ∧ pda ( y ) ∧ equivalent ( x. Given that Aishwarya studies computer science on Monday.com. Let Y be another normal variable with mean -1 and variance unknown.CS GATE Paper 2008 25.Q 27.36 How many of the following matrices have an eigenvalue 1? 1 0 0 1 1 0 0 0 0 1 29. b) means a and b are equivalent. If P ( X ≤ −1) = P ( Y ≥ 2 ) .R )(P. then the probability that the studies mathematics the next day is 0.6. A point on a curve is said to be an extremum if it is a local minimum or a local maximum.4. Let equivalent be another predicate such that equivalent (a.4 (D) 0. If she studies computer science on a day. and pda(y) means that y is a pushdown automaton. Ltd. The number of distinct extrema for the curve 3x 4 − 16x3 + 24x2 + 37 is (A) 0 26.24 28.R + Q ) Simplifies to (A) P.R (B) 2 (C) 2 (D) 1 Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton. y ) ) © All rights reserved by GATE Forum Educational Services Pvt. (B) 0. then (P + Q)(P. Discuss this questions paper at www.gateforum. y ) ) (D) ∀x ∃y ( fsa ( y ) ∧ pda ( x ) ∧ equivalent ( x. (A) one (C) 0. the standard deviation of Y is (A) 3 30. www. what is the probability that she studies computer science on Wednesday? (A) 0.com (B) 1 (C) 2 (D) 3 (C) P. If she studies mathematics on a day. Aishwarya studies either computer science or mathematics everyday. No part of this booklet may be reproduced or utilized in any form without the written permission. y ) ) (B) ~ ∀y ( ∃x fsa ( x ) ⇒ pda ( y ) ∧ equivalent ( x.gateforum.Q + P. then the probability that the studies computer science the next day is 0. (B) P. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automaton (A) ( ∀x fsa ( x )) ⇒ ( ∃y pda ( y ) ∧ equivalent ( x.6 − 1 −1 0 and 1 1 − 1 (B) two (C) three (D) four Let X be a random variable following normal distribution with mean +1 and variance 4.R + Q If P.Q + R (D) P. R are Boolean variables. Q. Page 5 of 20 . 32. ~ (~ P ∧ Q ) III. The amount of increment depends on the size of the data item accessed (A) I only 34. Discuss this questions paper at www. II and IV (D) All of I.gateforum. then an additional ALU is required for effective address calculation III. It must be a privileged instruction III. Page 6 of 20 . II and III only For inclusion to hold between two cache levels L1 and L2 in a multi-level cache hierarchy. IV. L1 must be a write-through cache II.com. Which of the following logical expressions are equivalent? I. II and III (C) Only I. The associativity of L2 must be greater than that of L1 IV. The L2 cache must be at least as large as the L1 cache (A) IV only (B) I and IV only (C) I.CS GATE Paper 2008 31. the seek latency is not linearly proportional to the seek distance due to (A) non-uniform distribution of requests (B) arm starting and stopping inertia (C) higher capacity of tracks on the periphery of the platter (D) use of unfair arm scheduling policies 33. II and IV only (D) I. P and Q are two propositions. II.com (P ∧ Q ) ∨ (P ∧ ~ Q ) ∨ (~ P ∧ ~ Q ) (P ∧ Q ) ∨ (P ∧ ~ Q ) ∨ (~ P ∧ Q ) (A) Only I and II (B) Only I. P∨ ~ Q II. III and IV © All rights reserved by GATE Forum Educational Services Pvt. which of the following are necessary? I. II III and IV For a magnetic disk with concentric circular tracks. An exception cannot be allowed to occur during execution of an RFE instruction 35. Which of the following is/are true of the auto-increment addressing mode? I. It is useful in creating self-relocating code II. It must be a trap instruction II. L2 must be a write-through cache III. No part of this booklet may be reproduced or utilized in any form without the written permission. www.gateforum. (A) I only (B) II only (C) I and II only (D) I. If it is included in an Instruction Set Architecture. Ltd. (B) II only (C) III only (D) II and III only Which of the following must be true for the RFE (Return From Exception) instruction on a general purpose processor? I. Discuss this questions paper at www. Register saves and restores III. Control hazard penalties can be eliminated by dynamic branch prediction (A) I and II only 37. Instruction fetches (A) I only 38. (B) I and III only (C) II and III only (D) I. Bypassing can handle all RAW hazards II. Page 7 of 20 . Register renaming can eliminate all register carried WAR hazards III. and h(n) is true? 40. (A) f (n) = O ( g (n) ) . What is the maximum number of node splitting operations that may take place? (A) 3 42.com Which of the following are NOT true in a pipelined processor? I. g(n). g (n) = O (h (n) ) (B) f (n) = Ω ( g (n) ) . (B) Θ (logn) (B) 4 (C) 5 (D) 6 G is a graph on n vertices and 2n-2 edges.CS GATE Paper 2008 36.gateforum. www. Ltd. Function locals and parameters II. The edges of G can be partitioned into two edge-disjoint spanning trees. the induced subgraph has at most 2k-2 edges © All rights reserved by GATE Forum Educational Services Pvt. Consider the following functions: f (n) = 2n g (n) = n! h (n) = nlogn Which of the following statements about the asymptotic behaviour of f(n). h (n) = O ( f (n) ) (D) h (n) = O ( f (n) ) . II and III In an instruction execution pipeline.gateforum. II and III The use of multiple register windows with overlap causes a reduction in the number of memory accesses for I. g (n) = O (h (n) ) (C) g (n) = O ( f (n) ) . (B) II only (C) III only (D) I. (C) Θ (log* n) (D) Θ (1) A B-tree of order 4 is built from scratch by 10 successive insertions. the earliest that the data TLB (Translation Lookaside Buffer) can be accessed is (A) Before effective address calculation has started (B) During effective address calculation (C) After effective address calculation has completed (D) After data cache lookup has completed 39.com. g (n) = Ω ( f (n) ) The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n integers is (A) Θ (n) 41. No part of this booklet may be reproduced or utilized in any form without the written permission. Which of the following is NOT true for G? (A) For every subset of k vertices. (A) only vertex a (B) only vertices a. Suppose there is a procedure for finding a pivot element which splits the list into two sub-lists each of which contains at least one-fifth of the elements. Ltd.com (B) The minimum cut in G has at least two edges (C) There are two edge-disjoint paths between every pair of vertices (D) There are two vertex-disjoint paths between every pair of vertices 43. Let T(n) be the number of comparisons required to sort n elements.…. No part of this booklet may be reproduced or utilized in any form without the written permission. Consider the Quicksort algorithm. Then (A) T (n) ≤ 2T (n / 5) + n (B) T (n) ≤ T (n / 5) + T ( 4n / 5) + n (C) T (n) ≤ 2T ( 4n / 5) + n (D) T (n) ≤ 2T (n / 2 ) + n The subset-sum problem is defined as follows: Given a set S of n positive integers and a positive integer W. −3 b 1 e 2 1 −5 c a 3 2 h f 3 2 2 d 2 1 g Dijkstra’s single source shortest path algorithm when run from vertex a in the above graph. of a binary search tree on the n elements 1.CS GATE Paper 2008 www. determine whether there is a subset of S Whose elements sum to W. You have to determine the unique binary search tree that has P as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this? (A) Θ (logn) (B) Θ (n) (C) Θ (nlogn) (D) None of the above. as the tree cannot be uniquely determined © All rights reserved by GATE Forum Educational Services Pvt.gateforum. 44. b. Page 8 of 20 . c. 2.gateforum. f. h (C) only vertices a.com. d (D) all the vertices You are given the postorder traversal. g. computes the correct shortest path distance to 46. Which of the following statements is false? (A) Q solves the subset-sum problem in polynomial time when the input is encoded in unary (B) Q solves the subset-sum problem in polynomial time when the input is encoded in binary (C) The subset sum problem belongs to the class NP (D) The subset sum problem is NP-hard 45. e. Discuss this questions paper at www. P.n. An algorithm Q solves this problem in O(nW) time.. com (B) Θ (n) (C) Θ (nlogn) ( ) (D) Θ n2 Which of the following statements is false? (A) Every NFA can be converted to an equivalent DFA (B) Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine (C) Every regular language is also a context-free language (D) Every subset of a recursively enumerable set is recursive 49. No part of this booklet may be reproduced or utilized in any form without the written permission. All ε-productions can be removed from any context-free grammar by suitable transformations III.CS GATE Paper 2008 47. Page 9 of 20 . II and IV only © All rights reserved by GATE Forum Educational Services Pvt.com. The total time required for this is (A) Θ (logn) 48. Given below are two finite state automata (→ indicates the start state and F indicates a final state) a b Y: a b →1 1 2 Z: 2 (F ) 2 1 →1 2 2 2 (F ) 1 1 Which of the following represents the product automaton Z×Y? a b (A) →P S R Q R S S Q P R (F ) Q P 50. is always regular IV. III and IV only (C) I. II.gateforum. The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees (A) I. a →P (B) b a b S Q Q R S S P Q R (F ) Q P (C) →P Q S Q R S S Q P a (D) R (F ) Q P b →P S Q Q S R S Q P R (F ) Q P Which of the following statements are true? I.gateforum. www. We have a binary heap on n elements and wish to insert n more elements (not necessarily one after another) into this heap. w is a string of terminals and Y is a non-terminal). Ltd. The language generated by a context-free grammar all of whose productions are of the form X → w or X → wY (where. Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa II. Discuss this questions paper at www. III and IV only (D) I. III and IV (B) II. H − S (B) E − R. G − S. 1 Q. Ltd. 1 1 0 1 0 0 0 0 0 1 R. Number of formal parameters in the declaration of a function agrees with the number of actual parameters in use of that function Q. H − Q (C) E − R.gateforum. ε + 0 (10 * 1 + 10 ) * 10 * 1 © All rights reserved by GATE Forum Educational Services Pvt. X → XbX XcX G. G − Q. 0 1 1 0 0 1 0 1.m ≥ 1 F. H − Q Match the following NFAs with the regular expressions they correspond to P.com. X → bXb cXc ε } dXf g (A) E − P. 1 S. Page 10 of 20 .com Match the following: { E. Arithmetic expressions with matched pairs of parentheses R. ε + 0 (10 * 1 + 00 ) * 0 3. G − Q. F − R. F − P. H − S (D) E − P. Palindromes S. L = anbmcndm n ≥ 1. F − P. 52. No part of this booklet may be reproduced or utilized in any form without the written permission.CS GATE Paper 2008 51. Checking that identifiers declared before their use are P. ε + 0 (10 * 1 + 10 ) * 1 4.gateforum. www. F − R. ε + 0 ( 01 * 1 + 00 ) * 01 * 2. G − S. Discuss this questions paper at www. L = {wcw w ∈ (a b) *} H. A programming language which does not permit global variables of any kind and has no nesting of procedures/functions. In the slow start phase of the TCP congestion control algorithm. n 2m } n ≥ 0. Ltd. S − 4 Which of the following are regular sets? III. S − 4 (C) P − 1. Programming languages which permit a function to return a function as its result cannot be implemented with a stack-based storage allocation scheme for activation records (A) II and V only (B) I. No part of this booklet may be reproduced or utilized in any form without the written permission. {a b {a b {a b IV. www.b} *} I. R − 3. 55. Recursion in programming languages cannot be implemented with dynamic storage allocation IV. S − 4 (D) P − 3. Q − 3. m ≥ 0 } n m n = 2m n m n≠m } (A) I and IV only 54. y. III and IV only (C) I. Q − 2. Nesting procedures/functions and recursion require a dynamic heap allocation scheme and cannot be implemented with a stack-based allocation scheme for activation records V. S − 4 (B) P − 1. but permits recursion can be implemented with static storage allocation II.com (B) I and III only (C) I only (D) IV only Which of the following are true? I. the size of the congestion window (A) does not increase (B) increases linearly (C) increases quadratically (D) increases exponentially © All rights reserved by GATE Forum Educational Services Pvt. Discuss this questions paper at www. Multi-level access link (or display) arrangement is needed to arrange activation records only if the programming language being implemented has nesting of procedures/functions III.CS GATE Paper 2008 53. {xcy x. Page 11 of 20 .com. R − 1. II and V only (D) II. R − 3. (A) P − 2. R − 2. III and V only An LALR(1) parser for a grammar G can have shift-reduce (S-R) conflicts if and only if (A) The SLR(1) parser for G has S-R conflicts (B) The LR(1) parser for G has S-R conflicts (C) The LR(0) parser for G has S-R conflicts (D) The LALR(1) parser for G has reduce-reduce conflicts 56. Q − 1. ∈ {a.gateforum. II. Q − 2.gateforum. 255. No part of this booklet may be reproduced or utilized in any form without the written permission.pr int f ("\ n ") . Which one of the following events could take place? (A) connect () system call returns successfully (B) connect () system call blocks (C) connect () system call returns an error (D) connect () system call results in a core dump 60.gateforum. The token bucket is filled at a rate of 2Mbps. a bind () and a listen () system call in that order. Ltd. } (A) 18 61. pr int f (" %d".gateforum. * *ppz + = 1. Consider the following situation: the server process S executes a socket (). What is the maximum duration for which the computer can transmit at the full 10Mbps? (A) 1. f ( c. a = &b. b = &c. a) ) . If a class B network on the Internet has a subnet mask of 255. www. Subsequently. int * *ppz ) { int y. (B) 19 void main ( ) { int c. } (C) 21 (D) 22 Choose the correct option to fill ? 1 and ? 2 so that the program below prints an input string in reverse order. Assume that the input string is terminated by a newline character. c = 4. void recerse ( void) { int c.6 seconds 59. pr int f ("\ n ") . return x + y + z. * b. the client process P executes a socket () system call followed by connect () system call to connect to the server process S. Page 12 of 20 . if (?1) reverse ( ) . } © All rights reserved by GATE Forum Educational Services Pvt. * *a. (B) 1023 (C) 2046 (D) 2047 A computer on a 10Mbps network is regulated by a token bucket. ?2 } main ( ) { pr int f ( "Enter Text ") .0. What is printed by the following C program? int f (int x. z. It is initially filled to capacity with 16Megabits. what is the maximum number of hosts per subnet? (A) 1022 58.b. z = *ppz.com. y = *py. * py + = 2.CS GATE Paper 2008 57. following which it is preempted. Discuss this questions paper at www. x + = 3. reverse ( ) .248.com (B) 2 seconds (C) 5 seconds (D) 8 seconds A client process P needs to make a TCP connection to a server process S. The server process has not executed any accept () system call. int * py. 3. p = list. What will be the contents of the list after the function completes execution? struct node { int value.com ) ! = '\ n ') ? 2 is getchar ( c ) . } } (A) 1. struct node * next. 7. 7. 6 (D) 2.3. The function is called with the list containing the integers 1. q = p ? p− > next : 0. Two binary semaphores xb and yb are used to implement the semaphore operations P(s) and V(s) as follows: © All rights reserved by GATE Forum Educational Services Pvt. Assume that Pb and Vb the wait and signal operations on binary semaphores are provided. q = list − > next. Ltd. Discuss this questions paper at www.2.2. Page 13 of 20 . where s is a counting semaphore. V ( s ) : s = s + 1.6. Void rearrange ( struct node * list ) { struct node * p. 62. 4. while ( q) { temp = p− > value. * q. if (!list !list − > next ) return. 3. 6.com. 4. 7 63.4.3. q− > value = temp.5.gateforum.5. (C) ?1 is ( c ! = '\ n ') ? 2 is putchar ( c ) . (B) ?1 is ( c = getchar ( ) ) ! = '\ n ') ? 2 is getchar ( c ) .5. 6.5.3. 4.gateforum. ifs <= 0 then wakeup a process waiting on s. int temp.CS GATE Paper 2008 (A) ?1 is ( getchar ( www.5. The following C function takes a single-linked list of integers as a parameter and rearranges the elements of the list.1 The P and V operations on counting semaphores. (B) 2.p− > value = q− > value. ifs < 0 then wait. 7 (C) 1. are defined as follows: P ( s ) : s = s − 1. (D) ?1 is ((c = getchar ( ) ) ! = '\ n ') ? 2 is putchar ( c ) . 6.1. 4.7 in the given order. }.p = q− > next. 2. No part of this booklet may be reproduced or utilized in any form without the written permission. (B) 0 and 1 (C) 1 and 0 (D) 1 and 1 Which of the following statements about synchronous and asynchronous I/O is NOT true? (A) An ISR is invoked on completion of I/O in synchronous I/O but not in asynchronous I/O (B) In both synchronous and asynchronous I/O. Which of the following is NOT true of deadlock prevention and deadlock avoidance schemes? (A) In deadlock prevention. { } else Vb ( xb ) . i + + ) for ( ). Vb ( yb ) . Page 14 of 20 . an ISR (Interrupt Service Routine) is invoked after completion of the I/O (C) A process making a synchronous I/O call waits until I/O is complete. the process waiting for the completion of I/O is woken up by the ISR that is invoked after the completion of I/O 65. Ltd. i < n.CS GATE Paper 2008 www. but a process making an asynchronous I/O call does not wait for completion of the I/O (D) In the case of synchronous I/O.com.gateforum. The total number of child processes created is (A) n (B) 2n − 1 (C) 2n (D) 2n+1 − 1 © All rights reserved by GATE Forum Educational Services Pvt. the request for resources is always granted if the resulting state is safe (B) In deadlock avoidance. A process executes the following code for (i = 0.com P ( s ) : Pb ( xb ) . Pb ( yb ) . The initial values of xb and yb are respectively (A) 0 and 0 64. No part of this booklet may be reproduced or utilized in any form without the written permission. s = s − 1. the request for resources is always granted if the result state is safe (C) Deadlock avoidance is less restrictive than deadlock prevention (D) Deadlock avoidance requires knowledge of resource requirements a priori 66. if ( s <= 0 ) Vb ( xb ) .gateforum. V ( s ) : Pb ( xb ) . s = s + 1. Discuss this questions paper at www. if ( s < 0) Vb ( xb ) . 24 and 24 (C) 24. Q. following functional dependencies: Title Author → Catalog_no Catalog_no → Title Author Publisher Year Publisher Title Year → Pr ice Assume {Author.gateforum. Year. II and III (D) Only I. I. Catalog_ no. (B) 24. No part of this booklet may be reproduced or utilized in any form without the written permission. S2 ) Where {P. Q} is the key for both schemas.Q (R ) − ΠP. Each page table entry is of size 4 bytes. A three level page table is used for virtual to physical address translation. Title} is the key for both schemes. Author. Pr ice ) Collection ( Title. Catalog_ no ) Book with in the I.R2.Q (R ) − ( ΠP. Q. Ltd. III. S1.Q ( S ) ) ( ) (A) Only I and II (B) Only I and III (C) Only I. 25 and 24 Let R and S be two relations with the following schema R (P.R3) S (P. 20 and 20 68.com A processor uses 36 bit physical addresses and 32 bit virtual addresses.R1.gateforum. second and third level page tables are respectively (A) 20. Author. Publisher. II.Q (R ) ∩ ΠP. and • Bits 0-11 are used as offset within the page The number of bits required for addressing the next level page table (or page frame) in the page table entry of the first.CS GATE Paper 2008 67. ΠP ΠP. ΠP ( ΠP. III and IV Consider the following relational schemes for a library database: ( Title. Π P (R II. where the virtual address is used as follows • Bits 30-31 are used to index into the first level page table • Bits 21-29 are used to index into the second level page table • Bits 12-20 are used to index into the third level page table. Which of the following statements is true? (A) Both Book and Collection are in BCNF (B) Both Book and Collection are in 3NF only (C) Book is in 2NF and Collection is in 3NF (D) Both Book and Collection are in 2NF only © All rights reserved by GATE Forum Educational Services Pvt. Page 15 of 20 . Which of the following queries are equivalent? 69.Q ( S ) ) IV. www.com. 24 and 20 (D) 25. Π P (R ) S) ΠP ( S ) III. Discuss this questions paper at www. with a page frame size of 4 Kbytes. Array ARR is located in memory starting at the beginning of virtual page 0xFF000 and stored in row major order. Ltd. i + + ) for ( j = 0. Each record is 32 bytes long and its key field is of size 6 bytes.0. A program to be run on this machine begins as follows: double ARR 1024 1024. int i.i < 1024. No part of this booklet may be reproduced or utilized in any form without the written permission. The size of double is 8Bytes. Page 16 of 20 .gateforum. The total size of the tags in the cache directory is (A) 32Kbits 72.com Consider a file of 16384 records. If the secondary index is built on the key field of the file. (C) 64Kbits (D) 68Kbits Which of the following array elements has the same cache index as ARR [0] [0]? (A) ARR [0] [4] 73. Discuss this questions paper at www. j .com.CS GATE Paper 2008 70.gateforum. The file is ordered on a non-key field. j + + ) ARR i j = 0. j < 1024. the number of first-level and second-level blocks in the multi-level index are respectively (A) 8 and 0 (B) 128 and 6 (C) 256 and 4 (D) 512 and 5 Common Data for Questions: 71 72 and 73 Consider a machine with a 2-way set associative data cache of size 64Kbytes and block size 16bytes. /* Initialize array ARR to 0. and the size of a block pointer is 10 bytes. The file is stored in a file system with block size 1024 bytes. www. and the file organization is unspanned.0 * / for (i = 0. (B) 34Kbits (B) ARR [4] [0] (C) ARR [0] [5] (D) ARR [5] [0] The cache hit ratio for this initialization loop is (A) 0% (B) 25% (C) 50% (D) 75% © All rights reserved by GATE Forum Educational Services Pvt. The only data memory references made by the program are those to array ARR 71. The cache is managed using 32 bit virtual addresses and the page size is 4Kbyts. and a multi-level index scheme is used to store the secondary index. The cache is initially empty and no pre-fetching is done. } 74. } return X n. Y 1 = 2. ( ) Θ (2 ) and Θ (2 ) (B) Θ 2n and Θ (n) (D) n n F1 (8) and f2 (8) return the values (A) 1661 and 1640 (B) 59 and 59 (C) 1640 and 1640 (D) 1640 and 1661 © All rights reserved by GATE Forum Educational Services Pvt. Y i = 2 * X i. for (i = 2. X 0 = Y 0 = Z 0 = 0. No part of this booklet may be reproduced or utilized in any form without the written permission. Z 1 = 3. Z i = 3 * X i. Z N. i <= n. X 1 = 1.CS GATE Paper 2008 www. } int f2 ( int n ) { int i. Discuss this questions paper at www. Ltd. i + + ) { X i = Y i − 1 + Z i − 2. else return (2 * f1 (n − 1) + 3 * f1 (n − 2 ) ) . Y N . int X N .com Common Data for Questions: 74 and 75 Consider the following C functions: int f1 ( int n ) { if (n = = 0 n = = 1) return n. Page 17 of 20 . The running time of f1 (n) and f2 (n) are (A) Θ (n) and Θ (n) ( ) (C) Θ (n) and Θ 2n 75.gateforum.com.gateforum. 76 to 85 Carry Two Marks Each Statement for Linked Answer Questions: 76 & 77 Delayed branching can help in the handling of control hazards 76. I3 or I4 can legitimately occupy the delay slot without any other program modification? (A) I1 (B) I2 (C) I3 (D) I4 Statement for Linked Answer Questions: 78 & 79 Let xn denote the number of binary strings of length n that contain no consecutive 0s. I2. and positive integer W. S = {a1 .CS GATE Paper 2008 www. X. For all delayed conditional branch instructions. (B) xn = x n/2 +1 (C) xn = x n/2 +n (D) xn = xn −1 + xn−2 The value of x5 is (A) 5 (B) 7 (C) 8 (D) 16 Statement for Linked Answer Questions: 80 & 81 The subset-sum problem is defined as follows.gateforum. with n rows and W+1 columns.com. The following code is to run on a pipelined processor with one branch delay slot: I1 : I2 : ADD R2 ← R7 + R8 SUB R4 ← R5 − R6 I3 : ADD R1 ← R2 + R3 I4 : STORE Memory R4 ← R1 BRANCH to Label if R1 = = 0 Which of the instructions I1.com Linked Answer Questions: Q. irrespective of whether the condition evaluates to true or false (A) The instruction following the conditional branch instruction in memory is executed (B) The first instruction in the fall through path is executed (C) The first instruction in the taken path is executed (D) The branch takes longer to execute than any other instruction 77.. Given a set of n positive integers. Discuss this questions paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission. an } .. Which of the following recurrences does xn satisfy? (A) xn = 2xn−1 79.. a2 . 78.. Ltd.gateforum. © All rights reserved by GATE Forum Educational Services Pvt. is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array. Page 18 of 20 . a3 . 0 ≤ j ≤ W. k. 9.N1. R2 is (A) 2 83. f (int Y 10 .. The program is erroneous. j = 9. if ( Y k < x ) i = k. W (B) X n. 5. j = X i − 1.P1.P1. implies that there is a subset whose elements sum to W? (A) X 1. 10. j ∧ X i. j. No part of this booklet may be reproduced or utilized in any form without the written permission. j ∨ X i. j = X i − 1.N2} (C) {M1. j ∨ X i − 1. j − ai (D) X i. 6. j = X i − 1. i = 0.P1} Statement for Linked Answer Questions: 84 & 85 Consider the following C program that attempts to locate an element x in an array Y[ ] using binary search.gateforum. } while ( ( Y k ! = x ) & & (i < j) ) . } © All rights reserved by GATE Forum Educational Services Pvt.M3. 4. j ∧ X i − 1.M2. N. j = X i − 1. j . Which of the following is valid for 2 ≤ i ≤ n and ai ≤ j ≤ W ? (A) X i.com X i. do { k = (i + j) / 2. 2. 3. else pr int f (" x is not in the array ") .n Statement for Linked Answer Questions: 82 & 83 Consider the following ER diagram M1 M3 M2 R1 M 82. N1 R2 P N2 N The minimum number of tables needed to represent M. ai } whose elements sum to j. j − ai (B) X i. if TRUE. W (D) X n − 1. ( Y k = = x ) pr int f (" x is in the array ") .. R1.gateforum.1 ≤ i ≤ n. 8.else j = k.com. is TRUE if and only if there is a subset of {a1 . 80.P1} (B) {M1. P2 P1 (B) 3 (C) 4 (D) 5 Which of the following is a correct attribute set for one of the tables for the correct answer to the above question? (A) {M1. j − ai Which entry of the array X.CS GATE Paper 2008 www. j − ai (C) X i.. a2 . 81.N1} (D) {M1. 1. 0 (C) X n. Discuss this questions paper at www. int x ) { int u. P. Ltd.. if 7. Page 19 of 20 . © All rights reserved by GATE Forum Educational Services Pvt. (D) Change line 7 to:} while ( ( Y k = = x ) & & (i < j) ) . Page 20 of 20 . else j = k + 1.com On which of the following contents of Y and x does the program fail? (A) Y is 1 2 3 4 5 6 7 8 9 10 and x < 10 (B) Y is 1 3 5 7 9 11 13 15 17 19 and x < 1 (C) Y is 2 2 2 2 2 2 2 2 2 2 and x > 2 (D) Y is 2 4 6 8 10 12 14 16 18 20 and 2 < x < 20 and x is even 85. else j = k.CS GATE Paper 2008 84. (B) Change line 6 to:if ( Y k < x ) i = k − 1. (C) Change line 6 to:if ( Y k < = x ) i = k. Ltd.gateforum. Discuss this questions paper at www.gateforum. The correction needed in the program to make it work properly is (A) Change line 6 to:if ( Y k < x ) i = k + 1. www.com. else j = k − 1. No part of this booklet may be reproduced or utilized in any form without the written permission. Ltd. (D) (0B17)16 (B) 3 (C) 4 (D) 5 How many 32K x 1 RAM chips are needed to provide a memory capacity of 256Kbytes? (A) 8 8. (C) By checking the interrupt register after finishing the execution of the current instruction.com Q. 2. (C) At least three vertices have the same degree. No.CS GATE Paper 2009 www.y)} on the set {x. (D) By checking the interrupt register at fixed time intervals. Which one of the following is TRUE? (A) R is symmetric but NOT antisymmetric (B) R is NOT symmetric but antisymmetric (C) R is both symmetric and antisymmetric (D) R is neither symmetric nor antisymmetric 5. (z. (D) All vertices have the same degree.gateforum.y). No part of this booklet may be reproduced or utilized in any form without the written permission. 4. Page 1 of 13 .z}. (1217)8 is equivalent to (A) (1217)16 6. Discuss this questions paper at www. (A) 2 3.y. © All rights reserved by GATE Forum Educational Services Pvt. (B) At least two vertices have the same degree. (C) (2297)10 What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2-input NOR gates? (A) 2 7.gateforum. 1 – 20 Carry One Mark Each 1. Which one of the following in NOT necessarily a property of a Group? (A) Commutativity (B) Associativity (C) Existence of inverse for every element (D) Existence of identity What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n ≥ 2.x). Consider the binary relation R = {(x. (B) (028F)16 (B) 32 (C) 64 (D) 128 A CPU generally handles an interrupt by executing an interrupt service routine (A) As soon as an interrupt is raised (B) By checking the interrupt register at the end of fetch cycle. (B) 3 (C) n-1 (D) n Which one of the following is TRUE for any simple connected undirected graph with more than 2 vertices? (A) No two vertices have the same degree. (z. (x.z).com. What is the number of swaps required to sort n elements using selection sort. Then which one of the following is TRUE? (A) There is no polynomial time algorithm for πA .1} is described by the regular expression: (0+1)*0(0+1)*0(0+1)*? (A) The set of all strings containing the substring 00. 15. www. Which one of the following languages over the alphabet {0. (D) πA may be undecidable. (D) The set of all strings that begin and end with either 0 or 1. Finds whether any negative weighted cycle is reachable from the source. (C) The set of all strings containing at least two 0’s. Q. 13. Belady’s anomaly may occur? (A) FIFO 10. then it is NP-complete. No part of this booklet may be reproduced or utilized in any form without the written permission. 14. (C) Strings that begin and end with the same symbol (D) All even length palindromes.CS GATE Paper 2009 9. In which one of the following page replacement policies. Ltd.The language generated by the above grammar over the alphabet {a. in the worst case? (A) θ(n) 12. Discuss this questions paper at www. then P = NP.gateforum.com. © All rights reserved by GATE Forum Educational Services Pvt. Page 2 of 13 .gateforum. (B) If πA can be solved deterministically in polynomial time. Which of the following statement(s) is / are correct regarding Bellman-Ford shortest path algorithm? P.b} is the set of (A) All palindromes. if one exists.com (B) Optimal (C) LRU (D) MRU The essential content(s) in each entry of a page table is / are (A) Virtual page number (B) Page frame number (C) Both virtual page number and page frame number (D) Access right information 11. (B) All odd length palindromes. Always finds a negative weighted cycle. (B) θ(n log n) (C) θ(n2 ) (D) θ(n2 log n) S → aSa bSb a b . (A) P only (B) Q only (C) both P and Q (D) Neither P nor Q Let πA be a problem that belongs to the class NP. (B) The set of all strings containing at most two 0’s. (C) If πA is NP-hard. Match all items in Group 1 with correct options from those given in Group 2. } t = fun (n. S-3 Consider the program below: # include < stdio. Regular expression 1. S-2 (C) P-3.1. } The value printed is (A) 6 19. } int main() { int x = 15.com. Syntax analysis Q. int * f_p) { int t. fun(5. Group 1 18. www. Lexical analysis S. f = t+ * f_p. (D) Every nondeterministic PDA can be converted to an equivalent deterministic PDA.gateforum. f_p). Ltd. Discuss this questions paper at www. printf (" % d\ n". Control coupling V. No part of this booklet may be reproduced or utilized in any form without the written permission. Page 3 of 13 . return 1. (B) 8 (C) 14 (D) 15 The coupling between different modules of a software is categorized as follows: I. (C) Complement of every context-free language is recursive. Q-1. 17. R-4. S-3 (B) P-3. Code generation R. Pushdown automata 2. f. S-2 (D) P-2.gateforum. R-2. Q-1. Code optimization (A) P-4. Group 2 P. Register allocation 4. Common coupling III. R-1.com Which one of the following is FALSE? (A) There is unique minimal DFA for every regular language (B) Every NFA can be converted to an equivalent PDA. return f. R-4.h > int fun(int n. * f_p = t. return 0. Content coupling II.CS GATE Paper 2009 16. Dataflow analysis 3. & x)). Q-4. if (n <= 1) { * f_p = 1. IV Stamp coupling Data coupling Coupling between modules can be ranked in the order of strongest (least desirable) to weakest (most desirable) as follows: (A) I-II-III-IV-V (B) V-IV-III-II-I (C) I-III-V -II-IV (D) IV-II-V -III-I © All rights reserved by GATE Forum Educational Services Pvt. Q-1. Page 4 of 13 .CS GATE Paper 2009 20. Ltd. 3.492 d d c a b Which one of the following choices is correct? 23. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. 3. numbered from 1 to 6) is thrown.453 22. If the probability that the face is even given that it is greater than 3 is 0. 2. 3 (C) 2. Discuss this questions paper at www. 2. www. c are generators (C) c. The following notations are used: G(x): x is a gold ornament S(x): x is a silver ornament P(x): x is precious ( )) ( (C) ∃x ( ( G ( x ) ∧ S ( x ) ) → P ( x ) ) (A) ∀x P ( x ) → G ( x ) ∧ S ( x ) ) (( ) (D) ∀x ( ( G ( x ) ∨ S ( x ) ) → P ( x ) ) (B) ∀x G ( x ) ∧ S ( x ) → P ( x ) © All rights reserved by GATE Forum Educational Services Pvt.468 (C) 0. which one of the following options is closest to the probability that the face value exceeds 3? (A) 0. 2. 3 and 2. 3. No. d are generators (D) d. a are generators Which one of the following is the most appropriate logical formula to represent the statement? “Gold and silver ornaments are precious”. 2. 3.com Consider the HTML table definition given below: < table border=1> <tr> <td rowspan=2> ab </td> <td colspan=2> cd </td> </tr> <tr> <td> ef </td> <td rowspan=2> gh </td> </tr> <tr> <td colspan=2> ik </td> </tr> </table> The number of rows in each column and the number of columns in each row are: (A) 2.gateforum. 3 Q. (B) 0.2 (D) 2. (A) a.2 and 2.75. b are generators (B) b.2 and 2.com. 21 – 56 Carry Two Marks Each 21. An unbalanced dice (with 6 faces. 3 and 2.gateforum.485 For the composition table of a cyclic group shown below * a b c a b c d a b c d b a d c c d b a (D) 0.2 (B) 2. No part of this booklet may be reproduced or utilized in any form without the written permission. B=0. I3. ) ( III. S4 is shown below: S1 S2 S3 S4 I1 2 1 1 1 I2 1 3 2 2 I3 2 1 1 3 I4 1 2 2 2 © All rights reserved by GATE Forum Educational Services Pvt.CS GATE Paper 2009 24. (B) 1 Consider the following well-formed formulae: I.gateforum. B=1 with Output=1? (A) 3 (B) 4 (C) 5 (D) 6 28. what is the minimum length of an input string which will take the machine to the state A=0. one input and one output: Present Next Present Next Input Output State B State B State A State A 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 If the initial state is A = 0. Consider a 4 stage pipeline processor. Ltd.com. ¬∃x ¬P ( x ) ) (C) II and III ( IV. No part of this booklet may be reproduced or utilized in any form without the written permission. S3.com The binary operation □ is defined as follows P T T F F Q T F T F P□Q T T F T Which one of the following is equivalent to P ∨ Q ? (A) ¬Q¬P π/4 25. ∫ (B) P¬Q (1 − tan x ) / (1 + tan x ) dx (C) ¬PQ (D) ¬P¬Q (C) ln 2 (D) 1 ln 2 2 evaluates to 0 (A) 0 26. ( ¬∃x P ( x ) Which of the above are equivalent? (A) I and III (B) I and IV 27. ( ¬∀x P ( x ) ) II. The number of cycles needed by the four instructions I1. Page 5 of 13 . I4 in stages S1. I2. S2. Discuss this questions paper at www.gateforum. www. ¬∃x ¬P ( x ) ) (D) II and IV Given the following state table of an FSM with two states A and B. (D) All three processes will be in deadlock. 73.gateforum. (B) 23 (C) 28 (D) 30 Consider a 4-way set associative cache (initially empty) with total 16 cache blocks. Which one of the following memory block will NOT be in cache if LRU replacement policy is used? (A) 3 30. A non-preemptive resource allocation policy is used. I2. 155. The main memory consists of 256 blocks and the request for memory blocks is in the following order: 0. 32. Three processes P1. 6. No part of this booklet may be reproduced or utilized in any form without the written permission. R3 (3 units). what is the time taken to satisfy all requests if it takes 1ms to move from one cylinder to adjacent one and shortest seek time first policy is used? (A) 95ms (B) 119ms (C) 233ms (D) 276ms © All rights reserved by GATE Forum Educational Services Pvt. 48. 133. Consider a disk system with 100 cylinders. 159. 129. R4 (2 units).com. 31.} (A) 16 29. 92. 8. 20 Assuming that the head is currently at cylinder 50. t=7: releases 1 unit of R3 t=9: Finishes t=8: requests 2 units of R4 t=10: Finishes Which one of the following statements is TRUE if all three processes run concurrently starting at time t=0? (A) All processes will finish without any deadlock (B) Only P1 and P2 will be in deadlock. (B) 8 (C) 129 (D) 216 Consider a system with 4 types of resources R1 (3 units). 34. R2 (2 units). P3 request the sources as follows if executed independently. a request is not entertained if it cannot be completely satisfied.gateforum.com What is the number of cycles needed to execute the following loop? For (i=1 to 2) {I1. Page 6 of 13 . 216. Process P1: Process P2: Process P3: t=0: requests 2 units of R2 t=0: requests 2 units of R3 t=0: requests 1 unit of R4 t=1: requests 1 unit of R3 t=2: requests 1 unit of R4 t=2: requests 2 units of R1 t=3: requests 2 units of R1 t=4: requests 1 unit of R1 t=5: releases 2 units of R1 t=5: releases 1 unit of R2 t=6: releases 1 unit of R3 t=7: requests 1 unit of R2 t=8: Finishes t=8: requests 1 unit of R3 and 1 unit of R1. The requests to access the cylinders occur in following sequence: 4.CS GATE Paper 2009 www. 15. 7. 2. Ltd. 19. I4. 63. 3. (C) Only P1 and P3 will be in a deadlock. 1. 10. 255. 73. I3. At any given instance. 8. P2. Discuss this questions paper at www. 4. III. Page 7 of 13 . The solution is starvation free. it would result in another process making transition A immediately. II.com. IV. assume that there are always some processes in the ready state: B Start A Re ady Running D Ter min ated C E F Blocked Now consider the following statements: I. The OS uses preemptive scheduling.CS GATE Paper 2009 32. Ltd. Discuss this questions paper at www. } In the above solution. Which of the above statements is TRUE? (A) I only (B) I and II (C) II and III (D) IV only © All rights reserved by GATE Forum Educational Services Pvt.gateforum. (B) I and III (C) II and III (D) II and IV The enter_CS() and leave_CS() functions to implement critical section of a process are realized using test-and-set instruction as follows: void enter_CS(X) { while ( test-and-set(X)) . The OS uses non-preemptive scheduling. A process P2 in blocked state can make transition E while another process P1 is in running state. Which of the above statements are TRUE? (A) I and II 33. The above solution to CS problem is deadlock-free II. If a process makes a transition D. III. X is a memory location associated with the CS and is initialized to 0. IV More than one process can enter CS at the same time. www. } void leave_CS(X) { X=0.com In the following process state transition diagram for a uniprocessor system. No part of this booklet may be reproduced or utilized in any form without the written permission. Now consider the following statements: I.gateforum. The processes enter CS in FIFO order. (B) It helps to reduce the size of page table needed to implement the virtual address space of a process.15 18 What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0.gateforum. 2.CS GATE Paper 2009 34. (D) It helps to reduce the number of page faults in page replacement algorithms. No part of this booklet may be reproduced or utilized in any form without the written permission.gateforum.com. 2 5. 18. The running time of an algorithm is represented by the following recurrence relation: n T(n) = n T 3 + cn n≤ 3 otherwise Which one of the following represents the time complexity of the algorithm? (A) θ(n) 36. Page 8 of 13 . 35. What is the resultant hash table? (A) 37. Discuss this questions paper at www. (D) θ(n2 log n) The keys 12. 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h(k) = k mod 10 and linear probing. (C) It is required by the translation lookaside buffer. 3. 13. Ltd. (A) 2 38. (C) θ(n2 ) (B) 3 (C) 4 (D) 5 Consider the following graph: b e 2 5 5 6 a 6 4 d g 3 6 3 4 5 c 6 f © All rights reserved by GATE Forum Educational Services Pvt.3. (B) θ(n log n) 0 (B) 1 0 (C) 0 (D) 1 1 0 1 2 2 2 12 2 12 2 3 23 3 13 3 13 3 13. 23. 23 15 4 5 5 4 5 2 3 4 5 4 5 6 6 6 23 6 7 7 7 5 7 8 18 8 9 15 9 8 18 8 9 18 9 12.com A multilevel page table is preferred in comparison to a single level page table for translating virtual address to physical address because (A) It reduces the memory access time to read or write a memory location. www. e) (e. No part of this booklet may be reproduced or utilized in any form without the written permission.com.f) (b. the (n/4)th smallest element is selected as pivot using an O(n) time algorithm. where L1 and L2 are languages as defined below: { = {ab c } L1 = am bm c an bm | m.c) (f.c) (a. IV Code improving transformations can be performed at both source language and intermediate code level.k ≥ 0 Then L is (A) Not recursive (B) Regular (C) Context free but not regular (D) Recursively enumerable but not context free. Ltd.c) (f. for sorting n elements.d) (C) (b.gateforum. (A) I and II (B) I and IV (C) III and IV (D) I.c) (f.n ≥ 0 L2 i j k } | i. (A) (b. 41.e) (e.c) (b. (B) θ(n log n) (C) θ(n2 ) (D) θ(n2 log n) Let L = L1 I L 2 .f) (a. II A programming language which allows recursion can be implemented with static storage allocation. What is the worst case time complexity of the quick sort? (A) θ(n) 40. Discuss this questions paper at www. j. (A) begin either with 0 or 1 (B) end with 0 (C) end with 00 (D) contain the substring 00. Which of the following statements are TRUE? I There exist parsing algorithms for some programming languages whose ( ) complexities are less than θ n3 .d) (B) (b.f) (a.1} that 42. Page 9 of 13 . III and IV © All rights reserved by GATE Forum Educational Services Pvt. III No L-attributed definition can be evaluated in the framework of bottom-up parsing.f) (b.g) (c.d) In quick sort.com Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal’s algorithm? 39.g) (c.gateforum.d) (D) (b.c) (c.g) (b. 1 1 0 0 0 1 The above DFA accepts the set of all strings over {0.c) (e.g) (c.CS GATE Paper 2009 www.e) (a.c) (f.e) (e. M' = Me mod φ(n) ( ) M = M' d mod φ(n) © All rights reserved by GATE Forum Educational Services Pvt. the private and public keys are (e. No part of this booklet may be reproduced or utilized in any form without the written permission. (D) III and IV In the RSA public key cryptosystem.tree is initially empty. The order of internal nodes is the maximum number of tree pointers in each node.c Which of the above queries are equivalent? (A) I and II (B) I and III (C) II and IV 46.c=S.c} and S={c}.gateforum. www. where n=p*q and p and q are large primes. 6. S2. 4. Discuss this questions paper at www. IV ( πR − S (r ) − πR − S πR − S (r ) × s − πR − S.S (r ) {t | t ∈ π {t | t ∈ π ) R −S (r ) ∧ ∀u ∈ s ( ∃v ∈ r (u = v s ∧ t = v R − S ) )} R −S (r ) ∧ ∀v ∈ r ( ∃u ∈ s (u = v s ∧ t = v R − S ) )} Select R. I M' = Me mod n ( ) ' M= M d II. 2. The B+ . 3. S4 of T1 and T2 as given below: T1 : R1 x W1 x W1 y T2 : R 2 x R 2 y W2 y S1 : R1 x R2 x R2 y W1 x W1 y W2 y S2 : R1 x R 2 x R 2 y W1 x W2 y W1 y S3 : R1 x W1 x R 2 x W1 y R2 y W2 y S4 : R 2 x R 2 y R1 x W1 x W1 y W2 y Which of the above schedules are conflict-serializable? (A) S1 and S2 44.n) respectively. 1 The maximum number of times leaf nodes would get split up as a result of these insertions is (A) 2 45. II. 10. and four schedules S1. Now consider the following equations.tree in which order of the internal nodes is 3. Besides.S Where R. Now consider the following queries on the database: I. Page 10 of 13 .a.com Consider two transactions T1 and T2. ed ≡ 1mod n mod n III.com. (B) 3 (C) 4 (D) 5 Let R and S be relational schemes such that R={a.n) and (d. ed ≡ 1mod φ (n) IV. n is public and p and q are private. S3. Ltd.gateforum. and the order of leaf nodes is the maximum number of data items that can be stored in it. Let M be an integer such that 0<M<n and φ (n) = (p − 1) ( q − 1) . in the sequence given below.CS GATE Paper 2009 43.b. III.b From R. 8. R. and that of the leaf nodes is 2. (B) S2 and S3 (C) S3 only (D) S4 only The following key values are inserted into a B+ . 0. III Control information should not be represented in a DFD. 10 platters each with 2 recording surfaces and 1000 cylinders. 0 . and so on 51. The address <400. where a decision is effectively any conditional statement in the module. Which of the following statements are TRUE? I The context diagram should depict the system as a single bubble. The clock counter increments once per millisecond. III. Which one of the choices given below is closest to the minimum permissible rate at which sequence numbers used for packets of a connection can increase? (A) 0.015/s (B) 0.135/s (D) 0. While opening a TCP connection. (B) 505036 th The address of the 1039 (C) 505037 (D) 505038 sector is © All rights reserved by GATE Forum Educational Services Pvt. Let G(x) be the generator polynomial used for CRC checking. The address of a sector is given as a triple c.com. 49. the 0th sector is addressed as 0. Page 11 of 13 . Consider the following statements about the cyclomatic complexity of the control flow graph of a program module. What is the condition that should be satisfied by G(x) to detect odd number of bits in error? (A) G(x) contains more than two terms (B) G(x) does not divide 1+xk. II and III Common Data Questions: 51 & 52 A hard disk has 63 sectors per track. the initial sequence number is to be derived using a time-of-day (ToD) clock that keeps running even when the host is down. where c is the cylinder number. 29> corre4sponds tp sector number: (A) 505035 52.1 . The cyclomatic complexity of a module is equal to the maximum number of linearly independent circuits in the graph. II. the 1st sector as 0. Thus. (A) I and II (B) II and III (C) I and III (D) I. (A) II and III (B) II and III (C) I and III (D) I. for any k not exceeding the frame length (C) 1+x is a factor of G(x) (D) G(x) has an odd number of terms. II and III 50. Ltd.064/s (C) 0. The cyclomatic complexity of a module is the number of decisions in the module plus one. The low order 32 bits of the counter of the ToD clock is to be used for the initial sequence numbers. II External entities should be identified clearly at all levels of DFDs. 16. Discuss this questions paper at www. The maximum packet lifetime is given to be 64s. s .CS GATE Paper 2009 www.327/s 48. The cyclomatic complexity can also be used as a number of linearly independent paths that should be tested during path coverage testing.h. Which of these are TRUE? I.gateforum.com Which of the above equations correctly represent RSA cryptosystem? (A) I and II (B) I and III (C) II and IV (D) III and IV 47. No part of this booklet may be reproduced or utilized in any form without the written permission. h is the surface number and s is the sector number. IV A data store can be connected either to another data store or to an external entity. 0.gateforum. if i.31 (D) 0. We wish to find the length of the longest common sub-sequence (LCS) of X[m] and Y[n] as l(m. 53.com.j) may be computed in a row major order or column major order of L(M.sid FROM Catalog C WHERE C. 31 Common Data Questions: 53 & 54 A sub-sequence of a given sequence is just the given sequence with some elements (possibly none or all) left out. where M = m+1 and N=n+1.16. city:string. with indexes of X and Y starting from 0.s] if either p<r or q<s.N]. Which one of the following statements would be TRUE regarding the dynamic programming solution for the recursive definition of l(i. Ltd. 30 (C) 0.j). if either i=0 or j=0 = expr1. pname:string.16.j) to be properly computed. if i.sid NOT IN (SELECT C. Consider the following relational query on the above database: SELECT S.N). (B) exp r1 ≡ l (i. l (i.15. j − 1) . sname:string. using an array L[M. l (i.j) ) The values of l(i.sname FROM Suppliers S WHERE S.CS GATE Paper 2009 (A) 0.j) cannot be computed in either row major order or column major order of L(M. street:string) Parts(pid:integer.j)? (A) All elements L should be initialized to 0 for the values of l(i. cost:real) 55.17.gateforum. 31 www. j) .color<> 'blue')) © All rights reserved by GATE Forum Educational Services Pvt.pid FROM Parts P WHERE P.pid NOT (SELECT P. Discuss this questions paper at www. j) = 0. j − 1) ) ( (D) exp r2 ≡ max l (i − 1.q] needs to be computed before L[r. (C) The values of l(i.j) to compute the length of the LCS of X[m] and Y[n] is given below: l (i.gateforum. respectively. We are given two sequences X[m] and Y[n] of lengths m and n. j) + 1 ( (C) exp r2 ≡ max l (i − 1. No part of this booklet may be reproduced or utilized in any form without the written permission. (D) L[p.com (B) 0.N).j) could be obtained by dynamic programming based on the correct recursive definition of l(i. color:string) Catalog(sid:integer. such that L[i. pid:integer. Common Data Questions: 55 & 56 Consider the following relational schema: Suppliers(sid:integer. (B) The values of l(i.j] = l(i.j-1) 54.j>0 and X i-1 = Y j − 1 Which one of the following options is correct? (A) exp r1 ≡ l (i − 1. Page 12 of 13 .n).j) of the form given above.j>0 and X i-1 = Y j − 1 = expr2. where an incomplete recursive definition for the function l(i. 13. Which one of the following array represents a binary max-heap? (A) {25. The propagation time is 25ms. 8. 8.13.13. 8.16. Consider a binary max-heap implemented using an array.12.10. each supplier and each street within a city has a unique name. and (sname. in the suppliers relation above.60 Carry Two Marks Each Statement for Linked Answer Questions: 57 & 58 57. (D) Find the names of all suppliers who have not supplied only blue parts.10} © All rights reserved by GATE Forum Educational Services Pvt. 8.12. 58. 8. 8. 60.) (A) 16ms (B) 18ms (C) 20ms (D) 22ms Statement for Linked Answer Questions: 59 & 60 59. 8.12.14. where l is the number of bits identified in the earlier part and acknowledgements are always piggy backed.10.57 to Q.10} (C) {14.14} (B) {25. (A) l=2 (B) l=3 (C) l=4 (D) l=5 Suppose that the sliding window protocol is used with the sender window size of 2l. what is the minimum time the sender will have to wait before starting transmission of the next frame? (Identify the closest choice ignoring the frame processing time.12} (C) {25.10} (D) {14.16} What is the content of the array after two delete operations on the correct answer to the previous question? (A) {14.10. Assume that. What is the minimum number of bits (l) that will be required to represent the sequence numbers distinctly? Assume that no time gap needs to be given between transmission of two frames.10. 56. (B) Find the names of all suppliers who have not supplied a non-blue part.EX CS GATE Paper 2009 www.13.12. (C) Find the names of all suppliers who have supplied only blue parts.com Assume that relations corresponding to the above schema are not empty. After sending 2l frames.12. 8} (B) {14.12} (D) {25. Frames are to be transmitted into this link to maximally pack them in transit (within the link).12.gateforum.13.gateforum.14.14. Page 13 of 13 . Which one of the following is TRUE about the above schema? (A) The schema is in BCNF (B) The schema is in 3NF but not in BCNF (C) The schema is in 2NF but not in 3NF (D) The schema is not in 2NF Linked Answer Questions: Q. Ltd. Frames of 1000 bits are sent over a 106 bps duplex link between two hosts. city) forms a candidate key.13. Discuss this questions paper at www.13. No part of this booklet may be reproduced or utilized in any form without the written permission.com.13.16.16. No other functional dependencies are implied other than those implied by primary and candidate keys. Which one of the following is the correct interpretation of the above query? (A) Find the names of all suppliers who have supplied a non-blue part.10. gateforum.CS GATE Paper 2010 www. (D) S = T + 1 (B) 3. 1 – 25 Carry One Mark Each 1. Q. ω2}. No. 7. The time taken for a single refresh operation is 100 nanoseconds. The 2’s complement representation of P is (F87B)16. 1 .com Q. 8.676 (C) 3. If S and T are two different trees with ξ ( S ) = ξ ( T ) . ω.607 What is the possible number of reflexive relations on a set of 5 elements? (A) 210 4. No part of this booklet may be reproduced or utilized in any form without the written permission.575 3. R) = PQ + QR + PR is (A) m2 + m4 + m6 + m7 (B) m0 + m1 + m3 + m5 (C) m0 + m1 + m6 + m7 (D) m2 + m3 + m4 + m5 A main memory unit with a capacity of 4 megabytes is built using 1M×1-bit DRAM chips.5 as the initial value.com. (B) e-2 (C) e-1/2 (D) 1 The minterm expansion of f (P. Discuss this question paper at www. Each DRAM chip has 1K rows of cells with 1K cells in each row. If * denotes the multiplication operation. Ltd. (C) S = T Newton-Raphson method is used to compute a root of the equation x2 − 13 = 0 with 3. then (A) S = 2 T 2. where id is the number of d vertices of degree d in G.gatementor. Define ξ ( G) = ∑i d × d . Let G=(V. where ω and ω2 are cube roots of unity. The time required to perform one refresh operation on all the cells in the memory unit is (A) 100 nanoseconds (B) 100*210 nanoseconds (C) 100*220 nanoseconds (D) 3200*220 nanoseconds P is a 16-bit signed integer.667 (D) 3. The 2’s complement representation of 8*P is (A) ( C3D8 )16 (B) (187B )16 (C) (F878 )16 (D) ( 987B )16 © All rights reserved by Gateforum Educational Services Pvt. *) forms (A) A group (B) A ring (C) An integral domain (D) A field 2n 5. E) be a graph. 1 What is the value of lim 1 − ? n→∞ n (A) 0 6. (B) S = T − 1 (B) 215 (C) 220 (D) 225 Consider the set S = {1. the structure (S. The approximation after one iteration is (A) 3. } int i = 0. Q (B) 1 (C) ( n − 1) / 2 (D) n-1 What does the following program print? #include < stdio. } (A) 2 2 12. j = 1. int main ( ){ f(&i. What is the smallest value of k for which package B will be preferred over A? (A) 12 13. (C) 0 1 (D) 0 2 Two alternative packages A and B are available for processing a database having 10k records. i. Discuss this question paper at www. Every node is considered to be its own descendant.h > void f (int * p. & j). j) .CS GATE Paper 2010 9. every node has an odd number of descendants. return 0.gateforum. * p = 2. 2 . Package A requires 0. (B) 2 1 (B) 10 (C) 6 (D) 5 Which data structure in a compiler is used for managing information about variables and their attributes? (A) Abstract syntax tree (B) Symbol table (C) Semantic stack (D) Parse table © All rights reserved by Gateforum Educational Services Pvt.gatementor. What is the number of nodes in the tree that have exactly one child? (A) 0 11.com The Boolean expression for the output f of the multiplexer shown below is (A) P ⊕ Q ⊕ R R R (B) P ⊕ Q ⊕ R f R R (C) P + Q + R P (D) P + Q + R 10. int * g) { p = q.com. www.0001n2 time units and package B requires 10nlog10n time units to process n records. Ltd. In a binary tree with n nodes. pr int f ( "%d %d \ n ". No part of this booklet may be reproduced or utilized in any form without the written permission. com Which languages necessarily need heap allocation in the runtime environment? (A) Those that support recursion (B) Those that use dynamic scoping (C) Those that allow dynamic data structures (D) Those that use global variables 15. Ltd.gateforum. No part of this booklet may be reproduced or utilized in any form without the written permission. pname.CS GATE Paper 2010 14. Which one of the following is not a client server application? (A) Internet chat 17. What is the minimum number of keys in any non-root node? (A) 1 19. Which of the following statements best explains the need for this field? (A) It can be used to prioritize packets (B) It can be used to reduce delays (C) It can be used to optimize throughput (D) It can be used to prevent packet looping 16. (B) 2 (C) 3 (D) 4 A relational schema for a train reservation database is given below Passenger (pid. www. (B) Web browsing (C) E-mail (D) Ping Let L1 be a recursive language. Discuss this question paper at www. Consider a B+-tree in which the maximum number of keys in a node is 5.gatementor. Let L2 and L3 be languages that are recursively enumerable but not recursive. cass. Which of the following statements is not necessarily true? (A) L2 – L1 is recursively enumerable (B) L1 – L3 is recursively enumerable (C) L2 ∩ L1 is recursively enumerable (D) L2 ∪ L1 is recursively enumerable 18. One of the header fields in an IP datagram is the Time to Live (TTL) field. age ) Re servation (pid.com. tid) Table : Passenger pid 'pname Age 0 ' Sachin' 65 1 'Rahul' 66 2 ' Sourav ' 67 3 ' Anil' 69 Table : Re servation pid 0 1 2 5 1 3 class ' AC ' ' AC ' ' SC ' ' AC ' ' SC ' ' AC ' tid 8200 8201 8201 8203 8204 8202 © All rights reserved by Gateforum Educational Services Pvt. 3 . Requirements Capture 1.S-1 (B) P-2. Q-3.S-4 (D) P-2.CS GATE Paper 2010 www. Performance Tuning (A) P-3.R-4. Implementation 3. Ltd. 2-phase locking II.com What pids are returned by the following SQL query for the above instance of the tables? SELECT pid FROM Re servation WHERE class = ' AC ' AND EXISTS (SELECT * FROM Passenger WHERE age > 65 AND Passenger. Q-2.S-4 (C) P-3. Time-stamp ordering 21.pid) (A) 1. 0 20. What is the cyclomatic complexity of the sequential integration shown on the right hand side? A A B B (A) 19 22. (B) 21 (C) 20 (D) 10 What is the appropriate pairing of items in the two columns listing various activities encountered in a software li fe cycle? P.gateforum.R-4. 4 . Maintenance 4.S-1 © All rights reserved by Gateforum Educational Services Pvt. No part of this booklet may be reproduced or utilized in any form without the written permission. (A) I only (B) II only (C) Both I and II (D) Neither I nor II The cyclomatic complexity of each of the modules A and B shown below is 10. Q-2.R-1.pid = Reservation. Discuss this question paper at www. Design 2. Domain Analysis R. 2 (C) 1. Q-3.R-1. Structural and Behavioral Modeling S. 3 (D) 1. (B) 1. 5 Which of the following concurrency control protocols ensure both conflict serializability and freedom from deadlock? I.com.gatementor. Module Development and Integration Q. II and III Q. 4. How many page faults will occur? (A) 196 25. (1 − q) p (B) 4/625 (C) 12/625 (D) 16/625 The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. 6. www. 5. The company therefore subjects each computer to a testing process. 1 II. S2 = not (S1). 5 . Which of the following sequences can not be the degree sequence of any graph? I.com Consider the methods used by processes P1 and P2 for accessing their critical sections whenever needed.gateforum. No. Discuss this question paper at www. (B) 192 (C) 197 (D) 195 Which of the following statements are true? I. 2. The system first accesses 100 distinct pages in some order and then accesses the same 100 pages but now in the reverse order. 3. This testing process gives the correct result for any computer with a probability of q. 2 © All rights reserved by Gateforum Educational Services Pvt. while ( S 1 != S 2 ) . Preemptive scheduling may cause starvation III. 3.gatementor. No part of this booklet may be reproduced or utilized in any form without the written permission. It has 4 page frames with no pages loaded to begin with. Ltd. 6. The initial values of shared boolean variables S1 and S2 are randomly assigned. Critica1 Section Critica1 Section S1 = S2.CS GATE Paper 2010 23. 2. (C) (1 − p ) q (D) pq What is the probability that divisor of 1099 is a multiple of 1096? (A) 1/625 28.com. as given below. Which one of the following statements describes the properties achieved? (A) Mutual exclusion but not progress (B) Progress but not mutual exclusion (C) Neither mutual exclusion nor progress (D) Both mutual exclusion and progress 24. The probability of a faulty assembly of any computer is p. 3. Shortest remaining time first scheduling may cause starvation II. 6. 6. Round robin is better than FCFS in terms of response time (A) I only (B) I and III only (C) II and III only (D) I. 6. 4. A system uses FIFO policy for page replacement. 7. Consider a company that assembles computers. 26 – 55 Carry Two Marks Each 26. Method used by PI Method used by P2 while ( S 1 = = S 2 ) . What is the probability of a computer being declared faulty? (A) pq + (1 − p ) (1 − q) (B) 27. 1 (A) I and II (C) IV only (D) II and IV (C) x = −3. Discuss this question paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission.00.gateforum.00 1 T T Q Q Clock (C) 10.11 (D) 11. 4. t ))? (A) Everyone can fool some person at some time (B) No one can fool everyone all the time (C) Everyone cannot fool some person all the time (D) No one can fool some person at some time 31.11. y = 10 (B) III and IV Consider the following matrix 2 3 A= x y If the eigenvalues of A are 4 and 8. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F ( x. Ltd. 1.CS GATE Paper 2010 29. 4.01. 6 . y = 9 (D) x = −4. 6. f P R Q R In the sequential circuit shown below. y. 7.01. y = 10 30. 7. t) is used to represent the statement that person x can fool person y at time t.01 Q0 Q1 © All rights reserved by Gateforum Educational Services Pvt. what are the next four values of Q1Q0? (A) 11.10.10. 6.01. 7. 2 IV. www. (B) x = 5. if the initial value of the output Q1Q0 is 00.com. y.gatementor. 8. 2. 3. then (A) x = 4. 2. What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below? P Q (A) Q + R Q R (B) P + Q (C) P + R (D) P + Q + R 32. y = 8 Suppose the predicate F(x. 4.00 (B) 10. 6.com III.00. . keeping the order of the remaining elements the same. OF and WO stages take 1 clock cycle each for any instruction. Discuss this question paper at www. a1. a0 + Y ) 35.n − 1).. 3 clock cycles for MUL instruction.h > int f(int * a. and 6 clock cycles for DIV instruction respectively. } (A) -9 36. © All rights reserved by Gateforum Educational Services Pvt. Operand forwarding is used in the pipeline.CS GATE Paper 2010 33. Then X is equal to (A) max ( Y. Instruction Decode (ID). 4. else if(*a % 2 = = 0) return * a + f(a + 1. a1 . Let X denote the maximum possible weight of a subsequence of a0 .R 2 .…. return 0.R5 .gatementor.R 6 (A) 13 34. f(a.R1 I1 : DIV R5 .an-1 of real numbers is defined as a0 + a1 / 2 + . 6}.R 4 I2 : ADD R 2 . A 5-stage pipelined processor has Instruction Fetch (IF). It modifies the list by moving the last element to the front of the list and returns the modified list. pr int f ("%d". What is the number of clock cycles needed to execute the following sequence of instructions? Instruction Meaning of instruction I0 : MUL R 2 .R 2 I3 : SUB R 5 ... Ltd. 7 . A subsequence of a sequence is obtained by deleting some elements from the sequence. The PO stage takes 1 clock cycle for ADD and SUB instructions.R 3 . a0 + 2Y) (D) a0 + Y / 2 What is the value printed by the following C program? #include < stdio. int n) { if (n <= 0)return 0.com R2 R5 R2 R5 ← R0 ← R3 ← R5 ← R2 * R1 / R4 + R2 − R6 (B) 15 (C) 17 (D) 19 The weight of a sequence a0. Some part of the code is left blank. 6)).R 0 . www. No part of this booklet may be reproduced or utilized in any form without the written permission. else return * a − f(a + 1. an−1. The IF. n − 1).. 13.com. 7. Perform Operation (PO) and Write Operand (WO) stages. a0 + Y /2) (C) max ( Y. } int main ( ) { int a[ ] = {12. + an−1 / 2n−1. ID.gateforum. (B) 5 (C) 15 (D) 19 The following C function takes a simply-linked list as input argument. 11. Operand Fetch (OF).. (B) max( Y. head = p.gatementor. e. p->next = head. 8 . Node *move_to_front(Node *head) { Node *p. while (p-> next !=NULL) { q=P. The program below uses six temporary variables a. c. *q. Discuss this question paper at www. q->next = NULL. p=p->next. struct node *next. if ((head = = NULL: || (head->next = = NULL)) return head. f.gateforum. q = NULL. (A) q = NULL. p = head. what is the minimum number of registers needed to execute t h i s program without spilling? (A) 2 38. (B) q->next = NULL. p->next = head.com.com typedef struct node { int value. } Node. b. No part of this booklet may be reproduced or utilized in any form without the written permission. (B) 3 (C) 4 (D) 6 The grammar S → aSa|bS|c is (A) LL(1) but not LR(1) (B) LR(1) but not LR(1) (C) Both LL(1) and LR(1) (D) Neither LL(1) nor LR(1) © All rights reserved by Gateforum Educational Services Pvt. head = p. head = p. } Choose the correct alternative to replace the blank line. (D) q->next = NULL. Ltd. d.CS GATE Paper 2010 www. a=1 b = 10 c = 20 d = a+b e=c+d f =c+e b =c+e e=b+f d=5+e return d + f Assuming that all operations take their operands from registers. p->next = q. 37. } _______________________________ return head. (C) head = p. p->next = head. L is the set of all bit strings with even number of 1s.com. What is the maximum number of tuples possible in the natural join R S? (A) 100 (B) 200 (C) 300 (D) 2000 © All rights reserved by Gateforum Educational Services Pvt. www. (B) n (C) n+1 (D) 2n-1 Consider the following schedule for transactions T1. Ltd. (A) ( 0 * 10 * 1) * (B) 0 * (10 * 10 *) * (C) 0 * (10 * 1 *) * 0 * (D) 0 * 1 (10 * 1) * 10 * Consider { the languages { } { } { } i j i j i j L1 = 01 | i ≠ j .CS GATE Paper 2010 39. Discuss this question paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission. Let L be the set of all substrings of w. 1}*. i. (A) T1 → T3 → T2 (B) T2 → T1 → T3 (C) T2 → T3 → T1 (D) T3 → T1 → T2 The following functional dependencies hold for relations R(A.e. T2 and T3: T1 T2 T3 Re ad ( X ) Re ad ( Y ) Re ad ( Y ) Write ( Y ) Write ( X ) Write ( X ) Re ad ( X ) Write ( X ) Which one of the schedules below is the correct serialization of the above? 43. } L4 = 01 | i ≠ 2j . L2 = 01 | i = j . i j (A) Only L2 is context free (B) Only L2 and L3 are context free (C) Only L1 and L2 are context free (D) All are context free Let w be any string of length n in {0. B. L3 = 01 | i = 2j + 1 .com Let L = {w ∈ ( 0 + 1) * | w has even number of 1s} . D. What is the minimum number of states in a non-deterministic finite automaton that accepts L? (A) n-1 42.gatementor. C) and S(B. A→C The relation R contains 200tuples and the relation S contains 100tuples.gateforum. Which one of the following statements is true? 41. E) B → A. 9 . Which one of the regular expressions below represents L? 40. Process P0 while (true) { wait (S0). T4 (D) T1. and k processes P0.Pk-1. Release (S0). The exact values are not given.gateforum.com The following program is to be tested for statement coverage: begin if ( a = = b ) {S1. www. } How many times will process P0 print ‘0’? (A) At least twice 46.k = 19 © All rights reserved by Gateforum Educational Services Pvt. 10 . release (S2). S3 and S4? (A) T1. release (S0). T2. exit. Ltd. } In which one of the following situations is a deadlock possible? (A) n = 40. S1=0. T1 : a. (B) T2. if (i+2<n)request Rn-i-2 . b. T4 The following program consists of 3 concurrent processes and 3 binary semaphores. Process P1 Process P2 wait (S1). (B) Exactly twice (C) Exactly thrice (D) Exactly once A system has n resources R0. S2=0.} else {S3. T2. exit. is as follows: if (i% 2==0) { if (i<n) request Ri .. } else { if (i<n) request Rn-i.} S4.CS GATE Paper 2010 44. T4 (C) T3.k = 26 (B) n = 21. T2. S2. print ‘0’ release (S1). b.com. The semaphores are initialized as S0=1.} else if ( c = = d) {S2. The implementation of the resource request logic of each process Pi. if (i+2<n)request Ri+2 .…. c and d are all distinct T3 : a=b and c !=d T4 : a !=b and c=d Which of the test suites given below ensures coverage of statements S1. wait (S2). c and d. T3 and T4 given below are expressed in terms of the properties satisfied by the values of variables a.k = 10 (D) n = 41. b. No part of this booklet may be reproduced or utilized in any form without the written permission.….k = 12 (C) n = 20. T3 45. Discuss this question paper at www.gatementor. c and d are all equal T2 : a. end The test cases T1.Rn-1. 113 and 10. L1 Cache 48. No part of this booklet may be reproduced or utilized in any form without the written permission. Which of the values of N given below should not be used if A and B should belong to the same network? (A) 255.CS GATE Paper 2010 47.255. j}. L2 cache and main memory unit respectively. 20 nanoseconds and 200 nanoseconds for L1 cache. Entry Wij in the matrix W below is the weight of the edge {i.255.91 respectively and they both use the same net mask N. (B) 8 (C) 9 (D) 10 What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges? (A) 7 (B) 8 (C) 9 (D) 10 © All rights reserved by Gateforum Educational Services Pvt. 3. 49. Data Bus 4 words L2 Cache Data Bus 4 words Main Memory When there is a miss in L1 cache and a hit in L2 cache.1. 0 1 8 1 4 1 0 12 4 9 W = 8 12 0 7 3 1 4 7 0 2 4 9 3 2 0 50. The memory access times are 2 nanoseconds.255.224 Common Data Questions: 48 & 49 A computer system has an L1 cache.gateforum. The block size in L2 cache is 16 words. 4}. a block is transferred from L2 cache to L1 cache. 2. www.105.255. and a main memory unit connected as shown below.255. and then a block is transferred from L2 cache to L1 cache. The block size in L1 cache is 4 words. What is the time taken for this transfer? (A) 2 nanoseconds (B) 20 nanoseconds (C) 22 nanoseconds (D) 88 nanoseconds When there is a miss in both L1 cache and L2 cache.com Suppose computers A and B have IP addresses 10.255. Ltd.255.192 (D) 255.com. 11 .gatementor. What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T? (A) 7 51.0 (B) 255. What is the total time taken for these transfers? (A) 222 nanoseconds (B) 888 nanoseconds (C) 902 nanoseconds (D) 968 nanoseconds Common Data Questions: 50 & 51 Consider a complete undirected graph with vertex set {0.255. 1.105.128 (C) 255. an L2 cache. first a block is transferred from main memory to L2 cache.1. Discuss this question paper at www. 23. 46. 52 How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above? (A) 10 (B) 20 (C) 30 (D) 40 Statement for Linked Answer Questions: 54 & 55 Consider a network with 6 routers R1 to R6 connected with links having weights as shown in the following diagram R2 7 R4 6 R1 8 2 3 4 R3 54. the table is as shown below 0 1 2 42 3 23 4 34 5 52 6 46 7 33 8 9 52. 12 . After inserting 6 values into an empty hash table. 33 (D) 42.gatementor. 23.CS GATE Paper 2010 www. 52. 34. 42. 42. 42. 52. Each router starts with its routing table initialized to contain an entry for each neighbour with the weight of the respective connecting link. After all the routing tables stabilize. 23.com Linked Answer Questions: Q. 46 (C) 46. 33. how many links in the network will never be used for carrying any data? (A) 4 (B) 3 (C) 2 (D) 1 © All rights reserved by Gateforum Educational Services Pvt.gateforum.55 Carry Two Marks Each Statement for Linked Answer Questions: 52 & 53 A hash table of length 10 uses open addressing with hash function h(k)=k mod 10.52 to Q.com. R6 1 9 R5 All the routers use the distance vector based routing algorithm to update their routing tables. 34. Ltd. 53. and linear probing. 33 (B) 34. 33. Discuss this question paper at www. 34. No part of this booklet may be reproduced or utilized in any form without the written permission. Which one of the following choices gives a possible order in which the key values could have been inserted in the table? (A) 46. 52. 23. If 137+276=435 how much is 731+672? (A) 534 62. (C) betrayed (D)suppressed Which of the following options is closest in meaning to the word Circuitous. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Hari’s age + Gita’s age > Irfan’s age + Saira’s age ii. Ltd.e. we would leave a better planet for our children.gatementor. www. (A) uphold 59. Discuss this question paper at www. No part of this booklet may be reproduced or utilized in any form without the written permission. Then the number of persons playing neither hockey nor football is: (A) 2 60. There are no twins. 13 .CS GATE Paper 2010 55. Irfan (I) and Saira (S) are siblings (i. (B) restrain (B) 17 (C) 13 (D) 3 The question below consists of a pair of related words followed by four pairs of words. Given the following facts: i. (A) cyclic 58. (B) 1403 (C) 1623 (D)1513 Hari (H). brothers and sisters). (B) belied (B) indirect (C) confusing (D) crooked Choose the most appropriate word from the options given below to complete the following sentence: If we manage to ____________ our natural resources. The age difference between Gita and Saira is 1 year. Choose the most appropriate word from the options given below to the complete the following sentence: His rather casual remarks on politics ___________ his lack of seriousness about the subject. © All rights reserved by Gateforum Educational Services Pvt.gateforum. All were born on 1st january.com Suppose the weights of all unused links in the previous question are changed to 2 and the distance vector algorithm is used again until all routing tables stabilize. No. Select the pair that best expresses the relation in the original pair. However Gita is not the oldest and Saira is not the youngest.com. How many links will now remain unused? (A) 0 (B) 1 (C) 2 (D) 3 Q. No. 17 of them play football and 10 of them play both hockey and football. (A) masked 57. Unemployed: Worker (A) fallow: land (B) unaware: sleeper (C) wit: jester (D) renovated:house Q. (C) cherish (D) conserve 25 persons are in a room. iii. 15 of them play hockey. Gita (G). 56 – 60 Carry One Mark Each 56. 61 – 65 Carry Two Marks Each 61. CS GATE Paper 2010 www.gateforum.com In what order were they born (oldest first)? (A) HSIG 64. (C) IGSH (D) IHSG 5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall? (A) 20 63. (B) SGHI (B) 18 (C) 16 (D) 15 Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the above passage: (A) Modern warfare has resulted in civil strife. (B) Chemical agents are useful in modern warfare. (C) Use of chemical agents in warfare would be undesirable (D) People in military establishments like to use chemical agents in war. 65. Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed? (A) 50 (B) 51 (C) 52 (D) 54 © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. Discuss this question paper at www.gatementor.com. 14 |CS-GATE-2013 PAPER| Q. No. 1 – 25 Carry One Mark Each 1. Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three? (A) 1/8 (B) 1 (C) 7 (D) 8 Answer:-(C) Exp:- P(edge) = 1 2 Number of ways we can choose the vertices out of 8 is 8c 3 (Three edges in each cycle) 3 1 Expected number of unordered cycles of length 3 = 8C 3 × = 7 2 2. Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. (A) P only (B) Q only (C) Both P and Q (D) Neither P nor Q Answer:- (C) Exp:- Q: Sum of degrees of all vertices = 2 × ( number of edges ) 3. Function f is known at the following points: x 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 f(x) 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of 3 ∫ f ( x ) dx computed using the trapezoidal rule is 0 (A) 8.983 Answer:- (B) 9.003 (C) 9.017 (D) 9.045 (D) 3 Exp:- h ∫ f ( x ) dx = 2 f ( x ) + f ( x ) + 2 ( f ( x ) + f ( x ) + ... + f ( x ) ) 0 10 1 2 9 0 = 0.3 9.00 + 2 ( 25.65 ) = 9.045 2 India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 |CS-GATE-2013 PAPER| 4. Which one of the following functions is continuous at x = 3 ? (A) 2, if x = 3 f ( x ) = x − 1, if x > 3 x + 3 , if x < 3 3 ( B) 4, if x = 3 f (x) = 8 − x if x ≠ 3 ( C) x + 3, if x ≤ 3 f (x) = x − 4 if x > 3 ( D) f (x) = 1 , if x ≠ 3 x − 27 3 Answer:-(A) Exp:- lim f ( x ) = lim ( x − 1) = 2 = f ( 3 ) x → 3+ x →3+ x +3 lim f ( x ) = lim = 2 = f ( 3) x → 3− 3 ∴ f ( x ) is continuous at x = 3 x → 3− 5. Which one of the following expressions does NOT represent exclusive NOR of x and y? (A) xy + x ' y ' (B) x ⊕ y ' (C) x '⊕ y (D) x '⊕ y ' Answer: -(D) Exp:- (A) x y = xy + x y (B) x ⊕ y = x y + x y = xy + x y = x y ( C) x ⊕ y = x y + x y = x y + xy = x y ( D) 6. () x ⊕ y = (x) y + x y = x ⊕ y In a k-way set associative cache, the cache is divided into v sets, each of which consists of k lines. The lines of a set are placed in sequence one after another. The lines in set s are sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards. The main memory block numbered j must be mapped to any one of the cache lines from (A) ( j mod v ) * k to ( j mod v ) *k + ( k − 1) (B) ( j mod v ) to ( j mod v ) + ( k − 1) (C) ( j mod k ) to ( j mod k ) + ( v − 1) (D) ( j mod k ) * v to ( j mod k ) * v + ( v − 1) Answer: -(A) Exp:- Position of main memory block in the cache (set) = (main memory block number) MOD (number of sets in the cache). As the lines in the set are placed in sequence, we can have the lines from 0 to (K – 1) in each set. Number of sets = v, main memory block number = j First line of cache = (j mod v)*k; last line of cache = (j mod v)*k + (k – 1) India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 |CS-GATE-2013 PAPER| 7. What is the time complexity of Bellman-Ford single-source shortest path algorithm on a complete graph of n vertices? ( ) (A) Θ n 2 ( (B) Θ n 2 log n ) ( ) (C) Θ n 3 ( (D) Θ n 3 log n ) Answer:-(C) Exp:- Bellman-ford time complexity: Θ( V × E ) For complete graph: E = n(n − 1) 2 V =n n(n − 1) 3 ∴Θ n × = Θ(n ) 2 8. Which of the following statements are TRUE? (1) The problem of determining whether there exists a cycle in an undirected graph is in P. (2) The problem of determining whether there exists a cycle in an undirected graph is in NP. (3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A. (A) 1,2 and 3 (B) 1 and 2 only (C) 2 and 3 only (D) 1 and 3 only Answer: -(A) Exp:- 1. Cycle detection using DFS: O(V + E) = O(V2 ) and it is polynomial problem 2. Every P-problem is NP ( sin ce P ⊂ NP ) 3. NP − complete ∈ NP Hence, NP-complete can be solved in non-deterministic polynomial time 9. Which of the following statements is/are FALSE? (1) For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine. (2) Turing recognizable languages are closed under union and complementation. (3) Turing decidable languages are closed under intersection and complementation (4) Turing recognizable languages are closed under union and intersection. (A) 1 and 4 only (B) 1 and 3 only (C) 2 only (D) 3 only Answer: -(C) Exp:- (1) NTM ≅ DTM (2) RELs are closed under union & but not complementation (3) Turing decidable languages are recursive and recursive languages are closed under intersection and complementation (4) RELs are closed under union & intersection but not under complementation India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 |CS-GATE-2013 PAPER| 10. Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes? (A) X : P ( a ) P ( b ) P ( c ) Y : P ( b ) P ( c ) P ( d ) Z : P ( c ) P ( d ) P ( a ) (B) X : P ( b ) P ( a ) P ( c ) Y : P ( b ) P ( c ) P ( d ) Z : P ( a ) P ( c ) P ( d ) (C) X : P ( b ) P ( a ) P ( c ) Y : P ( c ) P ( b ) P ( d ) Z : P ( a ) P ( c ) P ( d ) (D) X : P ( a ) P ( b ) P ( c ) Y : P ( c ) P ( b ) P ( d ) Z : P ( c ) P ( d ) P ( a ) Answer:-(B) Exp:- Suppose X performs P(b) and preempts, Y gets chance, but cannot do its first wait i.e., P(b), so waits for X, now Z gets the chance and performs P(a) and preempts, next X gets chance. X cannot continue as wait on ‘a’ is done by Z already, so X waits for Z. At this time Z can continue its operations as down on c and d. Once Z finishes, X can do its operations and so Y. In any of execution order of X, Y, Z one process can continue and finish, such that waiting is not circular. In options (A),(C) and (D) we can easily find circular wait, thus deadlock 11. An index is clustered, if (A) it is on a set of fields that form a candidate key (B) it is on a set of fields that include the primary key (C) the data records of the file are organized in the same order as the data entries of the index (D) the data records of the file are organized not in the same order as the data entries of the index Answer:-(C) Exp:- Clustered index is built on ordering non key field and hence if the index is clustered then the data records of the file are organized in the same order as the data entries of the index. 12. Assume that source S and destination D are connected through two intermediate routers labeled R. Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D. S R R D (A) Network layer – 4 times and Data link layer-4 times (B) Network layer – 4 times and Data link layer-3 times (C) Network layer – 4 times and Data link layer-6 times (D) Network layer – 2 times and Data link layer-6 times India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 |CS-GATE-2013 PAPER| Answer:-(C) Exp:Application Application Transport Transport Network Datalink Physical Source (S ) Network Network Network DataLink DataLink Datalink Physical Physical Physical R R Destination (D ) From above given diagram, its early visible that packet will visit network layer 4 times, once at each node [S, R, R, D] and packet will visit Data Link layer 6 times. One time at S and one time at D, then two times for each intermediate router R as data link layer is used for link to link communication. Once at packet reaches R and goes up from physical –DL-Network and second time when packet coming out of router in order Network – DL- Physical 13. The transport layer protocols used for real time multimedia, file transfer, DNS and email, respectively are (A) TCP, UDP, UDP and TCP (B) UDP, TCP, TCP and UDP (C) UDP, TCP, UDP and TCP (D) TCP, UDP, TCP and UDP Answer:Exp:- (C) Real time multimedia needs connectionless service, so under lying transport layer protocol used is UDP File transfer rums over TCP protocol with port no-21 DNS runs over UDP protocol within port no-53 Email needs SMTP protocol which runs over TCP protocol within port no – 25 14. Using public key cryptography, X adds a digital signature σ to message M, encrypts <M, σ >, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations? (A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key (B) Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key (C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key (D) Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 |CS-GATE-2013 PAPER| Answer:-(D) Exp:- X Y X − public X − private Y − public Y − private Source has to encrypt with its p r ivate key for formin g Digital signature for Authentication. Encryption source has to encrypt the M, σ with Y ' s public key to send it confidentially Destination Y has to decrypt first Decryption with its private key, then decrypt u sin g source public key 15. Match the problem domains in Group I with the solution technologies in Group II. Group I Group II (p) Services oriented computing (1) Interoperability (q) Heterogeneous communicating systems (2) BPMN (R) Information representation (3) Publish-find bind (S) Process description (4) XML (A) P – 1, Q – 2, R – 3, S – 4 (C) P – 3, Q – 1, R – 4, S – 2 Answer:-(C) (B) P – 3, Q – 4, R – 2, S – 1 (D) P – 4, Q – 3, R – 2, S – 1 16. A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero(the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero? (A) This algorithm is equivalent to the first-come-first-serve algorithm (B) This algorithm is equivalent to the round-robin algorithm (C) This algorithm is equivalent to the shortest-job-first algorithm (D) This algorithm is equivalent to the shortest-remaining-time-first algorithm Answer:-(B) Exp:- The given scheduling definition takes two parameters, one is dynamically assigned process priority and the other is ‘T’ time unit to re-evaluate the process priorities. This dynamically assigned priority will be deciding processes order in ready queue of round robin algorithm whose time quantum is same as ‘T’ time units. As all the processes are arriving at the same time, they will be given same priority but soon after first ‘T’ time burst remaining processes will get higher priorities India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 |CS-GATE-2013 PAPER| 17. What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production ( i.e., of type A → ∈ and A → a ) to parse a string with n tokens? (A) n/2 (B) n-1 (C) 2n-1 (D) 2n Answer: -(B) Exp:- To have maximum number of reduce moves, all the productions will be of the type A →αβ (where α and β could be terminals or non-terminals). Consider the following illustration then: Input String : a1 a 2 a 3 ........ a n − 2 a n −1a n ↑ a1a 2 a 3 ........... a n − 2 A ↑ a1a 2 a 3 ..................A n − 1 moves a1 a 2 A 18. Consider the languages L1 = Φ and L2 = {a} . Which one of the following represents L1 L*2 U L*1 ? (A) {∈} (B) Φ (C) a * (D) {ε, a} Answer: -(A) Exp:- Concatenation of empty language with any language will give the empty language and L1* = Φ* =∈ . Hence L1 L*2 U L*1 = {∈} 19. Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of n nodes? (A) O(1) (B) O(log n) (C) O(n) (D) O(n log n) Answer:-(C) Exp:- For skewed binary search tree on n nodes, the tightest upper bound to insert a node is O(n) 20. Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort? (A) O(log n) (B) O(n) (C) O(n log n) (D) O(n2) Answer:-(B) Exp:- The maximum number of swaps that takes place in selection sort on n numbers is n India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 |CS-GATE-2013 PAPER| 21. In the following truth table, V = 1 if and only if the input is valid. Inputs Outputs D0 D1 D2 D3 X0 X1 V 0 0 0 0 X X 0 1 0 0 0 0 0 1 X 1 0 0 0 1 1 X X 1 0 1 0 1 X X X 1 1 1 1 What function does the truth table represent? (A) Priority encoder (B) Decoder (C) Multiplexer (D) Demultiplexer Answer: -(A) Exp:- 4 to 2 priority encoder. 22. The smallest integer than can be represented by an 8-bit number in 2’s complement form is (A) -256 (B) -128 (C) -127 (D) 0 Answer: -(B) Exp:- −28−1 = −128 . Range is -2(n-1) to +2(n-1)-1 23. 1 x x2 Which one of the following does NOT equal 1 y y 2 ? 1 z z2 1 x ( x + 1) x + 1 (A) 1 y ( y + 1) y + 1 1 z ( z + 1) (C) ( B) 1 x + 1 x2 +1 1 y + 1 y2 + 1 1 z + 1 z2 + 1 ( D) 2 x + y x 2 + y2 2 y + z y2 + z 2 1 z z2 z +1 0 x − y x 2 − y2 0 y − z y2 − z2 1 z z2 Answer:- (A) Exp:- If matrix B is obtained from matrix A by replacing the lth row by itself plus k times the mth row, for l ≠ m then det(B)=det(A). With this property given matrix is equal to the matrices given in options (B),(C) and (D). 24. Suppose p is number of cars per minute passing through a certain road junction between 5 PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? (A) 8 / ( 2e 3 ) (B) 9 / ( 2e 3 ) (C) 17 / ( 2e 3 ) (D) 26 / ( 2e 3 ) India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 8 |CS-GATE-2013 PAPER| Answer:-(C) Exp:- P ( p < 3) = P ( p = 0 ) + P ( p = 1) + P ( p = 2 ) e −λ λ 0 e −λ λ1 e −λ λ 2 + + ( where λ = 3) 0! 1! 2! e −3 × 9 = e−3 + e −3 × 3 + 2 9 17 = e−3 1 + 3 + = 3 2 2e = 25. A binary operation ⊕ on a set of integers is defined as x ⊕ y = x 2 + y 2 . Which one of the following statements is TRUE about ⊕ ? (A) Commutative but not associative (B) Both commutative and associative (C) Associative but not commutative (D) Neither commutative nor associative Answer:Exp:- (A) x ⊕ y = x 2 + y2 = y2 + x 2 = y ⊕ x ∴ commutative Not associative, since, for example (1 ⊕ 2) ⊕ 3 ≠ 1 ⊕ ( 2 ⊕ 3) Q. No. 26 – 51 Carry Two Marks Each 26. Which one of the following is NOT logically equivalent to ¬∃x ( ∀y ( α ) ∧ ∀z ( β ) ) ? (A) ∀x ( ∃z ( ¬β ) → ∀y ( α ) ) (B) ∀x ( ∀z ( β ) → ∃y ( ¬α ) ) (C) ∀x ( ∀y ( α ) → ∃z ( ¬β ) ) (D) ∀x ( ∃y ( ¬α ) → ∃z ( ¬β ) ) Answer: -(A) and (D) [marks to all] Exp:- ¬∃x ( ∀ y ( α ) ∧ ∀z ( β ) ) ≡∀ × ∀ y ( α ) →∃z ( ¬β ) option "C" ≡∀x ∀ z ( β ) → ∃y ( ¬α ) option "B" 27. ∵¬ ( p ∧ q ) ≡ p ⇒ ¬q [∵p ⇒ q ≡ ¬q ⇒ ¬p] A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8) . The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is (A) 4 (B) 5 (C) 6 (D) 7 Answer: -(B) India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 9 |CS-GATE-2013 PAPER| Exp:- RAM chip size = 1k × 8[1024 words of 8 bits each ] RAM to construct =16k × 16 Number of chips required = 16k × 16 = 16 × 2 [16 chips vertically with each having 2 chips 1k × 8 horizontally] So to select one chip out of 16 vertical chips, we need 4 x 16 decoder. Available decoder is – 2 x 4 decoder To be constructed is 4 x 16 decoder So we need 5, 2 x 4 decoder in total to construct 4 x 16 decoder. 28. Consider an instruction pipeline with five stages without any branch prediction: Fetch Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction (EI) and Write Operand (WO). The stage delays for FI, DI, FO, EI and WO are 5 ns, 7 ns, 10 ns, 8 ns and 6 ns, respectively. There are intermediate storage buffers after each stage and the delay of each buffer is 1 ns. A program consisting of 12 instructions I1 , I 2 , I3 ,......I12 is executed in this pipelined processor. Instruction I 4 is the only branch instruction and its branch target is I9 . If the branch is taken during the execution of this program, the time (in ns) needed to complete the program is (A) 132 (B) 165 (C) 176 (D) 328 Answer: - (B) Exp:- Clock period=Maximum stage delay+ overhead (Buffer) =10+1=11 ns Assume FI-1, DI-2, FO-3, EI-4, WO-5 India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 10 |CS-GATE-2013 PAPER| I1 : 1 2 3 4 5 I2 : I3 : I4 : I5 : − − − − 1 − − − 2 1 − − 3 2 1 − 4 5 3 4 5 2 3 4 5 1 2 3 4 5 I6 : I7 : I8 : I9 : − − − − − − − − − − − − − − − − − − − − 1 − − − 2 1 − − 3 2 1 − 4 5 3 4 5 2 3 4 5 1 2 3 4 5 I10 : − − − − − − − − − 1 2 3 4 5 I11 − − − − − − − − − − 1 2 3 4 5 I12 − − − − − − − − − − − 1 2 3 4 5 So number of clocks required to complete the program is = 15 clocks and time taken is = 15 ×11 ns=165 ns. 29. Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter MultiDequeue ( Q ) { m=k while ( Q is not empty ) and ( m > 0 ) { Dequeue ( Q ) m = m −1 } } What is the worst case time complexity of a sequence of n queue operations on an initially empty queue? (A) Θ ( n ) (B) Θ ( n + k ) (C) Θ ( nk ) ( ) (D) Θ n 2 Answer:- (A) Exp:- Initially the queue is empty and we have to perform n operations. i) One option is to perform all Enqueue operations i.e. n Enqueue operations. Complexity will be θ(n) or ii) We can perform a mix of Enqueue and Dequeue operations. It can be Enqueue for first n/2 times and then Dequeue for next n/2, or Enqueue and Dequeue alternately, or any permutation of Enqueues and Dequeues totaling ‘n’ times. Complexity will be θ(n) or iii) We can perform Enqueues and MultiDequeues. A general pattern could be as follows: India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 11 |CS-GATE-2013 PAPER| Enqueue Enqueue … (ktimes) MultiDequeue Enqueue Enqueue … (ktimes) MultiDequeue … Up to total n ---- k items enqueued -----k items deleted----k items enqueued----k items deleted -- and so on. The number of times this k-Enqueues, MutiDequeue cycle is performed = n So, Complexity will be k times Enqueue + 1 MultiDequeue) × n ( Which is θ 2k × n k +1 k +1 ) = θ(n ) k +1 or iv) We can just perform n MultiDequeues (or n Dequeues for that matter): Each time the while condition is false (empty queue), condition is checked just once for each of the ‘n’ operations. So θ(n). 30. The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree? (A) 10,20,15, 23, 25,35,42,39,30 (B) 15,10, 25, 23, 20,42,35,39,30 (C) 15, 20,10, 23, 25,42,35,39,30 (D) 15,10, 23,25, 20,35,42,39,30 Answer:-(D) Exp:- Pr eorder : 30, 20,10,15, 25, 23,39,35, 42 Inorder :10,15, 20, 23, 25,30,35,39, 42 30 BST : 20 10 39 25 35 42 15 23 31. What is the return value of f ( p, p ) if the value of p is initialized to 5 before the call? Note that the first parameter is passed by reference, whereas the second parameter is passed by value. int f ( int & x, int c ) { c = c − 1; if ( c == 0 ) return 1; x = x + 1; return f ( x,c ) * x; } (A) 3024 (B) 6561 (C) 55440 (D) 161051 India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 12 |CS-GATE-2013 PAPER| Answer:-(B) 9 6 Exp:- 7 8 9 f ( x, 5) 9×9×9×9 = 6561 9×9×9 ⇓ (1) f ( x, 4 ) × x ⇓ (2 ) f ( x, 3) × x 9×9 ⇓ (3 ) f ( x, 2 ) × x 9 ⇓ ( 4) f ( x, 1) × x 32. Which of the following is/are undecidable? 1. G is a CFG. Is L ( G ) = Φ ? 2. G is a CFG. IS L ( G ) = Σ *? 3. M is a Turning machine. Is L(M) regular? 4. A is a DFA and N is a NFA. Is L ( A ) = L ( N ) ? (A) 3 only (B) 3 and 4 only (C) 1, 2 and 3 only (D) 2 and 3 only Answer: -(D) Exp:- There is an algorithm to check whether the given CFG is empty, finite or infinite and also to convert NFA to DFA hence 1 and 4 are decidable 33. Consider the following two sets of LR(1) items of an LR(1) grammar X → c.X, c / d X → .cX, c / d X → .d, c / d X → c.X, $ X → .cX, $ X → .d, $ Which of the following statements related to merging of the two sets in the corresponding LALR parser is/are FALSE? 1. Cannot be merged since look aheads are different 2. Can be merged but will result in S–R conflict 3. Can be merged but will result in R–R conflict 4. Cannot be merged since goto on c will lead to two different sets (A) 1 only (B) 2 only (C) 1 and 4 only (D) 1, 2, 3 and 4 India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 13 P ( S) . S) .cX.cX. Merging of two states depends on core part (production rule with dot operator). Pr ocess X. $ x → c. Pr ocess Y. } EntryY ( R. c / d / $ 1.d. As there is no Reduce item in any of the state. The array a is shared by the two processes. i < n. for ( i = 0. b [i ] = g ( a [i ]) .cX.d. 4. private i. The processes employ two binary semaphores R and S. private i. V ( S) .$ x → . } EntryY ( R. A certain computation generates two arrays a and b such that a [i ] = f ( i ) for 0 ≤ i < n and b [i ] = g ( a [i ]) for 0 ≤ i < n . i + + ) { for ( i = 0. the merged state can not contain any S-R conflict 3. both initialized to zero. 2. i < n. S) { V ( R ).1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 14 .d. The two states are not containing Reduce item . } (B) ExitX ( R.X. c / d / $ x → . not on look aheads. V ( S) . S) { P ( R ). c / d x → . S) { P ( R ). ExitX ( R.X. so can’t have R-R conflict. c / d x → c. So all statements are false. } } Which one of the following represents the CORRECT implementations of ExitX and EntryY? (A) ExitX ( R. c / d x → .|CS-GATE-2013 PAPER| Answer:-(D) Exp:- x → c. The structures of the processes are shown below. Suppose this computation is decomposed into two concurrent processes X and Y such that X computes the array a and Y computes the array b. EntryY ( R. Merging of stats does not depend on further goto on any terminal. S) { P ( S) .$ x → . S) . i + + ) { a [i ] = f ( i ) . } India’s No.X.So after merging. V ( R ). 34. c / d / $ x → . } Answer:-(C) Exp:. 35. S) { V ( S) . } (D) ExitX ( R. what can we say about the average cohesion and coupling between modules in the system of two modules? Module M1 Module M2 m (A) There is no change (B) Average cohesion goes up but coupling is reduced (C) Average cohesion goes down and coupling also reduces (D) Average cohesion and coupling increase Answer:-(A) Module M1 Module M2 Exp:- m number of external links 2 = number of modules 2 number of internal links Cohesion of a module = number of methods 8 6 Cohesion of M1 = .|CS-GATE-2013 PAPER| (C) ExitX ( R. P ( R ). This requirement meets with implementation of ExitX and EntryY given in option C. P ( S) . Average cohesion=2 4 3 Coupling = India’s No. IF method m is moved to module M2 keeping the attributes where they are. } EntryY ( R. V ( R ). starting with X. S) { V ( R ).1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15 . P ( R ). So process X and Y should run in strict alteration manner. The filled circles represent methods and the unfilled circles represent attributes. The following figure represents access graphs of two modules M1 and M2. S) { V ( S) . first element a[i] should be computed using which b[i] can be computed. Cohesion of M 2 = .For computing both the array a[] and b[]. S) { P ( S) . } EntryY ( R. 000 km/s (A) 1 (B) 2 (C) 2. i. Cohesion of M 2 = . Determine the maximum length of cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10. 300 and 689 Answer:-(C) Exp:. Last fragment HLEN=10 . the sequence numbers of the first and the last bytes of the payload. the value of total length is 400 and the fragment offset value is 300. respectively are (A) Last fragment.So header length is 4×10=40.5 (D) 5 Answer:-(B) Exp:- 500 ×106 bits − − − − − −1 sec 5 × 108 104 1 = sec = sec 4 8 10 5 × 10 5 × 104 1 sec − − − − − −2 × 105 km ∴ 104 bits − − − − − − 1 2 × 105 sec − − − − − = 4 km 5 × 104 5 × 104 4 ∴ Maximum length of cable = = 2 km 2 ∴ India’s No. 2400 and 2759 (C) Last fragment. graph will become Module M1 Module M2 m Coupling = 2 2 6 8 Cohesion of M1 = . 3 4 ∴ answer is no change Average cohesion=2 36.00. as 4 is constant scale factor Total Length = 400(40 Byte Header + 360 Byte Payload) Fragment Offset = 300.000 bits. 2400 and 2789 (B) First fragment. In an IPv4 datagram. the value of HLEN is 10. The position of the datagram. the M bit is 0.e.M= 0 – Means there is no fragment after this. 2400 and 2759 (D) Middle fragment. Assume the signal speed in the cable to be 2. that means 300×8 Byte = 2400 bytes are before this last fragment So the position of datagram is last fragment Sequence number of First Byte of Payload = 2400 (as 0 to 2399 Sequence no are used) Sequence number of Last Byte of Payload = 2400+360-1=2759 37.|CS-GATE-2013 PAPER| After moving method m to M2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 16 . stores it to memory.. 39. Students(rollno: integer. Each of the processes W and X reads x from memory. Y . What is the maximum possible value of x after all processes complete execution? (A) –2 (B) –1 (C) 1 (D) 2 Answer:-(D) Exp:W X Y Z 1 R ( x) R ( x) R ( x) R ( x) 2 x++ x++ x=x-2. TRC and DRC in four statements respectively retrieve the required information. cname: string) Registration(rollno: integer. II and IV only (D) II. decrements by two. 3 w(x) w(x) w(x) w(x) R(x) is to read x from memory. stores it to memory. ∃R ∈ Re gistration (S.Four queries given in SQL.name)} (IV) {< S N >| ∃SR ∃R P ( < SR . Each process before reading x invokes the P operation (i. III and IV only Answer:. A shared variable x. signal) on the semaphore S after storing x to memory.rolln o = R.rollno=S. Y. Each of the processes Y and Z reads x from memory. Semaphore S is initialized to two. RA. x=x-2.107. sname: string) Courses(courseno: integer. w(x) is to store x in memory ( ) [ W is Preempted ] Y .(A) Exp:. Y ( x −2 ) [ Y is completed ] (I) w 1 x 0 (II) 1 2 3 India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 17 .percent>90 (II) Π sname ( σ courseno =107 ∧ percent > 90 ( Re gistration Students ) ) (III) {T | ∃S ∈ Students. is operated on by four concurrent processes W. II. III and IV (B) I. percent: real) Which of the following queries are equivalent to this query in English? “Find the distinct names of all students who score more than 90% in the course numbered 107” (I) SELECT DISTINCT S. and then terminates. II and III only (C) I.courseno = 107 ∧ R.S N >∈ Stu de nts ∧ < SR . R P >∈ Re gistration ∧ R P > 90 )} (A) I. Registration as R WHERE R.Courseno=107 AND R. X.. courseno. integer.|CS-GATE-2013 PAPER| 38. initialized to zero.e.sname FROM Students as S. increments by one.rolln o ∧ R.rollno AND R. Consider the following relational schema.percent > 90 ∧ T. wait) on a counting semaphore S and invokes the V operation (i.e. Z as follows. and then terminates.sname = S. (3) A is not minimal. Z3 x −4 ( ) [ Z is completed ] ) [ It increments local copy of x and stores & W is completed ] ( x 2 ) [X is completed ] (IV) W2 . 1} of length at least 2 (A) 1 and 3 only (B) 2 and 4 only (C) 2 and 3 only (D) 3 and 4 only Answer: . X 2 . A is the minimal DFA 4. Complement of L(A) is context–free 2. W3 x 1 (V) X1 . 1 (1) L(A) is regular. For the language accepted by A. L ( A ) = L ( (11* 0 + 0 )( 0 + 1) * 0 *1* ) 3. Z 2 . where each string contains ‘0’. A accepts all strings over {0. Consider the DFA given below. 1 1 0 0 0.1 Which of the following are FALSE? 1. (atleast length one) India’s No. (2) L ( A ) = (11*0 + 0 )( 0 + 1) * 0*1* = 1*0 ( 0 + 1) * Language has all strings where each string contains ‘0’.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 18 . X 3 Maximum value of x = 2 40. its complement is also regular and if it is regular it is also context free. it can be constructed with 2 states (4) Language has all strings.(D) Exp:1 1 A: 0 0 0.|CS-GATE-2013 PAPER| ( (III) Z1 . q. 2 2 . for ( i = n / 2. j = j* 2 ) k = k + n / 2. r ≥ 0 is regular L2 P q r } p. i + + ) for ( j = 2.|CS-GATE-2013 PAPER| 41. k = 0. r ≥ 0 L2 p q r } | p.q. Consider the following languages { = {0 1 0 } L1 = 0p1q 0r | p. − − − − − n 2 2 2 J = ( 2. + 2.q. } The return value of the function is (A) Θ ( n 2 ) Answer:Exp:- (B) Θ ( n 2 log n ) (C) Θ ( n 3 ) (D) Θ ( n 3 log n ) (B) n n n i = . 23 . return ( k ) . r ≥ 0.q. p ≠ r is CFL (A) L2 is CFL ( True ) (B) L1 ∩ L2 = CFL ( True ) (C) L2 complement is recursive ( True ) (D) L1 complement is CFL but not regular ( False ) as L1 is regular L1 is regular 42. + 1. − − − − − n ) n n k = Θ ( n log n ) n to n = + 1 times k = k + 2 2 2 Re peats n n n k = + + − − − − log n times = log n 2 2 2 India’s No. r ≥ 0.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 19 . p ≠ r Which one of the following statements is FALSE? (A) L 2 is context–free (B) L1 ∩ L 2 is context–free (C) Complement of L 2 is recursive (D) Complement of L1 is context–free but not regular Answer: -(D) Exp:- { = {0 1 0 } L1 = 0P 1q 0r p. 2 4 . j. j <= n. Consider the following function int unknown ( int n ){ int i. i <= n. 9. If Θ ( log n ) time is taken to sort using heap sort. sector no. Consider the following sequence of micro–operations MBR ← PC MAR ← X PC ← Y Memory ← MBR Which one of the following is a possible operation performed by this sequence? (A) Instruction fetch (B) Operand fetch (C) Conditional branch (D) Initiation of interrupt service India’s No. then number of elements that can be sorted is constant which is Θ (1) 44. Consider a hard disk with 16 recording surfaces ( 0 − 15) having 16384 cylinders ( 0 − 16383) and each cylinder contains 64 sectors ( 0 − 63) . the time to extract maximum element and then heapifying the heap takes Θ ( log n ) time by which we could say that Θ ( log n ) time is required to correctly place an element in sorted array..>.After constructing a max-heap in the heap sort .40 contains total 24 + ( 6 × 64 ) = 408 sec tors Next.9. if it is stored in a contiguous manner? (A) 1281 (B) 1282 (C) 1283 (D) 1284 Answer: -(D) 42797 × 1024 = 85594 sec tors Exp:. 40>.|CS-GATE-2013 PAPER| = n n n n log n + log n + log n − − − − + 1 times 2 2 2 2 n n = + 1 .42797 KB ≡ 512 Starting is 1200. --------. A file of size 42797 KB is stored in the disk and the starting disk location of the file is <1200. log n 2 2 = Θ ( n 2 log n ) 43. 1283 cylinders contains total 1024 × 83 = 84992 sec tors (∵ each cylinder contains 16 × 64 = 1024 sec tors ) ∴ Total = 408 + 84992 = 85400 sec tors ∴ The required cylinder number is 1284 which will contain the last sector of the file 45. Data are organized cylinder–wise and the addressing format is <cylinder no. The number of elements that can be sorted in Θ ( log n ) time using heap sort is (A) Θ (1) (B) Θ ( log n ) log n (C) Θ log log n (D) Θ ( log n ) Answer:-(A) Exp:. What is the cylinder number of the last sector of the file. Data storage capacity in each sector is 512 bytes.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 20 . 1201. India’s No. (R) The line graph of a planar graph is planar. • For any two edges e and e’ in G.|CS-GATE-2013 PAPER| Answer:-(D) Exp:. It represents a function call (routine). if and only if e and e’ are incident with the same vertex in G. (S) The line graph of a tree is a tree.PC content is stored in memory via MBR and PC gets new address from Y. (A) P only (B) P and R only (C) R only (D) P. which is matching with interrupt service initiation 46. Q and S only Answer: -(A) Exp:. (Q) The line graph of a clique is a clique. Consider the following planar graph (star graph) c a V(e1 ) d V(e1 ) V(e4 ) V(e5 ) b V(e3 ) e ⇒ L ( G) : V(e2 ) V(e5 ) V(e2 ) f V(e3 ) V(e4 ) S) Hence line graph of planar graph need not be planar(Here we got K5 which is not planar). Consider the following example. The line graph L(G) of a simple graph G is defined as follows: • There is exactly one vertex v(e) in L(G) for each edge e in G.P) The line graph of a cycle is a cycle V ( e1 ) a V ( e4 ) V ( e2 ) ⇒ L ( G ) : G V ( e3 ) d V ( e1 ) b V ( e4 ) c V ( e2 ) V ( e3 ) is also cycle graph R) Line graph of planar graph need not be planar always. Which of the following statements is/are TRUE? (P) The line graph of a cycle is a cycle.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 21 . L(G) has an edge between v(e) and v(e’). newc = "cda " (4) oldc = "abc". However. char * oldc. i < 5. Array A has a fixed length of five characters. newc = "dab" (2) oldc = "cde". j + + ) if ( A [i ] = = oldc [ j]) A [i ] = newc [ j] .” (A) ∃x ( F ( x ) ∧ ¬ P ( x ) ) (B) ∃x ( ¬F ( x ) ∧ P ( x ) ) (C) ∃x ( ¬ F ( x ) ∧ ¬ P ( x ) ) (D) ¬∃x ( F ( x ) ∧ P ( x ) ) Answer: -(D) Exp:. 47. char * newc ) { for ( int i = 0.|CS-GATE-2013 PAPER| a V (e 1 ) V ( e1 ) ⇒ L (G ) : b V ( e3 ) V ( e3 ) V ( e2 ) V ( e2 ) c d The line graph of a tree need not be tree. } The procedure is tested with the following four test cases (1) oldc = "abc". The characters to be replaced are supplied in array oldc. while their respective replacement characters are supplied in array newc. newc = "bac" India’s No.“None of my friends are perfect” = ∀x ( F ( x ) →¬P ( x ) ) = ∀x ( ¬F ( x ) ∨ ¬P ( x ) ) = ¬∃x ( F ( x ) ∧ P ( x ) ) Common Data Questions: 48 & 49 The procedure given below is required to find and replace certain characters inside an input character string supplied in array A. while arrays oldc and newc contain three characters each. the procedure is flawed void find _ and _ replace ( char * A.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 22 . What is the logical translation of the following statement? “None of my friends are perfect. newc = "bcd" (3) oldc = "bca ". i + + ) for ( int j = 0. j < 3. d = c * a. initially i = j = 0 A = "b c d a" ↑ i=0 oldc = "b c a " ↑ j=0 newc = " c d a" ↑ j=0 b = b so replaced by c Next i = 0 & j = 1 A = " c c d a" ↑ oldc = "b c a " ↑ j=1 i=0 newc = " c d a" ↑ j=1 c = c so replaced by d Likewise single character ‘b’ in A is replaced by ‘c’ and then by ‘d’. x = c * c. e = c + a.Test case (3) and (4) identifies this flaw as they are containing ‘oldc’ and ‘newc’ array characters arranged in specific manner. If the tester carries out this testing with the four test cases given above. ‘b’. Same way test case (4) can also catch the flaw 49. } India’s No. which should not be so. as explained in above question. If array A is made to hold the string “abcde”. both test case (3) and (4) will be successful in finding the flaw.|CS-GATE-2013 PAPER| 48.Now for string “abcde” in array A. ‘d’ and ‘e’ with duplicates allowed. if ( x > a ) { y = a * a. } else { d = d * d. ‘c’. which of the above four test cases will be successful in exposing the flaw in this procedure? (A) None (B) 2 only (C) 3 and 4 only (D) 4 only Answer:-(C) Exp:. The tester now tests the program on all input strings of length five consisting of characters ‘a’. Common Data Questions: 50 & 51 The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can have almost two source operands and one destination operand. how many test cases will be able to capture the flaw? (A) Only one (B) Only two (C) Only three (D) All four Answer:-(B) Exp:. if tested by test case (3). e = e * e.Flaw in this given procedure is that one character of Array ‘A’ can be replaced by more than one character of newc array.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 23 . Assume that all variables are dead after this code segment c = a + b. Following string can reflect flaw. 1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 24 . and e=c+a. R 2 ← R1 + R 2 x = c *c. Suppose the instruction set architecture of the processor has only two registers. R 3 ← R 2 * R1 e = c + a. The only allowed compiler optimization is code motion.(B) Exp:c = a + b.After applying the code motion optimization the statement d=c*a. c = a + b.(B) Exp:. R2 ← R2 * R2 India’s No. e = e * e. R 4 ← R 2 + R1 x = c *c.|CS-GATE-2013 PAPER| 50. d = d * d. } R 2 ← R1 * R 1 else{ R 2 ←[spillc ] d =c*a. can be moved down to else block as d and e are not used anywhere before that and also value of a and c is not changing. R 2 ← R1 + R 2 d =c*a. What is the minimum number of spills to memory in the compiled code? (A) 0 (B) 1 (C) 2 (D) 3 Answer:. e = c + a. R 2 ← R 2 * R 2 [spillc ] 1 memory spill to store the value of c in memory if ( x > a ) CMP R 2 R 1 { y = a *a. } R 2 ← R 2 * R1 R2 ←R2 * R2 R 2 ←[spillc ] R 2 ← R 2 + R1 R2 ←R2 * R2 In the above code total number of spills to memory is 1 51. What is the minimum number of registers needed in the instruction set architecture of the processor to compile this code segment without any spill to memory? Do not apply any optimization other than optimizing register allocation (A) 3 (B) 4 (C) 5 (D) 6 Answer:. which moves statements from one place to another while preserving correctness. A → BC.52 to Q. The relation R is (A) in INF. The processor used in the computer has a 1 MB 16 way set associative virtually indexed physically tagged cache.B → CFH and F → EG are partial dependencies. F = {CH → G. Each entry of T2 stores the base address of a page of the third–level table ( T3 ) 54. Hence it is in 1NF but not in 2NF Statement for Linked Answer Questions: 54 & 55 A computer uses 46–bit virtual address.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 25 .which occupies exactly one page. but not in 3NF (C) in 3NF. E → A. BD.|CS-GATE-2013 PAPER| if ( x > a ) { y = a *a. The cache block size is 64 bytes. but not in 2NF (B) in 2NF. Each entry of T3 stores a page table entry (PTE). } else { d = d * d. Fields of R contain only atomic values. What is the size of a page in KB in this computer? (A) 2 (B) 4 (C) 8 (D) 16 India’s No. A → BC. e = e * e. The PTE is 32 bits in size. B → CFH. The page table base register stores the base address of the first–level table ( T1 ) . ED and FD (D) 6 53. } CMP R 2 R 1 R1 ← R1 *R1 R3 ← R3 * R3 R4 ←R4 * R4 In the above code minimum number of registers needed are = 4 Linked Answer Questions: Q.Candidate keys are AD. F → EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R 52. How many candidate keys does the relation R have? (A) 3 (B) 4 (C) 5 Answer:-(B) Exp:. and a three–level paged page table organization. Each entry of T1 stores the base address of a page of the second–level table ( T2 ) .55 Carry Two Marks Each Statement for Linked Answer Questions: 52 & 53 Relation R has eight attributes ABCDEFGH. but not in BCNF (D) in BCNF Answer:-(A) Exp:. 32–bit physical address. . we are using 3-level paging. First level page table is contained in one page. . .|CS-GATE-2013 PAPER| Answer:-(C) Exp:- Let the page size be 2X Bytes.. it will be mapped with cache on any one of these 8 sets (set association mapping).For any two synonym to map with same set they should be colored with same color of that respective set. the page offset = X bits 46-x x Now. What is the minimum number of page colours needed to guarantee that no two synonyms map to different sets in the processor cache of this computer? (A) 2 (B) 4 (C) 8 (D) 16 Answer:. 55. ...1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 26 . .. Number of pages in cache=1MB/8KB=128 pages Number of set in cache=128/16=8 sets Take any page of LAS. . Each page table entry is 32-bit.(C) Exp:- As the page size is 213 Bytes and page coloring is asked so we divide cache size by page size and group 16 pages in one set. . Then. . .. 32 32 32 . India’s No. So minimum we need 8 colors for this mapping.. The size of T3 is = 246 * 22 = 246+2-x [ ∵ PTE=32 bit = 4B = 22B ] 2x The size of T2 is = 246+2-x * 22 = 246+4-2x 2x 246+4-2x * 22 = 246+6-3x = 2X [∵ T1 occupies exactly one page] x 2 ∴ 46 + 6 − 3x = x ⇒ x = 13 The size of T1 is = So.... . page size = 213 B = 23 kB = 8kB. a = 2 and d = 2 = ∴ Sum =11[ 4 + 21× 2] = 11× 46 = 506 Q.Nadir in the lowest point on a curve 59. Out of all the 2-digit integers between 1 and 100. What is the probability that the selected number is not divisible by 7? (A) 13/90 (B) 12/90 (C) 78/90 (D) 77/90 India’s No. 42.. a 2-digit number has to be selected at random.. n = 22. No. you ___________ in the sky. What will be the maximum sum of 44. Which one of the following options is the closest in meaning to the word given below? Nadir (A) Highest (B) Lowest (C) Medium (D) Integration Answer:-(B) Exp:. Were you a bird. ? (A) 502 (B) 504 (C) 506 (D) 500 Answer:-(C) Exp:- The maximum sum is the sum of 44. No. (A) would fly (B) shall fly (C) should fly (D) shall have flown Answer:-(A) 58. 42. 61 – 65 Carry Two Marks Each 61..|CS-GATE-2013 PAPER| Q. The sum of ‘n’ terms of an AP n 2a + ( n − 1) d 2 In this case. Choose the grammatically INCORRECT sentence: (A) He is of Asian origin (B) They belonged to Africa (C) She is an European (D) They migrated from India to Australia Answer:-(C) 60.-2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 27 . 56 – 60 Carry One Mark Each 56. . 40... Complete the sentence: Universalism is to particularism as diffuseness is to ________ (A) specificity (B) neutrality (C) generality (D) adaptation Answer:-(A) Exp:- The relation is that of antonyms 57.. Let ‘W’ be the labour wages.. Now.Let the total distance covered be ‘D’ Now.(D) Exp:.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28 . + 3− 2 + 1 80 + 81 4− 3 ( 2 ) − ( 1) ( 3 ) − ( 2 ) ( 4 ) − ( 3 ) 2 2 2 2 (D) 10 2 2 + . and ‘T’ be the working hours. is (A) 16....(B) Exp:... + 1+ 2 2+ 3 3+ 4 80 + 81 (A) 7 (B) 8 (C) 9 Answer:.The number of 2 digit multiples of 7 = 13 ∴ Probability of choosing a number Not divisible by 7 = 90 − 13 77 = 90 90 62. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period.120 Answer:. The average of the tourist in km/h during his entire journey is (A) 36 (B) 30 (C) 24 (D) 18 Answer:.180 (C) 11..500 (B) 15..|CS-GATE-2013 PAPER| Answer:..000 (D) 10.The expression can be written as 1 1+ 2 = + 1 2+ 3 2− 1 + + 1 3+ 4 + . half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h.200. average speed = = 63.2 W India’s No.. + 81 − 80 ( 81 ) − ( 2 80 ) 2 = 81 − 1 = 8 64. total cost is a function of W × T Increase in wages = 20% ∴ Revised wages = 1.. then the new cost of erection in Rs. The current erection cost of a structure is Rs.(B) Exp:.(C) Exp:. 13.. A tourist covers half of his journey by train at 60 km/h. D Total time taken D 1 120 = = = 24 km / hr 1 1 1 D D D 5 + + 2 4 + 4 120 120 40 + 60 30 10 Find the sum of the expression 1 1 1 1 + + + . the spider succeeded in having its net despite several failures. Robert Bruce went in exile and wanted to commit suicide. the spider failed but that did not deter it to refrain from making attempts. and the rest is history. he came across a spider attempting tirelessly to have its net. After several defeats in wars. Such attempts by the spider made Bruce curious. And then. Thus.15 × 13200 = 15180 65.15 WT ∴ Re vised Total cos t =1. Ultimately. Bruce started observing the nearimpossible goal of the spider to have the net. Which one of the following assertions is best supported by the above information? (A) Failure is the pillar of success (B) Honesty is the best policy (C) Life begins and ends with adventures (D) No adversity justifies giving up hope Answer:.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 29 .(D) India’s No. Just before committing suicide. Time and again.|CS-GATE-2013 PAPER| 100 Decrease in labour time = % 24 1 23 T ∴ Re vised time = 1 − T = 24 24 23 WT =1. Such act of the spider encouraged Bruce not to commit suicide. Bruce went back again and won many a battle.2 × 24 =1. ax 2 + b x + c = 0 5. = 98 ⇒ z 2 + 2 = 96 z z z The roots of ax 2 + bx + c = 0 are real and positive a. No. the minister said. India’s No. He could not understand the judges awarding her the first prize. If ( z + 1 / z ) = 98. What did the minister convey by the statement? (A) He wants all the money (B) He will return the money (C) He will assume final responsibility (D) He will resist all enquiries Answer: (C) 4.gateforum. This can be written as. 1 – 5 Carry One Mark Each 1. because he thought that her performance was quite ___________________.CS-GATE-2014 PAPER-01| www. (A) Superb (B) Medium (C) Mediocre (D) Exhilarating Answer: (C) 3. compute ( z 2 + 1 / z 2 ) 2 Answer: (96) Exp: Expanding 1 1 1 z 2 + 2 + 2. “The buck stops here”. (A) Adopt to (B) Adapt to (C) Adept in (D) Accept with Answer: (B) 2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 . In a press meet on the recent scam.z. This will have real roots ⇒ This will have 4 real roots. Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions. Choose the most appropriate word from the options given below to complete the following sentence. ax 2 + bx + c Discri min ant = b 2 − 4ac > 0 ax 2 − bx + c (− b) 2 − 4ac ⇒ b 2 − 4ac Is also >0. b and c are real.com Q. Then ax 2 + b x + c = 0 has (A) No roots (B) 2 real roots (C) 3 real roots (D) 4 real roots Answer: (D) Exp: ax2+bx+c=0 for roots to be real & +ve b2-4ac>0 This will have 2 real positive roots. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. is lower than the hilly terrain to its north and south. and consequently.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 . groups of 4 or more get a discount of 5% on the total fare. In addition. (B) Round–trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. What can be inferred from this passage? (A) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala (B) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low–lying (C) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala (D) Higher summer temperatures result in higher rainfall near the Palghat Gap area Answer: 7. 6 – 10 Carry One Mark Each 6. genetics will become the only relevant field for identifying psychiatric illnesses Answer: 8. If the one way single person fare is Rs 100. On which of the following assumptions does the statement above rely? (A) Strategies are now available for eliminating psychiatric illnesses (B) Certain psychiatric illnesses have a genetic basis (C) All human diseases can be traced back to genes and how they are expressed (D) In the future.No.gateforum. The Palghat Gap (or Palakkad Gap). a region about 30 km wide in the southern part of the Western Ghats in India. (C) Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia. a group of 5 tourists purchasing round–trip tickets will be charged Rs ___________ Answer: (850) Exp: One way force =100 Two way fare per person=200 5 persons=1000/Total discount applicable=10+5=15% Discount amount = 15 × 1000 = 150 100 Amount to be paid=1000-150=850 India’s No.CS-GATE-2014 PAPER-01| www. The exact reasons for the formation of this gap are not clear.com Q. that doctors will be able to eradicate these diseases through early identification and gene therapy. they were further asked to mention whether they own a car or scooter or both.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 . how many (new) internal planes are created with these lines? _______________________ Answer: (6) India’s No. If yes.CS-GATE-2014 PAPER-01| 9.gateforum. 300 respondents were asked whether they own a vehicle or not. www.com In a survey. What percent of respondents do not own a scooter? Own vehicle Men Women Car 40 34 Scooter 30 20 Both 60 46 20 50 Do not own vehicle Answer: (48) Exp: Total respondents=300 Those who don’t have scooter ⇒ Men= 40+20=60 Women = 34 + 50 = %= 84 144 144 × 100 = 48% 300 10. Their responses are tabulated below. When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners. Thus. Suppose you break a stick of unit length at a point chosen uniformly at random. 3. Then the expected length of the shorter stick is ________ . Let G is below graph A B Then G3 is a graph with below structure A B In G the numbers of strongly connected components are 2 where as in G3 it is only one. gold ( x ) ⇒ glitters ( x ) (C) ∃ x. . Then we can say “atleast one glitter object is not gold”. 2. India’s No. E1 ) where E1 = { ( u. therefore.25) Exp: The smaller sticks. No. or about a quarter of the stick. 1 – 25 Carry One Mark Each 1. v ) | ( v. v ) ∉ E} ( B) G 2 = ( V. Consider the statement: “Not all that glitters is gold” Predicate glitters (x) is true if x glitters and predicate gold (x) is true if x is gold. v ) | there is a path of length ≤ 2 from u to v in E} ( D ) G 4 = ( V4 . A B Then option A and D will be eliminated. glitters ( x ) ∧ ¬gold ( x ) Answer: (D) Exp: It means “It is false that every glitter is gold” or “some glitters are not gold”.CS-GATE-2014 PAPER-01| www. Answer: (0.gateforum. Then which one of the following graphs has the same strongly connected components as G? ( A) G1 = ( V. E 2 ) where E 2 = { ( u. Let G=(V.E) be a directed graph where V is the set of vertices and E the set of edges. the average length will be about 0.5 meters. Which one of the following logical formulae represents the above statement? (A) ∀ x. will range in length from almost 0 meters up to a maximum of 0. gold ( x ) ∧ ¬glitters ( x ) (D) ∃ x. E ) where V4 is the set of vertices in G which are not isolated Answer: (B) Exp: Take an example for Graph G . E 3 ) where E3 = {( u.com Q.25 meters. u ) ∉ E} ( C) G 3 = ( V.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 . with each length equally possible. v ) | ( u. glitters ( x ) ⇒ ¬ gold ( x ) (B) ∀ x. 1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 . R 4 → R 4 − R1 3 1 1 1 0 −4 3 −11 0 −1 −3 −8 0 −3 6 −3 1 3 1 1 R 3 → 4R 3 − R 2 0 −4 3 −11 0 0 −15 −21 R 4 → 4R 4 − 3R 2 21 0 0 15 1 3 1 1 0 −4 3 −11 R 4 → R 4 + R3 0 0 −15 −21 0 0 0 0 1 7 0 7 ρ ( A : B ) = ρ ( A ) = 3 = no. Answer: (0) India’s No.com Consider the following system of equations: 3x + 2y = 1 4x + 7z = 1 x + y + z=3 x − 2y + 7z = 0 The number of solutions for this system is __________________ Answer: (1) 3x + 2y =1 Exp: 4x + 7z =1 x+ y+z = 3 x − 2y + 7z = 0 Augmented matrix is 1 1 4 0 R1 ↔ R 3 3 2 1 −2 3 2 4 0 1 1 1 −2 0 7 1 7 1 1 3 0 3 1 1 0 R 2 → R 2 − 4R1 R 3 → R 3 − 3R1 . of variables ∴ Unique solution exists 5.gateforum.CS-GATE-2014 PAPER-01| 4 www. The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetric positive definite matrix is ______________. S) = PQ + PQR + PQRS The minimal sum-of products form of F is ( A) PQ + QR + QS ( B) P+Q+ R +S ( C) P+Q+ R +S ( D) PR + PRS + P Answer: (A) Exp: PQ + PQR + PQRS = PQ + PQ ( R + RS) ( ) = PQ + PQ ( R + R ) ( R + S ) ∵ A + BC = ( A + B )( A + C ) = PQ + PQ ( R + S) ∵ R + R = 1 = Q ( P + P ( R + S) ) ( ) = Q ( P + P ) ( P + R + S) ∵ A + BC = ( A + B )( A + C ) = Q ( P + R + S) ∵ P + P = 1 = PQ + QR + QS India’s No.CS-GATE-2014 PAPER-01| www.com Exp: ( The eigen vectors corresponding to distinct eigen values of real symmetric matrix are orthogonal) 6. 6 3 π π (II) There exists θ∈ . Which of the 6 2 following statement is / are TRUE? π π (I) There exists θ∈ . Consider the following Boolean expression for F: F ( P. and f ' ( θ ) denote the derivative of f with respect to θ . Let the function sin θ ( ) ( ) f ( θ ) = sin π 6 sin π 3 cos θ tan θ cos π 6 cos π 3 tan π 6 tan π 3 ( ) ( ) ( ) ( ) π π Where θ = ∈ .Q. R. such that f ' ( θ ) = 0 . 6 3 (A) I only (B) II only (C) Both I and II (D) Neither I nor II Answer: (C) Exp: (By Mean value theorem) 7.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 . such that f ' ( θ ) ≠ 0 .gateforum. since the total registers are 64. we can give maximum 16383. It needs to support 45 instructions. It has 64 registers. opcode must contain 6-bits Register operand1 requires 6 bits.1 20 Answer: (5) Exp: Let ‘x’ be the base or radix of the number system 2 × x o + 1× x + 3 × x 2 = 3 × x o + 1 × x + 1 × x −1 0 × xo + 2 × x ⇒ 2 + x + 3x 2 1 = 3+ x + 2x x ⇒ 3x 2 + x + 2 3x + x 2 + 1 = 2x x ⇒ 3x 2 + x + 2 = 6x + 2x 2 + 2 ⇒ x 2 − 5x = 0 ⇒ x ( x − 5) = 0 ⇒ x = 0 or x = 5 As base or radix of a number system cannot be zero. Answer: (16383) Exp: 1 Word = 32 bits Each instruction has 32 bits To support 45 instructions. with 1-word long instructions. Assuming that the immediate operand is an unsigned integer. www. the maximum value of the immediate operand is ____________. 312 = 13. which have an immediate operand in addition to two register operands.gateforum. A machine has a 32-bit architecture. Since 214 = 16384 ( from 0 to 16383) India’s No. each of which is 32 bits long.com The base (or radix) of the number system such that the following equation holds is____________.CS-GATE-2014 PAPER-01| 8. here x = 5 9.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 . Register operand 2 also requires 6 bits 6 6 6 opcode Re g opd 1 Re g opd 2 14 immediate opnd 32 bits 14-bits are left over for immediate Operand Using 14-bits. if(size==4) printf("this is a subtree of size 4"). } Which one of the following statements is TRUE? (A) Compilation fails. i + 5) . The best upper bound on the time required to determine the number of sub trees having exactly 4 nodes is 0 n a log b n .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 8 . pr int f ("%d \ n". so overall the running time will be O(V2). scanf ("%d".e So printf("%d\n".pi) places the value entered in console into variable i. Consider rooted n node binary tree represented using pointers. when G is represented as an adjacency matrix? (A) θ(n) (B) θ ( n + m ) (C) θ ( n 2 ) (D) θ ( m 2 ) Answer: (C) Exp: DFS visits each vertex once and as it visits each vertex. Finding all its neighbours in an adjacency matrix requires O(V ) time. } The above function on taking input the root of a binary tree prints all the subtrees of size 4 in O(n) time so a=1 . ( ) Then the value of a + 10b is_______ Answer: 1 Exp: int print_subtrees_size_4(node *n) { int size=0. What is the tightest upper bound on the running time of Depth First Search on G.h > main ( ) { int i.CS-GATE-2014 PAPER-01| 10. int * pi = &i. www. 12. if(node==null) return 0. return size.com Consider the following program in C language: # include < stdio. size=print_subtrees_size_4(node->left)+print_subtrees_size_4(node->right)+1. (D) On execution.gateforum. (C) On execution. the value printed is 5 more than the integer value entered. Let G be a graph with n vertices and m edges. the value printed is 5 more than the address of variable i. pi ) . Answer: (D) Exp: pi contains the address of i. 11. (B) Execution results in a run-time error. So scanf("%d".prints 5 more than the value entered in console. b=0 and then a+10b=1 India’s No. we need to find all of its neighbours to figure out where to search next.i+5). Let t1 and t2 and t2 be the number of comparisons made by P for the inputs [1 2 3 4 5] and [4 1 5 3 2] respectively.. (D) PSRQ is not the only one topological ordering as SPRQ is other possibility 14.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 9 . P Q R S Which one of the following is TRUE? (A) The graph does not have any topological ordering (B) Both PQRS and SRQP are topological orderings (C) Both PSRQ and SPRQ are topological orderings.. Let P be a quick sort program to sort numbers in ascending order using the first element as the pivot.q ) // A [ P. www.. u comes before v in the ordering. because P should come before Q in the ordering as there is a directed edge from P to Q (C) PSRQ and SPRQ are topological orderings as both of then satisfy the above mentioned topological ordering conditions. Answer: (C) Exp: Topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v..q ] x ← A [ P ] // pivot = A [ P ] i←P for j = P + 1 to q do if A [ j] ≤ x then i ← i + 1 exchange A [i ] ↔ A [ j] exchangeA [ P ] ↔ A [i] return i [returning where pivot element is there after partitioning] Recursively call the above algorithm for the two sub arrays [elements before and after pivot element] to complete the sorting.. (D) PSRQ is the only topological ordering. it has at least one topological ordering. SRQP cannot be topological ordering. P.gateforum.CS-GATE-2014 PAPER-01| 13.com Consider the directed graph given below. (A) As the given graph doesn’t contain any directed cycles. So option (A) is false (B) PQRS cannot be topological ordering because S should come before R in the ordering as there is a directed edge from S to R. Which one of the following holds? (A) t1 =5 (B) t1 < t2 (C) t1>t2 (D) t1 = t2 Answer: (C) Exp: Partition algorithm for quick sort Partition ( A. Topological ordering is possible iff graph has no directed cycles. India’s No. gateforum.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 10 .CS-GATE-2014 PAPER-01| Pivot = x = A [ B] x = pivot 1 2 i j 1 i 2 1 i 2 1 i 2 www.com 3 4 5 3 j 4 5 3 4 j 5 4 5 j 2 ≤ 1 ? NO 1 2 3 i j 4 5 1 2 i 3 4 j 5 2 i 3 4 5 j 3 ≤ 1 ? NO 3 1 4 ≤ 1 ? NO 3 ≤ 2 ? NO 4 ≤ 2 ? NO 5 ≤ 2 ? NO exchange A [ P ] & A [ J ] 5 ≤ 1 ? NO exchange A [ P ] & A [i ] 1 2 3 4 5 ≥ Pivot Pivot 1 Call recursively for this subarray 2 3 4 ≥ Pivot Pivot Call recursively for this x = Pivot = A [ P ] 1 1 2 3 i j 4 2 4 3 i 1 5 5 2 x = Pivot 4 5 i j 3 4 ≤ 3 ? NO exchange A [ P ] & A [i ] 5 j 5 ≤ 3 ? NO exchange A [ P ] & A [i ] 1 2 3 4 Pivot 1 2 Pivot 3 4 5 ≤ 4 ? NO 5 5 ≥ Pivot ∴ Total 10 conparisons ≥ Pivot India’s No. 1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 11 . (C) The language L = { w | w has 3k + 1b 's for some k ∈ N with Σ = {a. (B) n | n is prime} is regular. Which one of the following is TRUE? { The language L = {a } (A) The language L = a n b n | n ≥ 0 is regular. b} } is regular. Answer: Exp: (C) { (B) L = {a } (A) L = a n b n n ≥ 0 is a CFL but not regular.com x = pivot = A [ P ] 4 1 5 3 2 i j 1 ≤ 4?Yes i ← i + 1 exchange A [i ] & A [ j] & increment j 4 1 5 3 2 i j 5 ≤ 4? NO 4 1 5 3 2 i j 3 ≤ 4? Yes i ← i + 1 exchange A [i ] & A [ j] & increment j 4 1 3 5 2 i J 2 ≤ 4?Yes x = pivot = A ( P ) i ← i +1 4 1 3 2 5 2 1 i j i j 2 1 3 i j exchange A [ P ] & A [i ] 3 |4| 5 1 ≤ 2 ? yes |4| 5 3 ≤ 2 ? NO exchange A [ P ] & A [i ] 2 1 3 ≤ Pivot 4 Pivot 5 1 ≥ Pivot 2 3 4 5 Pivot ∴ 6 conparisons 15.1}} is neither regular nor CFL India’s No. it requires memory for the representation n } n is prime is neither regular nor CFL (C) L = {w | w has 3K + 1 b 's for some k ∈ N with} Σ = {a. (D) The language L = {ww | w ∈ Σ* with Σ = {0.gateforum. b} is a regular language. since the total count of b’s are multiple of 3 plus one. The regular expression is a * ba * ( a * ba * ba * ba *) * + ( a * ba * ba * ba *) * a * ba * (D) L = {ww | w ∈Σ * with Σ = {0.CS-GATE-2014 PAPER-01| www.1}} is regular. q 2 } (B) { q 0 . (C) Live variable analysis can be used for dead code elimination (D) x = 4 *5 ⇒ x = 20 is an example of common subexpression elimination Answer: (D) Exp: x = 4 × 5 ⇒ x = 20 is not an example of common sub-expression but it is constant folding.gateforum.1) = {q 0 . 4-c (C) 1-d. 4-c (D) 1-c. Evolutionary software models are iterative. In constant folding expression consisting of constants will be replaced by their final value at compile time.q 2 .q1} ∪ {q 2 } = {q 0 .1 q0 1 q1 0. They are characterized in manner that enables the software engineers to develop increasingly more complete version of software.011) Exp: = δ ( q 0 .q1 .q1 .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 12 . www. 4-d (B) 1-d. One phase has to be complete before moving onto the next phase. 18. 3-a. 1 0. 3-b.1) ∪ δ ( q1 . (B) Available expression analysis can be used for common subexpression elimination.1) = δ ( q 0 . Development can be divided in to smaller parts and more risky parts can be developed earlier which helps better risk management. 2-a. Match the following (1) Waterfall model (a) Specifications can be developed (2) Evolutionary model (b) Requirements compromises are inevitable (3) Component based software (c) Explicit recognition of risk (4) Spiral development (d) Inflexible partitioning of the project into stages (A) 1-a. In Spiral model. 4-d Answer: (B) Exp: The main drawback of the waterfall model is the difficulty of accommodating change after the process is underway.q1 } (C) { q 0 . Which one of the following is FALSE? (A) A basic block is a sequence of instructions where control enters the sequence at the beginning and exits at the end. 2-b.1 q3 What is the set of reachable states for the input string 0011? (A) { q 0 . Inflexible partitioning of the project into distinct stages in waterfall model makes it difficult to respond to changing customer requirements. India’s No. rather than doing the calculation in run-time.q 3 } (D) { q 3 } Answer: (A) δ ( q 0 .11) = δ ({q 0 . 2-b. 2-a. 3-b.1 q2 0.q1 . 3-c.0011) = δ ( q 0 .q 2 } 17.com Consider the finite automaton in the following figure.q1} .CS-GATE-2014 PAPER-01| 16. numbered from 0 to 200.105 and 110 ) 20. when one user level thread is blocked in the kernel all other threads of its process are blocked. all other threads of its process are blocked. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access. and there is a queue of disk access requests for cylinders 30. 85. Which one of the following is FALSE? (A) User level threads are not scheduled by the kernel. (B) When a user level thread is blocked. 90. (C) Context switching between user level threads is faster than context switching between kernel level threads. (D) Kernel level threads cannot share the code segment. 110. India’s No. Answer: (D) Exp: User threads are supported above the kernel and a managed without kernel support. The thread function library to implement user level threads usually runs on top of the system in user mode. Thus these threads with in a process are invisible to the operating system. Since the kernel is unaware of the existence of such threads.com Suppose a disk has 201 cylinders. PC and SP must be changed. the request for cylinder 90 is serviced after servicing ____________ number of requests. At some time the disk arm is at cylinder 100. but the memory context remains the same among kernel threads in the (same process). 100. Answer: (3) 100 Exp: 105 110 90 85 135 145 30 Request for cylinder is served after serving 3 requests (100. So options (A) and (B) are true (C) The OS is aware of kernel level threads. Kernel threads are scheduled by the OS’s scheduling algorithms and require a “lightweight” context switch to switch between (that is. www. data section and other operating system resources such as open files and signals.gateforum. User level threads are much faster to switch between as there is not context switch (D) False Kernel level threads within the same process share code section.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 13 . 135 and 145.CS-GATE-2014 PAPER-01| 19. 105. registers. G.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 14 . F. { E.{F} → { I. e INTEGER. d INTEGER. F. } {L} → {N} on R.gateforum. H. K. I. Given the following statements: S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL S2: Given the table R(a. H} (C) {E. F. L} (D) {E} (B) R ( EFGHI. H can’t be determined by any other attributes.com (B) {E. the following is a valid table definition. K & L functionally determine M and N respectively. H along with E determines K and L.CS-GATE-2014 PAPER-01| 21. N) and the set of functional dependencies {{E. H. FOREIGN KEY (a) references R) Which one of the following statements is CORRECT? (A) S1 is TRUE and S2 is a FALSE (B) Both S1 and S2 are TRUE (C) S1 is FALSE and S2 is a TRUE (D) Both S1 and S2 are FALSE India’s No. Consider the relation scheme R = (E. CREATE TABLE S ( a INTEGER. J. What is the key for R? (A) {E.JKLMN ) F ={ EF → G F → IJ EH → KL K→M L→Ν } ( EF) + = EFGIJ.F} → {G}. L} → ( M ) . K. H } → { K.J} .c) where a and b together form the primary key. 22. M. PRIMARY KEY (d). E & F Together functionally derive GIJ and if we observe given FDs. F} Answer: Exp: www.b. So H must be part of all the (candidate) keys. ∴ ( EFH ) = EFGIJHKLMN + ∴ EFH is the only candidate for key. {K} → {M} . L. S1 is false. a link state protocol will converge faster than a distance vector protocol. Which one of the following is correct about S1. Attribute a is declared as foreign key which is a single valued attribute and it is referencing the primary key (ab) of relation R (a. S2: The given table definition is not valid due to invalid foreign key declaration. but S3 is false (D) S1 and S3 are true. But the above declaration will fail to implement changes done in Department relation in terms of deletion & updation.CS-GATE-2014 PAPER-01| www. (C) S1 and S2 are true. DeptID) Department (DeptName.K) of relation Department.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15 .gateforum. Consider the following three statements about link state and distance vector routing protocols. ∴ 23. Let’s declare the foreign key by an equivalent check assertion as follows:CREATE TABLE Manager ( Name Varchar (10) DeptID INT (6) check (DeptID IN ( select Deptid from Department)). A single value attribute cannot refer a composite key. S2.com Answer: (D) Exp: S1: Manager (Name. but not a link state protocol. and S3 are all true (B) S1. PRIMARY KEY (Name) ). c). The above use of check assertion is good to declare the foreign key as far as insertion is considered for relation manager (will not insert any tuple in Manager containing such DeptID value which is not present in any tuple of Department). This is TRUE India’s No. Answer: (D) Exp: Statement S1 The Distance Vector routing protocols rely on the information from their directly connected neighbours in order to calculate and accumulate route information. Instead. Link State routing protocols have a system of databases that they use in order to calculate the best route to destinations in the network. [S3] After a topology change. but S2 is false. for a large network with 500 network nodes and 4000 links [S1] The computational overhead in link state protocols is higher than in distance vector protocols. then respective reference in Manager should also be deleted. Deptid) In given relation Manager DeptID is a foreign key referencing Deptid (P. S2. Distance Vector routing protocols require very little overhead as compared to Link State routing protocols as measured by memory and processor power while the Link State routing protocols do not rely solely on the information from the neighbours or adjacent router in order to calculate route information. [S2] A distance vector protocol (with split horizon) avoids persistent routing loops. S2. b. For an instance if a deptid present in Department gets deleted. and S3 are all false. which is a composite key. and S3? (A) S1. 4 S2 is false. The propagation speed of the signal is 2 x 108 m/s and the token transmission time is ignored. The web browser resolves the domain name using DNS.3 (B) 1. pass small event based triggered link state updates to all other routers.3 Answer: (A) Exp: First of all the browser must now know what IP to connect to.gateforum.No.2.com Statement S3 Distance Vector exchanges the routing updates periodically whether the topology is change or not.3 Q. After initial flood. The web server sends the requested webpage using HTTP. For this purpose browser takes help of Domain name system (DNS) servers which are used for resolving hostnames to IP addresses.3. of Stations (m) = 10 Propagation Speed (v) = 2 × 108 m/s THT = 2µs So. 24.1. of Active Stations * THT = 10 × 10-6 + 10 × 2 × 10-6 = 30 µs India’s No.3 (D) 2. and then the web server sends the requested webpage using HTTP. Identify the correct order in which the following actions take place in an interaction between a web browser and a web server. If each station is allowed to hold the token for 2 µsec.2. The web browser requests a webpage using HTTP. This will minimize the convergence time that’s why there is no chance of routing loops. As browser is an HTTP client and as HTTP is based on the TCP/IP protocols. this will maximize the convergence time which increases the chance of routing loops while the Link State routing protocols send triggered change based updates when there is a topology change. 2.1. TRT = TP in the Ring + No.CS-GATE-2014 PAPER-01| www.4 (C) 4. 25.2. Which one of the following are used to generate a message digest by the network security protocols? (P) RSA (Q) SHA-1 (R) DES (S) MD5 (A) P and R only (B) Q and R only (C) Q and S only (D) R and S only Answer: (C) Exp: RSA and DES are for Encryption where MD5 and SHA – 1 are used to generate Message Digest. the minimum time for which the monitoring station should wait (in µsec) before assuming that the token is lost is _______. This is TRUE. 3. first it establishes a TCP connection with the web server and requests a webpage using HTTP. Hence the order is 4. (A) 4. The web browser establishes a TCP connection with the web server. 1.1. 26 – 55 Carry Two Marks 26. Max. 4. Answer: (28µs to 30µs) Exp: Given Length (d) = 2 Km No.2.4. Consider a token ring network with a length of 2km having 10 stations including a monitoring station.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 16 .1. 5 Mbps link with a one-way latency of 50 msec. Threshold = (size of Cwnd) / 2 It means Threshold = 16KB Slow Start 2KB 1RTT 4KB 2RTT 8KB 3RTT 16KB ----------. Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs.CS-GATE-2014 PAPER-01| 27.gateforum. The time taken (in msec) by the TCP connection to get back to 32KB congestion window is ______ Answer: Exp: www. The round trip time of the connection is 100 msec and the maximum segment size used is 2kB. the minimum number of bits required to represent the sequence number field is ________. To achieve a link utilization of 60%. Total no.com (1100 to 1300) Given that at the time of Time Out. of RTTs = 11 → 11 * 100 = 1100 28. So Additive Increase Starts 4RTT 18KB 5RTT 20KB 6RTT 22KB 7RTT 24KB 8RTT 26KB 9RTT 28KB 10RTT 30KB 11RTT 32KB So.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 17 .Threshold reaches. for the next round of Slow Start. Congestion Window Size is 32KB and RTT = 100ms When Time Out occurs. India’s No. Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send data on a 1. 3 53 Tx = ⇒ 60 W = ⇒ W = 11.5Mbps Tp = 50ms η = 60% Efficiency formula for SR protocol is Tp W 60 W η= ⇒ = ∵ a = 1 + 2a 100 1 + 2a Tx L 8 × 103 = = 5. r3(x) . w1 (x) (C) r3 (x) . Consider the following four schedules due to three transactions (indicted by the subscript) using read and write on a data item x. w2 (x) (B) r2 (x) .CS-GATE-2014 PAPER-01| www. w2 (x) .9 ≈ 12 100 19. then the schedule is not conflict serializable. r3 (x) . denoted r (x) and w (x) respectively.3ms B 1.com Answer: (5) Exp: Given L = 1KB B = 1. w2(x) .5 × 106 Tp 50 500 = = = 9. r1 (x) . r3(x) .43 a= Tx 5. r2 (x) . r1 (x) . (A) T1 TT22 (B) T2 T1 T3 T3 Not conflict serializable not conflict serializable (C) (D) T1 T2 T3 Not conflict serializable T1 T2 T3 it is conflict equivalent to T2 → T3 → T1 & T3 → T2 → T1 India’s No. r2 (x) .86 ⇒ W = 2 n −1 = 12 ⇒ 2 n = 24 ⇒ 2n = 24 ≈ 25 ⇒ n = 5 29. Which one of them is conflict serializable? (A) r1 (x) .gateforum. w1 (x) (D) r2 (x) . w2 (x) . w1 (x) . r1(x) .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 18 . w1 (x) Answer: (D) Exp: If there is a cycle in precedence graph. 0 units of Y and 2 units of Z REQ2: P1 requests 2 units of X. 0 units of Y and 0 units of Z India’s No. 2 units of type Y and 2 units of type Z still available. E → C is a minimal cover for the set of functional dependencies AB → C. Y. and P2. 3NF and BCNF S2 : AB → C. Consider the following independent requests for additional resources in the current state: REQ1: P0 requests 0 units of X. 31.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 19 . D → E. Here. (C) S1 is FALSE and S2 is TRUE. 2NF.B) The possible FD sets are F1 = { F2 = { A→B B→A } Key : A and is in BCNF } Key : B and is in BCNF F3 = { F4 = { A→B B→A } Key : AB and is in BCNF } Key : A & B It is in BCNF If a table is in BCNF it is also in 1NF. The system is currently in a safe state. www.CS-GATE-2014 PAPER-01| 30. An operating system uses the Banker’s algorithm for deadlock avoidance when managing the allocation of three resource types X. and Z to three processes P0.gateforum. The table given below presents the current system state. the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution.com Given the following two statements: S1: Every table with two single-valued attributes is in 1NF. E → C Which one of the following is CORRECT? (A) S1 is TRUE and S2 is FALSE. Answer: (A) Exp: S1 : True Consider any table R with two attributes R ( A. 2NF and 3NF also S2 : False First FD set cannot cover second FD set because in second FD set AB can functionally derive E but that is not happing in first FD set. P1. Allocation X Y Z 1 P0 0 0 0 P1 3 2 1 P2 2 1 X 8 6 3 Max Y 4 2 3 Z 3 0 3 There are 3 units of type X. D → E. (B) Both S1 and S2 are TRUE. (D) Both S1 and S2 are FALSE. AB → E. Hence there is no safe sequence.CS-GATE-2014 PAPER-01| www. Answer: (B) Exp: REQ1 Once P0 is allocated with ( 0. 32.com Which one of the following is TRUE? (A) Only REQ1 can be permitted. (D) Neither REQ1 nor REQ2 can be permitted.0. P0 . 2. the status of the system will be as follows Allocated P0 P1 P2 X 0 5 2 Y 0 2 1 Z 1 0 1 Max X 8 6 3 Y 4 2 3 Need Z 3 0 3 X 8 1 1 Y 4 0 2 Available X Y Z Z 2 0 2 1 2 2 With available (1. REQ2 Once P1 is allocated with ( 2. 2 ) . India’s No.gateforum. P2 . (C) Both REQ1 and REQ2 can be permitted.0.P1 . Once P1 is executed. If we serve P2 then the safe sequence is P2 . 2. If we serve P1 then the safe sequence is P1 . Hence REQ1 can’t be permitted.0 ) only P1 can be served.0 ) we can’t serve either P0 or P2 . with ( 6.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 20 . 4. 4. All the times are given in milliseconds Process Name Arrival Time Execution Time A 0 6 B 3 2 C 5 4 D 7 6 E 10 3 Using the shortest remaining time first scheduling algorithm. available will be ( 6. we can serve either P1 or P2 . (B) Only REQ2 can be permitted. 2 ) . the status of the system will be as follows Allocation X 0 3 2 Y 0 2 1 Max Z 3 0 1 X 8 6 3 Y 4 2 3 Need Z 3 0 3 X 8 3 1 Y 4 0 2 Available X Y Z Z 0 0 2 3 2 0 With available ( 3.0 ) . P0 . Consider the following set of processes that need to be scheduled on a single CPU. the average process turnaround time (in msec) is ____________________. As true is at least one safe sequence we can permit REQ2.0 ) . On input symbol < the set has (A) a shift-reduce conflict and a reduce-reduce conflict.gateforum. (D) neither a shift-reduce nor a reduce-reduce conflict. 1. 6. > R Q → R. (C) a reduce-reduce conflict but not a shift-reduce conflict. 2.CS-GATE-2014 PAPER-01| Answer: www. 3.2) Exp: A 0 B A 3 C 5 E 8 Average turn around time = 12 D 15 21 (8 − 0 ) + ( 5 − 3) + (12 − 5) + ( 21 − 7 ) + (15 − 10 ) 5 36 = ⇒ 7. 4. Assume that there are 3 page frames which are initially empty.reduce or reduce-reduce conflict. (B) a shift-reduce conflict but not a reduce-reduce conflict. A canonical set of items is given below s → L. 5.>R Q → R. If the page reference string 1. 3. 2.R Inew From above diagram. 2. 4.2 ms 5 33. Iold > S →L >. India’s No. we can see that there is no shift. Answer: (D) Exp: S→L.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 21 . the number of page faults using the optimal replacement policy is ___________ Answer: (7) Exp: 1 2 3 4 2 1 5 3 2 4 3 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 6 1 1 1 1 1 1 5 3 3 3 3 F F F F H H F F H H F 7 page faults 34.com (7. Their total weight comes out to 323 gm. II. If a language L is recursive enumerable but not recursive then its complement is not a recursive enumerable. 0 *1(1 + 00 *1) * and ( 0 + 1) *1. There are 5 bags labelled 1 to 5. (B) One of L and L is r.e.e. Now. Which of the regular expressions given below represent the following DFA? 0 0 1 1 I) 0*1(1+00*1)* II) 0*1*1+11*0*1 III) (0+1)*1 (A) I and II only (B) I and III only (C) II and III only (D) I. www. 2.b+4.a+2. and III Answer: Exp: (B) Given DFA will accept all the strings over ε = {0.d+16.c+8. so both L and L are recursive enumerable but not recursive is not a viable possibility.e = 323 ⇒ a must be odd ⇒ a = 11 The equation then becomes: 11+2. Answer: Exp: 12 Let the weight of coins in the respective bags (1 through 5) be a.gateforum.CS-GATE-2014 PAPER-01| 35. All the coins in a given bag have the same weight. I pick 1. the other is not r.b+4.com Let L be a language and L be its complement. Then the product of the labels of the bags having 11 gm coins is ___. Which of the following is NOT a viable possibility? (A) Neither L nor L is recursively enumerable (r. others have coins of weight 11 gm.e = 323 India’s No. 4. but not recursive.c+8.e. Answer: Exp: (C) Recursive languages are closed under complement.c. Some bags have coins of weight 10 gm.1} which are ending with 1.d+16. 16 coins respectively from bags 1 to 5.d and e-each of which can take one of two values namely 10 or 11 (gm). 36. are the regular expressions for ending with 1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 22 . the given information on total weight can be expressed as the following equation: 1. (D) Both L and L are recursive.b.e. 37.). but not recursive. 8. (C) Both L and L are r. 38. iff C is in NP and every problem in NP is reducible to C in polynomial time).b+4. which asks whether polynomial time algorithms actually exist for NP-complete and all NP problems ( since a problem “C” is in NP-complete.com ⇒ 2. 3 and 4 contain 11 gm coins ⇒ Required Product = 1*3*4* = 12. Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. India’s No. bags labelled 1.e = 31 ⇒ e = 11 and e = 10 Therefore.c+4.e = 73 ⇒ 2.e = 156 ⇒ 2.d+4.d+4.d+8. NP and NP Complete (NPC)? NP P ( A) ( B) NP P NPC NPC P = NP = NPC NPC ( B) P = NP ( D) Answer: (D) Exp: The most important open question in complexity theory is whether the P = NP . Hence P=NP=NP-Complete.e = 156 ⇒ b must be even ⇒ b = 10 The equation then becomes: 10+2.d+4. In the given question it is given that some polynomial time algorithm exists which computes the largest clique problem in the given graph which is known NP-complete problem.c+8.e = 62 ⇒ d+2.CS-GATE-2014 PAPER-01| www.d+8. which one of the following represents the correct Venn diagram of the complexity classes P.d+8.c+4.e = 73 ⇒ c must be odd ⇒ c = 11 The equation now becomes: 11+2.e = 146 ⇒ c+2.e = 312 ⇒ b+2.gateforum.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 23 . In this scenario.c+4.d+16. Consider a hash table with 9 slots. The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is _________________. The maximum.CS-GATE-2014 PAPER-01| 39. For updating current – min 3. respectively. and average chain lengths in the hash table. Compare two elements Assign min = min of two numbers max = max of two numbers 2. min} 3. for finding min and max 2. The hash function is h ( k ) = k mod 9. Pick up first two elements. 1. 28.min Assign current − min = min {current − min. 0. take pairs wise and follow this process given below. 12. and 2 India’s No.max} Repeat above procedure for all the remaining pairs of numbers. 10.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 24 . for updating current – max But for initial pair we need only one comparison not 3. 15. 0. 33.max Assign current − max = max {current − max. so number of comparisons = 148. 17. Compare max and current .com (148) From the list of given n numbers [say n is even]. 3. compare them assign Current − min = min of two numbers Current − max = max of two numbers From the remaining n − 2 numbers. 19. 20. and 1 (B) 3. The following 9 keys are inserted in the order: 5. are (A) 3. and 1 (D) 3. and 3 (C) 4.gateforum. We can observe that each of pair requires 3 comparisons 1. ∴ total number of comparisons = 3( n − 2) 2 + 1= 3n 3n − 3 + 1= −2 2 2 Here n = 100. minimum. Compare min and current . Answer: Exp: www. The collisions are resolved by chaining. 40. 0. i < size.gateforum. unsigned int size) { int Y = 0. for(k = i. i < size. (B) maximum element in any sub-array of array E. int Z. for(i = 0. } return Y. 0 + 3 +1+1+ 0 +1+ 2 + 0 +1 =1 9 Consider the following C function in which size is the number of elements in the array E: int MyX(int *E. i++) for(j = i. if (Z > Y) Y = Z. i++) Y = Y + E[i]. k. (D) the sum of all the elements in the array E. k++) Z = Z + E[k]. int i. } The value returned by the function MyX is the (A) maximum possible sum of elements in any sub-array of array E. j.com (A) 0 1 28 2 20 3 12 19 10 4 5 5 6 15 33 7 8 17 ∴ M ax imum & min imum chain lengths are 3 & 0 respectively Average chain length = 41. j < size.CS-GATE-2014 PAPER-01| Answer: Exp: www.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 25 . for(i = 0. Answer: (A) India’s No. j++) { Z = 0. (C) sum of the maximum elements in all possible sub-arrays of array E. k <= j. 42. j + + ) calculates the sum of elements of { z = 0. j < size. What is the total number of multiplications to be performed? D= 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D=D*3 (A) Half of the product of the 3 consecutive integers (B) One-third of the product of the 3 consecutive integers. is assigned to Y.gateforum. that sum } return Y.com int Myx ( int * E. k + + ) z = z + E [ k ].i + + ) Calculates sum of the elements Y = Y + E [i ] of the array E and stores it in Y for ( i = 0.CS-GATE-2014 PAPER-01| Exp: www. j. un sin ged int sixe ) { int Y = 0. int z. if ( z > Y ) → Checks whether sum of elements of each subarray Y = z.i < size. int i. (C) One-sixth of the product of the 3 consecutive integers. (D) None of the above. k. if not 'Y ' will be the sum of elements of complete array } Ultimately returns the maximum possible sum of elements in any sub array of given array E. for ( i = 0.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 26 .k < = j. all posible subarrays of E for ( k = i. Consider the following pseudo code. is greaer than the sum of elements of array if so. i < size. Answer: (C) India’s No. i + + ) for ( j = i. Answer: (4) Exp: For 6 stages. where all stages are perfectly balanced.n − 1) ↓ S1 ↓ S2 ↓ S3 n −1 n ( n − 1) i =1 2 = ∑ Si = ∑ ↓ Sn −1 1 1 ∑ n2 − ∑ n 2 2 n n + 1 )( 2n + 1) − 1 n ( n + 1) = ( n − 1)( n )( n + 1) 1 ( = 2 6 2 2 6 = 43... j = 3. ∑ ( n − 1) = 1 + (1 + 2 )+ (1 + 2 + 3)+ . k = 4 to n ⇒ n − 3 times ∑ ( n − 1) times : i = 1.gateforum. There were 2 stall cycles for pipelining for 25% of the instructions 25 So pipe line time = 1 + 2 100 3 = = 1... k = n to n ⇒ 1 time : : i = n − 1..CS-GATE-2014 PAPER-01| www. j = n − 1. k = n to n ⇒ 1 time } ∑1 times ∴ Total number of multiplications ⇒ ∑ 1 + ∑ 2 + ∑ 3 + . j = n − 1. k = n − 1 to n ⇒ 2 times i = 1. Assume that there is no cycle-time overhead of pipelining. non. + (1 + 2 + 3 + . j = 2.. k = 4 to n ⇒ n − 3 times : : ∑ ( n − 2 ) times : : i = 2. j = n − 2. the speedup achieved with respect to non-pipelined execution if 25% of the instructions incur 2 pipeline stall cycles is ______________________. k = n to n ⇒ 1 time i = 2. k = 3 to n ⇒ n − 2 times i = 1.. j = n − 1. j = 1. Consider a 6-stage instruction pipeline.pipelining takes 6 cycles..1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 27 .5 2 Non − pipeline time 6 Speed up = = =4 Pipeline time 1. When an application is executing on this 6stage pipeline. j = 3. k = 3 to n ⇒ n − 2 times i = 2.5 India’s No.com Exp: i = 1.. k = 2 to n ⇒ n − 1 times i = 1. j = 2. R + PQR Exp: = PQ + PQ. What is the miss ratio if the access sequence is passed through a cache of associativity A ≥ k exercising least-recently-used replacement policy? (A) n/N Answer: 45.com (B) l/N (C) 1/A (D) k/n (A) Consider the 4-to-1 multiplexer with two lines S1 and S0 given below.gateforum.R + PQR QR QR P P QR QR 1 1 1 PQ 1 QR Hence the minimized expression is PQ + QR + PQR PQR 46. f"(x) + f(x) +tcosx = 0. The number of unique block addresses between two consecutive accesses to the same block address is bounded above K. Answer: Exp: -2 Given f "( x ) + f ( x ) + t cos x = 0 and f ( x ) = x sin x f ' ( x ) = x cos x + sin x f "( x ) = x ( − sin x ) + cos x + cos x = 2cos x − x sin x = 2cos x − f ( x ) ∴ 2cos x − f ( x ) + f ( x ) + t cos x = 0 ⇒ 2cos x = − t cos x ⇒ t = −2 India’s No.CS-GATE-2014 PAPER-01| 44.1 + PQ. www. 0 1 R R 0 1 4 − to − 1 2 Multiplexer 3 s1 s 0 P F Q The minimal sum of-products form of the Boolean expression for the output F of the multiplexer is (A) PQ + QR + PQR (B) PQ + PQR + PQR + PQR (C) PQR + PQR + QR + PQR (D) PQR Answer: (A) P Q. An access sequence of cache block addresses is of length N and contains n unique block addresses. The function f(x) = x sin x satisfies the following equation.O + PQ.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28 . The value of t is______. The number of 10.1}4 = {0. (1.1} → {0.1}X{0. Answer: (89) Exp: No twos: 1111111111⇒1 pennant Single two: 211111111⇒9!/8!1! = 9 pennants Two twos: 22111111⇒8!/6!.1) such that f(y) =f(2 – y) Answer: (A) Exp: Define g(x) =f(x)-f(x+1) in [0. (1. It is known that f(0) = f(2) = -1 and f(1) = 1.2)}. A pennant is a sequence of numbers.2]. f(y) = f(2 .1} .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 29 .1).2) is 1 (D) There exists a y in the interval (0.y) (C) The maximum value of the function in the interval (0. Note that the pennant (1.1}X{0. By intermediate value theorem there is y€(0.2) is a 4-pennant.CS-GATE-2014 PAPER-01| 47. The value of log2 log2 N is______. each number being 1 or 2.2! = 15 Five twos: 22222⇒1 Total = 89 pennants.1) such that g(y)=0 That is f(y) =f(y+1). For example. Thus answer is (a) 48.1]. For fair six-sided dice are rolled. Which one of the following statements must be true? (A) There exists a y in the interval (0. Answer: (16) Exp: The number of functions from A to B where size of A = |A| and size of B = |B| is |B||A| {0.4! = 35 Four twos: 222211⇒6!/4!. Answer: (10) Exp: 22 occurred in following ways 6 6 6 4 → 4ways 6 6 5 5 → 6ways Required probability = 6+ 4 10 = ⇒ x = 10 2296 2296 49. The set of all possible 1pennants is {(1)}.1}X{0.1)}and the set of all 3-pennants is {(2. www.1). (1. the set of all possible 2-pennants is {(2).pennants is ______________.1}.com A function f(x) is continuous the interval [0.1} = 16 |S| = 216 N = 2|S| loglog N = log log 2|S| = log |S| = log 216 = 16 50.2! = 28 Three twos: 2221111⇒7!/3!. The probability that the sum of the results being 22is X The value of X is _________ 1296.gateforum.1.1). An n-pennant is a sequence of numbers with sum equal to n.1) such that f(y) = f(y + 1) (B) For every y in the interval (0. 4 India’s No. g(0) is negative and g(1) is positive. Let S denote the set of all functions f : {0.2) is not the same as the pennant (2. Denote by N the number of functions from S to the set {0.1.1). (1. 0) is also not graphic. There is an edge between (a.2) is graphic iff (0.2.1..2) is graphic iff (1.0. 1 ≤ j ≤ 12}.0) is graphic (2. The vertex set of G is {i.2.com Consider an undirected graph G where self-loops are not allowed.CS-GATE-2014 PAPER-01| 51.3.0) is graphic (1.1. 2. 2.1.2. (1.2. 2) (C) (3.0.b) and (c. Answer: (506) Exp: The graph formed by the description contains 4 vertices of degree 3 and 40verices of degree 5 and 100 vertices of degree 8.0> is graphic (0.1.-1. f): 1 ≤ i ≤ 12.1.0) is graphic (0.1. (The process is always finding maximum degree and removing it from degree sequence.22-1. 3.1.1) is also graphic.2. 0) (D) (3.dn) with d1 ≥ d 2 ≥ .2-1) = (2. (0.0. 1. Which one of the following propositional logic formulas is TRUE when exactly two of p.1..0.2) is graphic iff (2.2) is also graphic. According to sum of the degrees theorem 4*3+40*5+100*8 = 2|E| |E| = 1012/2 = 506 52.1.1. 53.0. www.1) (0.0) is graphic Since (0.3.1.0) is graphic.1.1) is graphic.2.1.1) is graphic iff (0.3.2.3. Since (0. Consider option C now.. (3.0)(0.1) is graphic iff (0.1.2.1.1.1.1.1.-1. 1. An ordered n-tuple (d1. and r are TRUE? ( ( p ↔ q) ∧ r ) V ( p ∧ q∧ ~ r ) (C) ( ( p → q ) ∧ r ) V ( p ∧ q ∧ ~ r ) (A) (B) ( ~ ( p ↔ q ) ∧ r ) V ( p ∧ q ∧ ~ r ) (D) ( ~ ( p ↔ q ) ∧ r ) ∧ ( p ∧ q ∧ ~ r ) India’s No. 0) Answer: Exp: (C) According to havel-hakimi theorem (1.1.1..d2.0.3) is graphic iff (0.0.2.d 2 . 1) (B) (2. Since (0.2.1.gateforum.1) is not graphic (3. 1.0.2. q. 0.1.1) is graphic iff (0. 1.1) is graphic.d) if a − c ≤ 1 and b − d ≤ 1 The number of edges in the graph is _____________..0.1) is graphic iff (0. 2.0.1. 1. Which of the following 6-tuples is NOT graphic? (A) (1. 1.2) is graphic.2.1) is graphic iff<1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 30 .3.2.1.1) is graphic. subtract 1 from each degree for d times from right to left where d is maximum degree) (2.2.3. 3.…..0. 2. (1. 2. ≥ d n is called graphic if there exists a simple undirected graph with n vertices having degrees d1 . 1.0.1. 1.1. Note that before applying the havel-hakimi step degree sequence should be in non-increasing order..2.d n respectively.1. salary) departments(dept-id. After grouping. (C) It generates an error because of pairwise comparison.com (B) P=T q=F and r=T Option A will become false. the tuples of the resultant table will be filtered by using the condition “location-id=1700” and then will grouped on deptid(all the tuples having equal values under dept-id will come into one group). Option D is always false. Outer query takes each tuple from “employees” table and it will check whether dept-id and hire-date pair for this tuple is contained in the table given by inner sub query. After this. Format of the tuples in the resultant table will be dept-id in location-id 1700 along with the latest hire date in the respective dept (two columns). What is the outcome? (A) It executes but does not give the correct result. Option C will become false. manager-id. the columns dept-id in location-id 1700 and maximum of hire dates in that respective dept-id will be selected. “employees” and “departments” tables are joined by “using” clause (first Cartesian product of those two tables will be done and then and wherever these is a match on the dept-ids that tuple will be filtered). Answer: Exp: (B) In the inner sub query. dept-name. When using multiple expressions (like 2 columns . dept-id. Given the following schema: employees(emp-id. (D) It generates an error because the GROUP BY clause cannot be used with table joins in a sub-query. MAX(hire-date) FROM employees JOIN departments USING(dept-id) WHERE location-id = 1700 GROUP BY dept-id). last-name. If this is the case it will display the last-name of respective employee IN operator compares one or multiple expressions on the left side of the operator to a set of one or more values on the right side of the operator. the number and data types of expressions in the list must match on both sides of the operator. (B) It executes and gives the correct result. hire-date) IN (SELECT dept-id. India’s No.CS-GATE-2014 PAPER-01| Answer: Exp: www. location-id) You want to display the last names and hire dates of all latest hires in their respective departments in the location ID 1700. You issue the following query: SQL>SELECT last-name.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 31 .gateforum. hire-date FROM employees WHERE (dept-id. hire-date.pair wise comparison). first-name. 54. means.com 55.6) Exp: 1 cycle time for p1 = 109 = 1n. Assume p 2 clock frequency is x GHz. 6 cycles.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 32 .75. means.gateforum. Assume that under identical conditions.CS-GATE-2014 PAPER-01| www. for the same input. p 2 Takes 25% less time. p 2 Taken 6 cycles. Consider two processors P1 and P2 executing the same instruction set.s 1GH Assume p1 takes 5 cycles for a program then p 2 takes 20% more. Answer: (1. so 6 × 109 = 3.s. then p 2 takes 3. then the clock frequency of P2 (in GHz) is _________. x = 1.6 x GH India’s No. If the clock frequency of P1 is 1GHz.75 n. if p1 takes 5 n. a program running on P2 takes 25% less time but incurs 20% more CPI (clock cycles per instruction) as compared to the program running on P1.s. Column 1 Column 2 (1) eradicate (P) misrepresent (2) distort (Q) soak completely (3) saturate (R) use (4) utilize (S) destroy utterly (A) 1:S.CS-GATE-2014 PAPER-02| www.. No. 2:P. 3:Q.444 India’s No. (D) had you said Match the columns. Choose the most appropriate phrase from the options given below to complete the following sentence. 4:R (C) 1:Q. India is a post-colonial country because (A) it was a former British colony (B) Indian Information Technology professionals have colonized the world (C) India does not follow any colonial practices (D) India has helped other countries gain freedom Answer: (A) 2. The value of (A) 3.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 . 2:R. What is the average of all multiples of 10 from 2 to 198? (A) 90 (B) 100 (C) 110 Answer: (B) Exp: 10 + 190 → 200 20 − 180 → 9 : : 90 − 110 100 5. 3:R. is (B) 3. 2:Q. 3:S. 3:R.000 (D) 4. 2:P.com Q.464 ⇒ (D) 120 [(200) × 9 + 100] = 1900 = 100 19 19 12 + 12 + 12 + . 4:Q 4. 4:S (D) 1:S.932 (C) 4. 1 – 5 Carry One Mark Each 1..gateforum. Who ___________ was coming to see us this evening? (A) you said (B) did you say (C) did you say that Answer: (B) 3.. 4:P Answer: (A) (B) 1:P. = y www. 52 (D) 14. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. y = −3 Q. (D) If x is real and x 2 − 2x + 3 = 11 . It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively.com ⇒ 12 + y = y ⇒ 12 + y = y 2 ⇒ (y − 4)(y + 3) = 0 ⇒ y = 4.gateforum. 4 Answer: (B) 2. Kaliningrad is now a Russian territory and has a predominantly Russian population. 14 (C) 4. (B) The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. does not contradict this conclusion? (A) A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent (B) More cases of dengue are now reported because of an increase in the Municipal Office’s administrative efficiency (C) Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test (D) The number of people with malarial fever (also contracted from mosquito bites) has increased this year Answer: 8... as that was its original Russian name (D) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia Answer: 7. then possible values of − x 3 + x 2 − x include (A) 2. No. 52 (D) India’s No. The old city of Koenigsberg. After the events of the war. which had a German majority population before World War 2. if true.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 . Which of the statements below can be inferred from this passage? (A) Kaliningrad was historically Russian in its ethnic make up (B) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia (C) Koenigsberg was renamed Kaliningrad. Which one of the following statements.CS-GATE-2014 PAPER-02| Answer: (C) Exp: let = 12 + 12 + 12 + .. 6 – 10 Carry Two Marks Each 6. is now called Kaliningrad. gateforum.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 . by what percent did the number of male students increase in 2009? Ra tio of m ale to fe m ale stu de nts Answer: (140) Exp: m =3 f 3.5f %↑ = × 100 2.5 2 1. x = −2 Values of − x 3 + x 2 − x For x = 4 Value = 52 for x = −2 Value = 14 9.CS-GATE-2014 PAPER-02| www.5 1 0.5 3 2.5 0 2008 2009 2010 2011 2012 m = 2.4 8 % ↑= 140% India’s No.5 m=2. If the number of female students doubled in 2009.com x 2 − 2x + 3 = 11 Exp: ⇒ (x − 4)(x + 2) = 0 ⇒ x = 4.5f 7 = = 1. The ratio of male to female students in a college for five years is plotted in the following line graph.5f f m' =3 2f m ' = 6f m '− m = m 3. com At what time between 6 a. m.m.m will the minute hand and hour hand of a clock make an angle closest to 60°? (A) 6: 22 a. (D) 6:45 a.m.m. and 7 a. India’s No. (B) 6:27 a. (C) 6: 38 a. www.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 .m.gateforum.CS-GATE-2014 PAPER-02| 10. Answer: (A) Exp: Angle by minute’s hand 60 min → 360 ο 1min → 360 = 6ο 60 8min → 48o Angle → 48o with number ‘6’ Angle by hours hand 60 min = 30o 30 × 22 60 = 11 22 min → Total Angle=48+11=59o. Exp: Given words are THE. (The answer should be rounded to one decimal place. The maximum number of edges in a bipartite graph on 12 vertices is __________________________.8889) 2. One of the pieces is drawn at random from the box. BROWN. LAXY is 4 The length of the words QUICK.95) Exp: p= P [at least three computers are working] = P (3 or 4 computers working) = (4 ) × (6 ) + 4 C3 C1 10C4 C4 10C4 = 5 42 ⇒ 100 p = 11.9. Each of the nine words in the sentence ”The quick brown fox jumps over the lazy og” is written on a separate piece of paper. FOX. JUMPS. QUICK. The expected length of the word drawn is _____________. The system is deemed functional if at least three of the four computers inspected are working. OVER. No.8889 9 9 9 3. FOX. JUMPS. Answer: (3. is 5 The corresponding probabilities are given below x 3 4 5 P(X) 4/9 2/9 3/9 4 2 3 Expected length of the word= ∑ xp ( x ) = 3 + 4 + 5 = 3.gateforum. To check whether the system is functional. the officials inspect four of the computers picked at random (without replacement). These nine pieces of paper are kept in a box.11. LAXY.CS-GATE-2014 PAPER-02| www. BROWN. DOG is 3 The Length of the words OVER. DOG LET X be the random variable such that X =length of the word The Length of the words THE. THE. Answer: (11. Answer: (36) Exp: The number of edges in a bipartite graph on n-vertices is atmost n2 4 The maximum number of edges in a bipartite graph on 12 –vertices is n 2 12 × 12 = = 36 4 4 India’s No. THE.com Q. The security system at an IT office is composed of 10 computers of which exactly four are working. 1 – 25 Carry One Mark Each 1. Let the probability that the system is deemed functional be denoted by p Then 100p= _____________.85 .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 . . A non-zero polynomial f(x) of degree 3 has roots at x = 1... The number of self-dual functions with n Boolean variables is n n −1 (A) 2n (B) 2n-1 (C) 22 (D) 22 Answer: (D) Exp: A function F is self dual if it has equal number of minterms and maxterms. x = 1. 2.x = 2 and x = 3. 2n = 2n −1 2 Number of functions possible by taking any of the one term from the above mentioned The number of mutually exclusive terms (pair wise) is n −1 mutually exclusive pair is = 22 ..1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 . 3 lies between 0 and 4 and f(x) is of degree 3 ∴ f(0) and f(4) are of opposite signs ⇒ f(0). also mutually exclusive terms should not be included. the roots of f(x) = 0 i. +. single output will be 1 and remaining will be zero at a time. is the same expression as that of F with + and swapped.com If the matrix A is such that 2 A = −4 [1 9 5] 7 Then the determinant of A is equal to ________. Which one of the following must be TRUE? (A) f(0) f(4) < 0 (B) f(0) f(4) > 0 (C) f(0) + f(4) > 0 (D) f(0) + f(4) < 0 Answer: (A) Exp: Since.. www..gateforum. (D) k-bit Johnson counter. x n.x 2 . The output that is high will give the count of the ring counter at that time. (B) k-bit binary down counter. This circuit is equivalent to a (A) k-bit binary up counter. F is said to be self-dual if F = FD.. Let k = 2 n . A circuit is built by giving the output of an n-bit binary counter as input to an nto-2n bit decoder. The dual of a Boolean function F ( x1 .' ) .. 6. 18 5. Answer: (C) Exp: In case of decoder output. written as FD. 7. Answer: (0) Exp: 2 A = −4 7 ⇒ A =0 10 −36 20 63 35 (∵ R 2 = −2R1 ) .f(4)<0.e. India’s No.CS-GATE-2014 PAPER-02| 4. (C) k-bit ring counter. y = 10 ∴ Total number of solutions: 3 9. } The value returned by func(435)is __________. x = 2. of blocks = 214 = 29 25 block offset = 9bits 32 bits TAG TAG 29 No.CS-GATE-2014 PAPER-02| www. } return (count). y = 15 or. Consider the function func shown below: int func(int num) { int count = 0. The word length is 32 bits. The number of possible solutions is _____ . A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block size of 8 words. India’s No. Consider the equation (123)5 = (x8)y with x and y as unknown. while (num) { count++. of sets = = 27 4 set ofset = 7 bits TAG 20 SET BYTE OFFSET OFFSET 7 5 Byte offset = 8 × 4 Bytes = 32 Byte = 25 = 5 bits TAG = 32 − ( 7 + 5 ) = 20 bits 10. num>>= 1. The size of the physical address space is 4 GB. The number of bits for the TAG field is _____ Answer: (20) Exp: Physical address size = 32 bits Cache size = 16 k bytes = 214 Bytes block size = 8 words = 8 × 4 Byte = 32 Bytes ( where each word = b Bytes ) No. y = 30 or . x = 3.gateforum. Answer: (3) Exp : (123)5 = ( x 8 ) y Converting both sides to decimal: ⇒ 25 + 10 + 3 = xy + 8 ⇒ xy + 8 = 38 ⇒ xy = 30 ⇒ x = 1.com 8.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 . it might go beyond the range of unsigned integer (resulting overflow). //shifts all bits of num one slot to the right// } return(count). there will be less accuracy in final result of P. checks whether the num value is not zero// { count ++. while (num) //After each right shift. } Initially num = 110110011. num = 000000000 after 9th right shift.0. (C) p = n * (n – 1) / 3 * (n-2) / 2.CS-GATE-2014 PAPER-02| www. num ≫= 1. P = n * ( n − 1) 3* ( n − 2 ) 2 p1 p2 As there is a possibility of truncation in P1. 11. After nine right shifts. resultant p will be more accurate. its not certain to get integer always (truncation possible. so more accuracy) where as incase of n*(n-1)/3. which one of the following statements is most likely to set p correctly? (A) p = n * (n – 1) * (n-2) / 6. We wish to set p to n C3 . India’s No. Answer: (B) Exp: P = n C3 = n ( n − 1)( n − 2 ) 6 It we multiply n. count = 0 count = 1. and while loop terminates count = 9 will be returned. so less accuracy). P = n * ( n − 1) 2 * ( n − 2 ) 3 p1 p2 As P1 will be having no error. If n is even or odd n×(n-1)/2 will always result in integer value (no possibility of truncation. So options (A) and (D) are rested out. num = 0. (n-2) at once. (B) p = n * (n – 1) / 2 * (n-2) / 3. num = 101100110 after 1st right shift count =2. Suppose n and p are unsigned int variables in a C program.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 8 . (D) p = n * (n – 1) / 2 * (n-2) / 6.com Answer: (9) Exp: int func (int num) { int count = 0.gateforum. If n is large. num = 011001100 after 2nd right shift : : Count = 9. (n-1). Two new elements 1 and 7 are inserted into the heap in that order. 8. 2.com A priority queue is implemented as a Max-Heap. 2. 7. The level-order traversal of the heap is: 10. 5 Answer: (A) Exp: Initial max-heap is (D) 10. 3. 5 (B) 10. then T ( n ) = θ ( n log ab ) = θ ( n ) India’s No. 1. Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1? n T ( n ) = 2T + log n 2 (A) θ ( n ) (B) θ ( n log n ) ( ) (C) θ n 2 (D) θ ( log n ) Answer: (A) Exp: By Master’s theorem case (i) T ( n ) is O ( n ) Here a = 2. 1. If f ( n ) = O ( n log ab −∈ ) for some ∈> 0.CS-GATE-2014 PAPER-02| 12. i. 2.e. 8.. 2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 9 . in such a way that f ( n ) = O ( n log ab −∈ ) . 7. 1. 1. www. 3. 8. 8. 7. 5 13. 3. 5. b = 2. The level-order traversal of the heap after the insertion of the elements is: (A) 10. 7. 3. 1 after inserting 1 10 10 8 5 8 2 3 Heapification is not required as it satisfies max-heap property 5 2 3 1 After inserting 7 10 10 ⇒ 8 3 8 5 2 1 7 3 7 2 1 5 Hence level order traversal is 10. 3. 2.gateforum. 5. log n = O ( n log ab −∈ ) By master theorem. 2. 8. Initially. f ( n ) = log n log ab = log 22 = 1 we can choose ∈> 0. 5 (C) 10. 3. 7. 8. it has 5 elements. L2 is not {a n b n | n ≥ 0} because both the variable is independent in both languages. Which one of the following is FALSE? (A) If A ≤ m B and B is recursive then A is recursive.com Consider the tree arcs of a BFS traversal from a source node W in an unweighted. (B) the shortest path from W to every vertex in the graph.gateforum.L2 = a n b n | n ≥ 0 Which one of the following is CORRECT? (A) Only (I) (B) Only (II) (C) Both (I) and (II) (D) Neither (I) nor (II) Answer: (A) Exp: L1. if there is a computable function f : ε* → ε * where for every w. (C) the shortest paths from W to only those nodes that are leaves of T.CS-GATE-2014 PAPER-02| 14. w ∈ A ⇔ f ( w ) ∈ B If A ≤ mB and B is Turing recognizable then A is Turing recognizable. (D) If A ≤ m B and B is not recursively enumerable then A is not recursively enumerable. If A ≤ mB and B is not recursively enumerable then A is not recursively enumerable India’s No. Answer: (B) Exp: One of the application of BFS algorithm is to find the shortest path between nodes u and v. The tree T formed by the tree arcs is a data structure for computing (A) the shortest path between every pair of vertices.L2 is also regular since regular languages are closed under concatenation.L2 is a regular language { } (II) L1. Answer: (D) Exp: A language A is mapping reducible to a language B. (D) the longest path in the graph.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 10 . IfL1 = {a n | n ≥ 0} and L 2 = {b n | n ≥ 0} . connected. (C) If A ≤ m B and B is recursively enumerable then A is recursively enumerable. www. Consider (I) L1. Let A ≤ m B denotes that language A is mapping reducible (also known as many-to-one reducible) to language B. (B) If A ≤ m B and A is undecidable then B is undecidable. But L1. 16. But in the given question the BFS algorithm starts from the source vertex w and we can find the shortest path from w to every vertex of the graph 15. undirected graph. so ti is performed during sum time not during complete time. while * is right associative (B) + is right associative.com Consider the grammar defined by the following production rules. Answer: (C) India’s No. Dynamic memory allocation is when an executing pregoram request the oprating system to give it a block of main memory.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 11 . so + is right associative operator. 19. As the production rule P → Q + P is defined as right recursive rule. (B) Consistency and completeness of functional requirements are always achieved in practice.gateforum. (C) Prototyping is a method of requirements validation. while * is left associative (C) Both + and * are right associative (D) Both + and * are left associative Answer: (B) Exp: S→ T×P T → U|T×U P→Q+P|Q Q → Id U → Id As the production rule T → T × U is defined as left recursive rule.CS-GATE-2014 PAPER-02| 17. so * is left associate operator. Which one of the following is NOT performed during compilation? (A) Dynamic memory allocation (B) Type checking (C) Symbol table management (D) Inline expansion Answer: (A) Exp: Symbol table management is done during compitation to store and retriew the information about tokens. with two operators S → T*P and + T → U|T*U P →Q+P|Q Q → Id U → Id Which one of the following is TRUE? (A) + is left associative. Inline expansion is a compiler optimization that replaces a function call by the bodyof respective function. Type checking is one of the check performed during semantic analysis of compitation. Option (A) is answer 18. www. Which one of the following is TRUE? (A) The requirements document also describes how the requirements that are listed in the document are implemented efficiently. (D) Requirements review is carried out to find the errors in system design. the maximum size of a file that can be stored on this disk in units of 106 bytes is ____________. Given a 100 x 106 bytes disk on which the file system is stored and data block size is 103 bytes.4 9876 Swati swati@mech 18 9.65) Exp: Number of entries in the FAT = Disk Capacity/Block size = 108/103 = 105 Total space consumed by FAT = 105 * 4 B = 0. As we have 3 nonkey all (F.CS-GATE-2014 PAPER-02| 20. G.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 12 .4 * 106 B Maximum size of file that can be stored = 100 * 106 – 0.G.5 7853 Shankar Shankar@cse 19 9. The maximum number of super keys for the relation schema R (E.4 1287 Swati swati@ee 19 9.7 For (StudentName. Answer: (8) Exp: The maximum number of super keys for the relation schema R ( E.gateforum.6 21.F. H) with E as the key is __________. the value X should NOT be equal to____________. the pair value should not get repeated in any two tuples p and q (uniqueness in forced by the definition of key) Tuple Student Name Student Age P Shankar ⊗ → should not be 19 Q Shankar 19 India’s No. www. Given an instance of the STUDENTS relation as shown below: Student D StudentName Student Email Student Age CPI 2345 Shankar Shankar@math X 9. StudentAge) to be a key for this instance.3 8765 Ganesh ganesh@civil 19 8. H ) with E as the key is 23 = 8 as any subset of non key attributes along with key attribute will form the super key of R.4 * 106 = 99.6 * 106 B Answer: 99. student age) to be a key for given instance of STUDENTS relation.55 to 99. F. Answer: (19) Exp: For (Student Name. G and H) so subsets will be 23 22. Answer: (99.com A FAT (file allocation table) based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size. ISP2 ISP1 LAN L2 R S LAN L1 ISP1 Answer: (26) Exp: ISP1 LAN L2 S R LAN L1 India’s No. (d) The accept function is called by a TCP server to return the next completed connection from the front of the completed connection queue. the process is put to sleep (assuming the default of a blocking socket). The links within each ISP and across the two ISPs. the protocol address is the combination of either a 32-bit IPv4 address or a 128-bit IPv6 address. If the completed connection queue is empty. The initial value of the TTL field is 32. are all point-to-point’ optical links. (b) The bind function assigns a local protocol address to a socket. (c) The listen function converts an unconnected socket into a passive socket. L1 is an Ethernet LAN and L2 is a Token-Ring LAN. 25. Which one of the following is TRUE about the interior gateway routing protocols – Routing Information Protocol (RIP) and Open Shortest Path First (OSPF)? (A) RILP uses distance vector routing and OSPF uses link state routing (B) OSPF uses distance vector routing and RIP uses link state routing (C) Both RIP and OSPF use link state routing (D) Both RIP and OSPF use distance vector routing Answer: (A) Exp: RIP Uses Distance Vector Routing and OSPF uses Link State Routing. indicating that the kernel should accept incoming connection requests directed to this socket. In the diagram shown below.CS-GATE-2014 PAPER-02| www.com 23. along with a 16-bit TCP or UDP port number. With the Internet protocols.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 13 .gateforum. The maximum possible value of the TTL field when R receives the datagram is ____________. as shown. 24. An IP packet originates from sender S and traverses to R. Which one of the following socket API functions converts an unconnected active TCP socket into a passive socket? (A) connect (B) bind (C) listen (D) accept Answer: (C) Exp: (a) The connect function is used by a TCP client to establish a connection with a TCP server. Which one of the following is CORRECT? A R2 R1 (A) T1 < T2 < T3 (B) T1 > T2 > T3 (C) T2 = T3. Let T1. the file is split into 20 equal parts and these packets are sent from A to B. Q. the file is split into 10 equal parts. Assume that the bandwidth of each link is 106 bytes / sec. Each packet contains 100 bytes of header information along with the user data.CS-GATE-2014 PAPER-02| www. and reduced by every router on the route to its destination.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 14 . T2 and T3 be the times taken to transmit the file in the first.com The TTL field is set by the sender of the datagram. In the second case.gateforum. T3 > T2 B Answer: (D) Exp: Given Bandwidth = 106 bytes/sec L=103 bytes Case: 1 L = 1000 bytes Header size = 100 bytes Total Frame size = 1000 + 100 = 1100 bytes 1100 × 8 ∴ Tx = = 1100 µs 106 × 8 So. A user on host A sends a file of size 103 bytes to host B through routers R1 and R2 in three different ways. and these packets are transmitted from A to B. T2 = 2000 + 200 + 200 = 2400 µs India’s No. 26 – 55 Carry Two Marks Each 26. T3 < T1 (D) T1 = T3. there are 5visits at 5 routers and one visit at receiver R in above figure which leads 32 – 6 = 26. In the first case a single packet containing the complete file is transmitted from A to B. So. second and third case respectively. Consider only transmission time and ignore processing. Also assume that there are no errors during transmission. Consider the store and forward packet switched network given below. In the third case. queuing and propagation delays. No. T1 = 3300 µs Case: 2 L = 100 bytes Header size = 100 bytes Total Frame size = 100 + 100 = 200 bytes 200 × 8 ∴ Tx = 6 = 200 µs for 1 packet 10 × 8 For 10 packets ⇒ Tx = 2000 µs So. Consider the following four pieces of information: [I1] The URL of the file downloaded by Q [I2] The TCP port numbers at Q and H [I3] The IP addresses of Q and H [I4] The link layer addresses of Q and H Which of I1.CS-GATE-2014 PAPER-02| www. and I4 can an intruder learn through sniffing at R2 alone? (A) Only I1 and I2 (B) Only I1 (C) Only I2 and I3 (D) Only I3 and I4 Answer: (C) Exp: An Intruder can’t learn [I1] through sniffing at R2 because URLs and Download are functioned at Application layer of OSI Model. which one of the following is correct about the HTML webpage loading (including the embedded image)? India’s No. Assuming no caching. T3 = 3000 + 150 + 150 = 3300 µs ∴ T1 = T3 T3 > T2 27. R2. I3.com Case: 3 L = 50 bytes Header size = 100 bytes Total Frame size = 50 + 100 = 150 bytes ∴ Tx = 150 × 8 = 150 µs for 1 packet 106 × 8 For 20 packets ⇒ Tx = 3000 µs So. I2. Session layer encryption is used.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15 . An IP machine Q has a path to another IP machine H via three IP routers R1. and R3. An Intruder can learn [I2] through sniffing at R2 because Port Numbers are encapsulated in the payload field of IP Datagram. A graphical HTML browser resident at a network client machine Q accesses a static HTML webpage from a HTTP server S. and Q connects to H via HTTP and downloads a file. An Intruder can learn [I3] through sniffing at R2 because IP Addresses and Routers are functioned at network layer of OSI Model. An Intruder can’t learn [I4] through sniffing at R2 because it is related to Data Link Layer of OSI Model. with DES as the shared key encryption protocol. Q—R1—R2—R3—H H acts as an HTTP server. 28. The static HTML page has exactly one static embedded image which is also at S.gateforum. and this is possible without any TCP connection between Q and S Answer: (B) 29.T2 . T2 T3 ⇒ No cycle.T3 and T4 for each pair of transaction Ti and Tj . each necessarily in a separate TCP connection to server S (B) Q needs to send at least 2 HTTP requests to S. T4: T1 T2 T3 T4 Reads[X] Writes[X] Commit Writes [x] Commit Writes[Y] Reads [Z] Commit Reads[X] Reads[Y] Commit Which one of the following statements is CORRECT? (A) S is conflict-serializable but not recoverable (B) S is conflict-serializable but is recoverable (C) S is both conflict-serializable and recoverable (D) S is neither conflict-serializable nor is it recoverable Answer: (C) Exp: The precedence graph of schedule s is a follows. India’s No. T2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 16 .CS-GATE-2014 PAPER-02| www. such that Tj reads a data item previously written by Ti the commit operation of Tj appears after the commit operation of Ti hence the schedule is recoverable schedule.gateforum.com (A) Q needs to send at least 2 HTTP requests to S. so S is conflict serializable T1 T4 In the schedule S of transactions T1 . T3. and a single TCP connection between Q and S is necessary for this (D) A single HTTP request from Q to S is sufficient. but a single TCP connection to server S is sufficient (C) A single HTTP request from Q to S is sufficient. Consider the following schedule S of transactions T1. There are 3 buffers each of size equal to disk block size. (B) The consumer will remove no more than one item from the buffer. semWait (n) . but the consumer can never consume if given statement is false. because once producer produces an item and places in buffer. but the consumer can never consume it.com 30.s> This algorithm will involve nr*bs+br block transfers and nr+br seeks. (D) The starting value for the semaphore n must be 1 and not 0 for deadlock-free operation. out of which one buffer is reserved for intermediate results. Assuming size(r(R))<size(s(S)). So consumer will be definitely able to consume it by performing successful down operations on s and n. (C) Deadlock occurs if the consumer succeeds in acquiring semaphore s when the buffer is empty. Consider a join (relation algebra) between relations r(R)and s(S) using the nested loop method. 31.5. Answer: (C) Exp: (A) The producer will be able to add an item to the buffer.gateforum. SemWait (s). Relation r(R) should be in the outer loop to have fewer number of disk block accesses. removeFromBuffer ( ) . the join will have fewer number of disk block accesses if (A) relation r(R) is in the outer loop. the next turn to execute can be given to consumer ( ). For each tuple r in R do For each tuple s in S do If r and s satisfy the join condition then output the tuple <r. semWait (s) . [The value of s = 1 and n=1]. (B) relation s(S) is in the outer loop.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 17 . addToBuffer ( ). semsignal (s). } } } } Which one of the following is TRUE? (A) The producer will be able to add an item to the buffer. India’s No. (D) join selection factor between r(R) and s(S) is less than 0. Consider the procedure below for the Producer-Consumer problem which uses semaphores: Semaphore n = 0. semSignal (s). where br and bs are number of blocks in relations R and S respectively and nr is number of tuple in relation R. Answer: (A) Exp: A join between r(R) and s (S) using nested loop method will be as follows. Void producer ( ) Void consumer( ) { { while (true) while(true) { { Produce ( ). Now to have less block accesses. consume ( ) . (C) join selection factor between r(R) and s(S) is more than 0.5. semSignal (n). Semaphore s = 1.CS-GATE-2014 PAPER-02| www. nr should be less and it is already given that |R|<|S|. p ( s ) . it blocks consumer ] } } producer ( ) { while ( True ) { producer ( ) . s = 0. a process performs a single computation that requires tc CPU milliseconds and then initiates a single I/O operation that lasts for tio milliseconds.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 18 . (C) Dead lock occurs if the consumer succeeds in acquiring semaphore‘s’ when the buffer is empty. the scheduling overhead of the OS is negligible. there will be invalid execution of consumer on buffer empty condition. The processes have the following characteristics: India’s No. B and C each execute a loop of 100 iterations. n = 0. ( at a time). (c) will consume the added item. consumer ( ) { while ( True ) { p ( s ) .gateforum. s = 10 p ( s ) . Also. (D) Even if the starting value for the semaphore ‘n’ becomes 1.CS-GATE-2014 PAPER-02| www. Given statement is true as when buffer is empty initially if consumer gets the turn to execute as follows:S = 1. which should not happen. it blocks p ( ) } } So from the above execution both producer and consumer goes in block state waiting for each other to wake them up and hence dead lock occurs. Given statement is false as if p( ) produces and adds to buffer. It is assumed that the computer where the processes execute has sufficient number of I/O devices and the OS of the computer assigns different I/O devices to each process. 32. So statement is false. In each iteration of the loop. Three processes A. This statement would have been true if it was said that the consumer will remove no more than one item from the buffer one after the other. [ m = 0.com (B) The consumer will remove no more than one item from the buffer. this sequence of alteration (p and c) will always make consumer to remove items from buffer. gateforum. 2. Implementation of optimal page replacement policy for above given page reference string would be as follows: India’s No.com Process id tc tio A 100ms 500ms B 350ms 500ms C 200ms 500ms The processes A. The time in milliseconds at which process C would complete its first I/O operation is ___________. 2. 3. 3. and C are started at times 0. ------------100. C goes for I/O operation. ------------100. The current status of 20 frames shows page numbers from 101 to 120.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 19 . 2. A computer has twenty physical page frames which contain pages numbered 101 through 120. 4. so the time at which process C would complete its first I/O operations is 500+500 = 1000ms 33. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for this program? (A) Least-recently-used (B) First-in-first-out (C) Last-in-first-out (D) Most-recently-used Answer: (D) Exp: Page reference string for the program will be:1. 5 and 10 milliseconds respectively. B.Q A B C A A 0 B 50 C A 100 150 B 200 C 250 300 B C 350 B 400 C B 450 500 650 C goes for I o operation A goes for I o operation After finishing t c CPU ms at time 500ms. 1.CS-GATE-2014 PAPER-02| www. 4. 100 in that order. 1. 4. Now a program accesses the pages numbered 1. in a pure time sharing system (round robin scheduling) that uses a time slice of 50 milliseconds. Answer: (1000) Exp: Process id tc t io A. 2. ------------100. 3. that needs 500ms more. and repeats the access sequence THRICE.T A 100 ms 500 ms 0 ms B 350 ms 500 ms 5 ms C 200 ms 500 ms 10 ms TQ = 50ms The Gantt chart for Round robin algorithm for the first iteration execution for each of the 3 processes is as follows: R . …. gateforum. t0 = i * 1024 t1 = j * 32 t2 = k * 4 t3 = t1 + t0 t4 = t3 + t2 t5 = X[t4] Which one of the following statements about the source code for the C program is CORRECT? India’s No. Also it is visible that every time a replacement is done for the page which is most recently referred as it will be least recently referred in future. the following intermediate code is generated by a compiler. 34.com 0 101 1 40 41 80 81 60 61 100 1 40 41 80 1 102 2 39 42 79 82 2 103 3 38 43 78 83 3 104 4 37 44 77 84 4 105 5 36 45 76 85 5 106 6 35 46 75 86 6 107 7 34 47 74 87 7 108 8 33 48 73 88 8 109 9 32 49 72 89 9 110 10 31 50 71 90 10 111 11 30 51 70 91 11 112 12 29 52 69 92 12 113 13 28 53 68 93 13 114 14 27 54 67 94 14 115 15 26 55 66 95 15 116 16 25 56 65 96 16 117 17 24 57 64 97 17 118 18 23 58 63 98 18 119 19 22 59 62 99 19 120 20 21 60 61 100 1 40 41 80 81 20 21 60 61 100 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF 20PF 3rd time access 1st time access 2 nd time access So there would be 300 page faults in total (each access 100 page faults).1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 20 81 . So for the given page reference string optimal page replacement policy is working same as most recently used policy and thus number of page faults will be same in both of them. Assume that the size of an integer is 32 bits and the size of a character is 8 bits.CS-GATE-2014 PAPER-02| 20 21 www. For a C program accessing X[i] [j] [k]. Which one of the following is TRUE? (B) L2 is regular but not L1 (A) L1 is regular but not L2 (C) Both L1 and L2 are regular (D) Neither L1 nor L2 are regular Answer: (A) Exp: The automaton for L1 is as follows: 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0. and B = 32.1} . From t0 = i*1024. Let the array be declared as Type X[A][B][C] (where Type = int/char and A. 36. India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 21 . Let L = {<M> |M is a Turning machine that accepts a string of length 2014}. (D) X is declared as “char X[32] [16] [2]”. Answer: (A) Exp: It is given that Size of int is 4B and of char is 1B. Let L2 = {w ∈{0. Type = int. L is (A) decidable and recursively enumerable (B) undecidable but recursively enumerable (C) undecidable and not recursively enumerable (D) decidable but not recursively enumerable Answer: (B) Exp: The language accepted by the Turing machine is recursively enumerable.gateforum.C are natural numbers). (B) X is declared as “int X[4] [1024] [32]”. From t2 = k*4. Then.B. we conclude that C*(size of Type) = 32. Let L1 = w ∈{0. From t1 = j*32. The memory is byte addressable. we conclude that size of Type = 4. and C = 8. we conclude that B*C*(size of Type) = 1024.com (A) X is declared as “int X[32] [32] [8]”.1} * | w has at least as many occurrence of (000)’s as (111)’s}. 35.1} * | w has at least as many occurrences of (110)’s as (011)’s}.CS-GATE-2014 PAPER-02| www. If is undecidable as the Turing machine may halt or it may loop for the strings whose length is not equal to 2014. Let < M > be the encoding of a Turing machine as a string over Σ = { 0.1 No finite state automata can be constructed for L2. (C) X is declared as “char X[4] [32] [8]”. Q.gateforum. Answer: (358) Exp: The implementation of optimal algorithm for merging sequences is as follows. the maximum possible value of the expression represented by the tree is ___. www. Consider the expression tree shown. 24.CS-GATE-2014 PAPER-02| 37. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____. so x=4 and such common subsequences are as follows: (1) qpqr (2) pqrr (3) qprr So y = 3 (the number of longest common subsequences) hence x+10y = 4+10*3 = 34. 30. Over all possible choices of the values at the leaves. R. 38. 159 94 44 20 65 50 24 30 35 In the above implementation. Each leaf represents a numerical value. T are sorted sequences having lengths 20. total number of comparisons is (44-1)+(94-1)+(65-1)+(159-1) = 358 Hint: The number of comparisons for merging two sorted sequences of length m and n is m+n-1. which can either be 0 or 1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 22 . Answer: (34) Exp: Given is A = “qpqrr” B = “pqprqrp” The longest common subsequence (not necessarily contiguous) between A and B is having 4 as the length. Then x + 10y = ___. 35. Let x be the length of the longest common subsequence (not necessarily contiguous) between A and B and let y be the number of such longest common subsequences between A and B. 39. S.com Consider two strings A = "q pqrr " and B = "pqprqrp". Suppose P. 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. India’s No. 74) Exp: If condition given in function definition should be ‘TRUE’. 41.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 23 .CS-GATE-2014 PAPER-02| www. in addition to the PUSH and POP instructions.72 to 1. which reverses the order of elements on the stack. 40.73. The condition is as follows: if ( abs ( x × x − 3) < 0.gateforum. the maximum possible value of the expression represented by the tree is 6. Consider the following function double f (double x) { if ( abs (x*x – 3) < 0.01) return x. } Give a value q (to 2 decimals) such that f (q) will return q:______ Answer: (1. Which one of the following statements is TRUE with respect to this modified stack? India’s No. 01) return x. for f ( q ) to return value q.com + + − 0 /1 0 /1 Answer: (6) Exp: 0 /1 0 /1 + 0 /1 0 /1 1 + − 1 0 /1 0 /1 6 3 − 2 + − − + −1 0 1 + 1 3 + 2 − 1 0 1 1 So as per the above tree where leaves have been given the values. The above condition will be true when x=1.5/x). Suppose a stack implementation supports an instruction REVERSE. else return f (x / 2 + 1. Enqueue: Dequeue: (OR) 2.gateforum. (B) The function prints the string something for all values of j. (D) A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each. return 0. Answer: (D) Exp: For any value of ‘j’ other than 50 the function will return 0. if (i == j) { printf(“something”). Answer: (C) Exp: Option (a) is false because queue can be implemented by using the modified stack as by reversing the stack.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 24 . (B) A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions. Reverse Consider the C function given below int f(int j) { static int i = 50. (D) The function will exhaust the runtime stack or run into an infinite loop when j = 50. (C) The function returns 0 when j = 50. int k.CS-GATE-2014 PAPER-02| www. LIFO will become FIFO. Revesre POP Push Reverse. } Which one of the following is TRUE? (A) The function returns 0 for all values of j. Push. (C) A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction. POP. Implementation of ENQUEUE & DEQUEUE takes four sequence of instructions as follows: 1. k = f(i). for j=50. it will print “something” and function will be called recursively with same value till the run time stack overflows. India’s No. Reverse. Enqueue: Dequeue: 42. } else return 0. then condition (i==j) will be true.com (A) A queue cannot be implemented using this stack. 45. accordingly. the number of bits used for TAG comparator be effected. which one of the following is guaranteed to be NOT affected? (A) Width of tag comparator (B) Width of set index decoder (C) Width of way selection multiplexor (D) Width of processor to main memory data bus Answer: (D) Exp: When associativity is doubled.com 43. The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign. With of processor to main memory data bus is guaranteed to be NOT effected. 44. it improves the hit ratio for cache. the cache block (or cache line) size is an important Parameter.11001 × 23 S :1 E : ( 3 + 127 )10 = (10000010 )2 M :11001000 − − − − − Value stored: 11 0 00 0 0 10 1 1 00 1 0 0 0 0 − − − [C 1 6 4 0 0 0 0 ]H India’s No. 8 bits for biased exponent and 23 bits for mantissa. Width of wag selection multiplexer wil be effected when the block offset is changed. Width of set index decoder also will be effected when set offset is changed.gateforum.01)2 1110.01 × 20 = 1.25. The representation of X in hexadecimal notation is (A) C1640000H (B) 416C0000H (C) 41640000H (D) C16C0000H Answer: (A) Exp: (A) S E M 1 bit 8 bits 23 bits (14. Which one of the following statements is correct in this context? (A) A smaller block size implies better spatial locality (B) A smaller block size implies a smaller cache tag and hence lower cache tag overhead (C) A smaller block size implies a larger cache tag and hence lower cache hit time (D) A smaller block size incurs a lower cache miss penalty Answer: (D) Exp: When a cache block size is smaller.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 25 .25)10 = (1110. it could accommodate more number of blocks.CS-GATE-2014 PAPER-02| www. If the associativity of a processor cache is doubled while keeping the capacity and block size unchanged. so the miss penalty for cache will be lowered. A float type variable X is assigned the decimal value of −14. then the set offset will be effected. In designing a computer’s cache system. Which of the following is TRUE? (A) Only I Answer: (A) Exp: (B) Only II (C) Both I and II (D) Neither I nor II f ( x ) = 0.. is obtained for the function 0. the method diverges if x0 = 2 ∴ only (I) is true. 47. f 0 ' = −1 ∴ x1 = x 0 − f0 =0 f0 ' ⇒ f1 = 4.f 2 ' = −1 ∴ x3 = x 2 − f2 =0 f2 ' Also. x1 . f ' ( x ) = 2. www. x 2 . an initial guess of x 0 = 2 is made and the sequence x 0 . f 0 = −2. root does not lies between 0 and 1. So.CS-GATE-2014 PAPER-02| 46.75 x 3 − 2x 2 − 2x + 4.75x 3 − 2x 2 − 2x + 4 = 0 Consider the statements (I) x 3 = 0 .com In the Newton-Raphson method. f1 ' = −2 ∴ x 2 = x1 − f1 =2 f1 ' ⇒ f 2 = −2.25x 2 − 4x − 2 x 0 = 2.gateforum. Answer: (6) Exp: 1 0 Let A = 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 India’s No.. (II) The method converges to a solution in a finite number of iterations. The product of the non-zero eigenvalues of the matrix 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 is_______.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 26 . 3 product of non zero eigen values =2×3=6 48.259 to 0. n(A∩C) = 10 n(A∩B∩C) = 3 P(A∪B∪C) = P(A)+P(B)+P(C) – P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C) = 74/100 ( ) ∴ Required probability is P A ∩ B ∩ C = 1 − P ( A ∪ B ∪ C ) = 0. India’s No. product of prime factors ∴ Number of distinct positive integral factors of 2014 is (2)×(2)×(2) = 8. B = divisible by 3 and C = divisible by 5.CS-GATE-2014 PAPER-02| www.e. AX= λ X 1 0 0 0 1 0 0 0 1 x1 x1 1 1 1 0 x2 x2 1 1 1 0 x3 = λ x3 1 1 1 0 x4 x4 x 0 0 0 1 x 5 5 x1 + x 5 = λ x 5 x 2 + x 3 + x 4 = λx 2 x 2 + x 3 + x 4 = λx 3 x 2 + x 3 + x 4 = λx 4 x1 + x 5 = λ x 4 ⇒ x 1 + x 5 = λ x 5 = λ x 4 and x 2 + x 3 + x 4 = λx 2 = λx 3 = λx 4 (1) If λ ≠ 0 say x1 = x 5 = a x2 = x3 = x4 = b ⇒ x1 + x 5 = λa ⇒ 2a = λa ⇒ λ = 2 x 2 + x 3 + x 4 = λa ⇒ 3a = λa ⇒ λ = 3 (2) if λ = 0 ⇒ eigen value =0 ∴ Three distinct eigen values are 0.gateforum. then n(A) = 50. 3 or 5 is ______ . The number of distinct positive integral factors of 2014 is _________________________ Answer: (8) Exp: 2014 = 2×19×53 i.26. n(C) = 20 n(A∩B) = 16.2.com x1 x2 Let X = x 3 be eigen vector x4 x 5 By the definition of eigen vector.. Answer: (0. n(B) = 33.261) Exp: Let A = divisible by 2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 27 . 49. The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2. n(B∩C) = 6. A cycle on n vertices is isomorphic to its complement. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U.2.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28 . www.. Consider the following two statements: S1: There is a subset of S that is larger than every other subset.com Consider the following relation on subsets of the set S of integers between 1 and 2014.CS-GATE-2014 PAPER-02| 50. Both s1 and s2 are true. Answer: (5) Exp: The number of edges in Cn is n where as the number of edges in Cn’ is n c2 − n Cycle graph Cn and its complement Cn’ have different number of edges if n≠5 Consider a cycle on five vertices C5 v1 v1 C5 and C5 ' areisomorphic v5 v5 v2 v2 ∴n = 5 v4 v4 v3 v5 ( co m p le m en t G = C5 C5 52. of C 5 )= C ' 5 The number of distinct minimum spanning trees for the weighted graph below is 2 2 1 2 1 2 2 2 1 1 1 2 2 India’s No. Which one of the following is CORRECT? (A) Both S1 and S2 are true (B) S1 is true and S2 is false (C) S2 is true and S1 is false (D) Neither S1 nor S2 is true Answer: (A) Exp: From given data S1 is true .. S2: There is a subset of S that is smaller than every other subset.and S2 is true since the universal set {1. The value of n is _____.. 51..gateforum.2014} is smaller than every other set.since null set is larger than every other set . v8 } forms one minimum spanning tree. {v 2 . v 2 } . v 2 } and {v7 . v7 } can be choosen because of connectedness. v9 } ∴ There are 6 distinct minimum spanning trees. v5 . v 4 } . v5 } { v .{v . {v 2 . v } . v 4 } and {v 7 . Selection of {v1 . v 4 . Selection of {v 2 . will not form a cycle.gateforum.CS-GATE-2014 PAPER-02| www. v } .{v . so v1 v2 1 1 v5 1 v8 v3 v4 1 1 v6 2 v7 Selection of {v4 .{v 4 .com Answer: (6) Exp: Consider the connected weighted graph (Application of Kruskal’s Algorithm) v1 2 v2 2 1 1 v5 2 2 v4 1 v8 v3 2 2 1 v6 1 v9 2 2 v7 v9 Sort the edges by increasing edges costs (weights) [{v1 . v 6 } . v9 } forms one minimum spanning tree. Selection of {v1 . v8 } forms one minimum spanning tree. v 2 } and {v7 . {v8 . v1 . v9 }( Cost − 1) 3 { }{ [{v1 . v }( cos t − 2 )] 6 7 7 8 7 9 2 Selection of edges of cost-1. v5 } and {v1 .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 29 . v9 } forms one minimum spanning tree. v5 } forms a cycle. v3 } . so we will not consider the edges. v 4 } . The edge {v 6 .{v5 . v 4 } and {v7 . India’s No. v 6 } . v 4 } and {v 7 .{v 4 . v3 }. v 4 } and {v7 . v8 } forms two min imum spanning trees Selection of {v3 . Selection of {v3 . Selection of {v 2 . a=S.gateforum. and correspondingly defines the multiplicity of tuples in the result of joins.a = S. a (B) Select distinct R.a (D) Select R. * from R.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 30 . (select distinct a from S) as S1 where R. a (C) Select R.S where R.com Which one of the following Boolean expressions is NOT a tautology? ( A ) ( ( a → b) ∧ ( b → c) ) → ( a → c ) ( B) ( a ↔ c ) → ( ~ b → ( a ∧ c ) ) (C) ( a ∧ b ∧ c) → (c ∧ a ) ( D) a → ( b → a ) Answer: (B) Exp: (D) a → ( b → a ) ( ⇒ ¬a ∨ ( b → a ) ) ( ⇒ ¬a ∨ ( ¬b ∨ a ) ) ⇔ T ( tauto log y ) (C) ( a ∧ b ∧ c ) → ( c ∨ a ) ⇔ ¬ ( a ∧ b ∧ c ) ∨ ( c ∨ a ) ⇔ ( ¬a ∨ ¬b ∨ ¬c ) ∨ ( c ∨ a ) ⇔ ( ¬a ∨ a ) ∨ P ( where P is disjunction of literals ) ⇔T∨P⇒T a→b b→c (a) by hypothetical syllog ism ∴a → c (( a → b ) ∧ ( b → c )) → ( a → c ) is a tautology Answer is B which is not tautology. * from R.CS-GATE-2014 PAPER-02| 53 www. S where R. 54 SQL allows duplicate tuples in relations. * from R. S where R. a=S1. * from R. a and is unique R Answer: (C) Exp: Consider the following instances of R & S a b c 1 2 3 1 2 3 3 4 5 3 4 5 a d e India’s No. Which one of the following queries always gives the same answer as the nested query shown below: Select * from R where a in (select S. a=S. a from S) (A) Select R. a and S. and control signals. When a write request is made. but only one request can be on the bus at any time. the addressed memory module executes one cycle accepting and storing the data. the bus is occupied for 100 nanoseconds (ns) by the data.a’s value is repeated. 55 Consider a main memory system that consists of 8 memory modules attached to the system bus. and for 500 ns thereafter. The maximum number of stores (of one word each) that can be initiated in 1 millisecond is ____________ India’s No.gateforum. which is one word wide. address.CS-GATE-2014 PAPER-02| www.a and for that match S.com 1 2 3 2 3 4 3 4 6 3 4 6 O/P of given nested query is a b c 1 2 3 1 2 3 3 4 5 3 4 5 (A) O/P:- multiplicity of tuples is disturbed a b c 1 1 3 3 3 3 2 2 4 4 4 4 3 3 5 5 5 5 (B) O/P:- a b c 1 2 3 3 4 5 (C) O/P:- a b c Multiplicity of tuples is maintained 1 2 3 1 2 3 3 4 5 3 4 5 Multiplicity of duplicate tuples will be distributed when there is a match between R. The (internal) operation of different memory modules may overlap in time. During the same 100 ns.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 31 . CS-GATE-2014 PAPER-02| www.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 32 .s = stores 100 = 10000 stores India’s No. the bus is occupied for 100 n.gateforum.s Storing of data requires 100 n.s.com Answer: (10000) Exp: Each write request.s − 1 store 100 n.s = 1 store 106 106 1 m. In 100 n. Q.02 (D) 3.74 (C) 3.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 . There is no negative or partial marking in the examination. The table below has question-wise data on the performance of students in an examination. While trying to collect an envelope from under the table.gateforum. If she _______________ how to calibrate the instrument. Mr.34 (B) 1. Which number does not belong in the series below? 2. had (C) had known. will have (B) knew.No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination? (A) 1. Choose the word that is opposite in meaning to the word “coherent”. No. would have Answer: (C) 3. 17. The marks for each question are also listed. 10. 37. X fell down and I II III was losing consciousness. 64 (A) 17 (B) 37 (C) 64 (D) 26 Answer: (C) 5. 5. (A) sticky (B) well-connected (C) rambling (D) friendly Answer: (C) 4. could have (D) should have known.CS-GATE-2014 PAPER-03| www. she _______________ done the experiment. 50. 1 – 5 Carry One Mark Each 1.91 India’s No. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I (B) II (C) III (D) IV Answer: (D) 2. (A) knows.com Q. 26. 02 44 Q. A dance programme is scheduled for 10. 6 – 10 Carry One Mark Each 6.00 a.00 a.com Answer: (C) Exp: Total question 44×2=88 44×3=132 144 = 88 132 308 Total marks obtained= (21×2) + (15×3) + (23×2) =133 Total Number of students=44 Average = 133 = 3.m. By the beginning of the 20th century. (B) Participating students should come at 9.m. suggesting a paradigm shift in our understanding of the universe.m. Other students and parents should come in time for the programme. accompanied by a parent. Parents who accompany them should come at 9. (D) Participating students should come before 9.m. the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun.m. All others should come at 10.gateforum. (C) Students who are not participating should come by 10. several hypotheses were being proposed.m.m. (ii) and (iv) (B) (iii) only (C) (i) and (iv) (D) (iv) only Answer: (D) India’s No. and other parents and students should come by 10. Participating students should come at 9. and they should not bring their parents.00 a.m.00 a. No.CS-GATE-2014 PAPER-03| www.00 a.00 a.m. However.00 a. Answer: (B) 7. and parents should come at 10.00 a. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i).1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 .m. These students should be accompanied by a parent.00 a. The instruction you think that is appropriate for this is (A) Students should come at 9. Some students are participating in the programme and they need to come an hour earlier than the start of the event.00 a. Find Y.(Y)8 = (4364)8 .CS-GATE-2014 PAPER-03| www.5:1 Answer: (C) Exp: Take number of female students in 2011=100 ∴ Number of male in 2011=100 No.com 8. he ratio of male to female students in a college for five years is plotted in the following line graph.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 . 50/ USD to Rs. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. During the period 2012-2013 the exchange rate for the USD increased from Rs. where (X) N stands for X to the base N. India’s GDP in USD during the period 20122013 (A) increased by 5 % (B) decreased by 13% (C) decreased by 20% (D) decreased by 11% Answer: (D) Exp: Per 100 Rs final value 107 Rs 100 107 ⇒ Per Dollars final value 50 60 for 100 dollars____? 100 × 50 107 = × = 89.16 100 60 Decreased by 11%. of male in 2012=150 150 Ratio = = 1. 9.5 2 1. For international comparison. the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. of female in 2012=100 No. (A) 1634 (B) 1737 (C) 3142 (D) 3162 Answer: (C) India’s No.gateforum. 60/ USD.5: 1 100 2012 (D) 2.5:1 10.5 0 2008 2009 2010 2011 (A) 1:1 (B) 2:1 (C) 1. Consider the equation: (7526)8 . If the number of female students in 2011 and 2012 is equal.5 1 0.5 3 2. what is the ratio of male students in 2012 to male students in 2011? Ra tio of m ale to fe m ale stu de nts 3. f ( b ) = 1.2} f ( A ∩ B) = 1 ∴ Options (A). 2} f ( A ) ∩ f ( B ) = {1. and N is CORRECT? (A) Only L is TRUE. (C) are not true Hence. f ( A ∩ B) = min f ( A ) . Which one of the following statements is TRUE? (A) For any subsets A and B of X. b. No. Let X and Y be finite sets and f : X → Y be a function.c} .B = {b. f ( A ) = 2 . (C) Only N is TRUE.gateforum.c} be subsets of X then f ( A ∪ B ) = 2 . f ( A ) = {1.CS-GATE-2014 PAPER-03| www. 2} Let A = {a. (D) L. 1 – 25 Carry One Mark Each 1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 . f ( A ∩ B) = f ( A ) ∩ f ( B) { (C) For any subsets A and B of X. (B). f ( A ∪ B) = f ( A ) + f ( B) (B) For any subsets A and B of X. f ( B ) = 2 f ( A ∩ B ) = {2} .c} Y = {1.2} . M.f ( B ) = {1.f ( c ) = 2 where X = {a. M and N are TRUE. f −1 ( S ∩ T ) = f −1 (S) ∩ f −1 ( T ) Answer: (D) Exp: f : X → Y defined by f ( a ) = 1.com Q. f ( B) } (D) For any subsets S and T of Y. option (D) is true India’s No. c : mobile is cheap P : Good mobile phones are not cheap ≅ g → ¬ c ≅ ( ¬ g ∨ ¬ c ) [∵a → b ≡ ¬ a ∨ b] Q : Cheap mobile phones are not good ≅ c → ¬ g ≅ ( ¬ c ∨ ¬ g ) ∴ Both P and Q are equivalent which means P and Q imply each other 2. Answer: (D) Exp: g : mobile is good (B) Only M is TRUE. Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L. It is known that L ≠ G and that the size of L is at least 4. e4. (B) If the trace of the matrix is positive. e2. => Smallest possible dimension = 2. then the value of k is equal to _______. (D) If the product of the trace and determinant of the matrix is positive.e4} and {e3. e2. Hence it is 5. e5.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 . all its eigenvalues are positive. The size of L is _______. e6} respectively. The basis of V1 ∩ V2 would then be {e3. {e1.gateforum. say. Which one of the following statements is TRUE about every n × n matrix with only real eigenvalues? (A) If the trace of the matrix is positive and the determinant of the matrix is negative. order of subgroup can’t be 3 and 15. Let L be a subgroup of G. all its eigenvalues are positive. If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V. Answer: (A) Exp: If the trace of the matrix is positive and the determinant of the matrix is negative then atleast one of its eigen values is negative. then the smallest possible dimension of V1 ∩ V2 is _______. In order for V1 ∩ V2 to have smallest possible dimension V1 and V2 could be. e4}. (C) If the determinant of the matrix is positive. If ∫ 2π 0 x sin x dx = kπ. all its eigenvalues are positive. As subgroup has atleast 4 elements and it is not equal to the given group. Since determinant = product of eigen values. 4.com Let G be a group with 15 elements. e3. 3.e4.CS-GATE-2014 PAPER-03| 3. e5. at least one of its eigenvalues is negative. 6. e6}. e3. www. Answer: (5) Exp: Order of subgroup divides order of group (Lagrange’s theorem). Answer: (2) Exp: Let the basis of 6-dimensional vector space be {e1. 5 and 15 can be the order of subgroup. Answer: ( 4 ) 2π Exp: ∫ 0 π x sin x dx = Kπ ⇒ ∫ 2π x sin x dx + ∫ − ( x sin x ) dx π 0 π ∵ sin x = − sin x = Kπ π< x < 2π 2π ⇒ x ( − cos x ) −1( − sin x ) 0 − ( − x cos x + sin x ) π = Kπ ⇒ ( −π cos π + sin π ) − 0 − ( −2π cos 2π+ sin 2π ) − ( −π cos π + sin π ) = Kπ ⇒ π + 0 − − 2π+ 0 − ( π+ 0 ) = Kπ ⇒ 4π = Kπ ⇒ k = 4 India’s No. 5. 1.S) = P1 + P2 = QS + QS 1 φ P1 φ 1 P2 φ 1 8.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 . b where x. 7. where the two input lines are ‘a’ and ‘b’. ‘x’ is working as selection line. 13. 7. 8 and 13 are ‘do not care terms. b are inputs and y is the output. 5. 1 ns. Assume that the pipeline registers have zero latency.5 ns. F ( P. a. 0. so the function F ( x.S) = ∑ 0. 10. 2. www. Which processor has the highest peak clock frequency? (A) P1 (B) P2 (C) P3 I1 2 ×1 y MUX I0 x (D) P4 Answer: (C) India’s No. 1 ns. R. b) { if (x is 1) y = a. 2 ns. P3: Five-stage pipeline with stage latencies 0. R.com Consider the following minterm expression for F. y. else y = b. a.5 ns. 1. P2: Four-stage pipeline with stage latencies 1 ns. 2 ns. } Which one of the following digital logic blocks is the most suitable for implementing this function? (A) Full adder (B) Priority encoder (C) Multiplexor (D) Flip-flop Answer: (C) Exp: y = xb + xa a 9.5 ns. y.5 ns. b ) can be implemented using (2 × 1) multiplexer as follows: b Consider the following processors (ns stands for nanoseconds).gateforum. y. f (x. 1. 1 ns. 1 ns. 1.6 ns. Consider the following combinational function block involving four Boolean variables x.Q.5 ns. P1: Four-stage pipeline with stage latencies 1 ns. a. 1 ns.Q. 8. 15 The minterms 2.CS-GATE-2014 PAPER-03| 7. a. 1 ns.5 ns. 0. P4: Five-stage pipeline with stage latencies 0.1 ns. The minimal sum of-products form for F is (A) QS + QS (B) QS + QS (C) Q R S + Q R S + Q R S + QRS (B) P QS + P QS + PQS + P QS RS PQ Answer: (B) Exp: The K-map for the function F is as follows:- RS RS RS RS PQ 1 φ PQ PQ PQ P1 = QS and P2 = QS ∴ F ( P. 5.gateforum.CS-GATE-2014 PAPER-03| Exp: www. A [ j ] [ i ] = Temp – C . } for i = 1 to n do for j = 1 to n do output (A[ i ] [ j ]).6. for i = 1 to n do for j = 1 to n do { Temp = A[ i ] [ j ] + C .5.0. 2.5 ) =1.5. each upper triangular element will be interchanged by its mirror image in the lower triangular and after that the same lower triangular element will be again re-interchanged by its mirror image in the upper triangular.5ns CPP3 = Max ( 0. A[ i] [ j]=A[ j] [ i]. Consider the following pseudocode.com Clock period (CP) = max stage delay + overhead So CPP1 = Max (1. What is the expected output? C = 100. The minimum number of arithmetic operations required to evaluate the polynomial P ( X ) = X 5 + 4X 3 + 6x + 5 for a given value of X.0. 1 .5. using only one temporary variable is _____. 1.1ns As frequency α So. (A) The matrix A itself (B) Transpose of the matrix A (C) Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A (D) None of these Answer: (A) Exp: In the computation of given pseudo code for each row and column of Matrix A. so least clock period will give the highest peak clock frequency.1.1.1) =1ns CPP4 = Max ( 0.1. 1.1) = 2ns CPP2 = Max (1. Answer: (7) India’s No.1) =1.2. 1.P 1 =1GHz 1ns Let A be a square matrix size n × n. 11. f p3 = 10.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 .5. 1. resulting the final computed Matrix A same as input Matrix A.1. C. CS-GATE-2014 PAPER-03| Exp: www. t = 6*x [Evaluate 6x and store in memory] 7. Consider the following rooted tree with the vertex labelled P as the root P Q S R U T V W The order in which the nodes are visited during an in-order traversal of the tree is (A) SQPTRWUV (B) SQPTUWRV (C) SQPTWUVR (D) SQPTRUWV Answer: (A) Exp: The In order Traversal of Ternary Tree is done as follows: Left → Root → Middle → Right So the nodes are visited in SQPTRWUV order. t = x*x [Evaluate x 2 and store in memory] 2. t = x2 [Retinue x 2 from memory] 4.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 8 . India’s No. the total number of arithmetic operations required and 7 [4 Multiplications. t = t * ( x 2 + 4) [Evaluate x 3 ( x 2 + 4 ) and store in memory] 6.com P(x) = x 5 + 4x 3 + 6x + 5can be re written as follows P ( x ) = x 3 ( x 2 + 4 ) + 6x + 5 Now using only one temporary variable t and any number of data transfer as well as memory related operation the polynomial can be evaluated as follows 1. 3 Additions] So answer is 7 arithmetic operations. t = t *.gateforum.X [Evaluate x 3 and store in memory] 5. t = t + x 3 ( x 2 + 4 ) [Retrieve x 2 ( x 2 + 4 ) from memory and evaluate x 3 x 2 + 4 + 6x + 5 { ( } ) In the above 8 steps of evaluation. t=t+4 [Evaluate ( x 2 + 4 ) and store in memory] 3. 12. t =t+5 [Evaluate ( 6x + 5 ) and store in memory] 8. a*b* (ba)* a* Answer: (3) Exp: R. This will happen when the elements of the input array are already in order (ascending or descending). irrespective of position of pivot element in array.com Suppose depth first search is executed on the graph below starting at some unknown vertex.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 9 . ba. we start DFS at vertex numbered as 1 and continue calling recursive function for DFS on subsequent nodes numbered in ascending order. www.gateforum. b} ) of the following regular expression is _________. Then the maximum possible recursion depth (including the initial call) is _________. The length of the shortest string NOT in the language ( over Σ = {a. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. bb are present. 14. So it is 3 India’s No. Then the tightest upper bound for the worst case performance is ( A) 0( n2 ) ( B) 0 ( n log n ) ( C) θ ( n log n ) ( D) 0 ( n 2 ) Answer: (A) Exp: 15. The Worst case time complexity of quick sort is O (n2). Answer: 19 Exp: 1 2 3 17 18 19 6 5 4 16 15 14 7 8 9 11 12 13 10 Suppose. But 'bab ' is not present. The recursive calling sequence is shown as marked line in the above diagram which shows maximum possible recursion depth including the initial call is 19.CS-GATE-2014 PAPER-03| 13. b ) also aa.ab. You have an array of n elements.E= a * b * ( ba ) * a * Length 0 is present as it accepts ∈ all length 1 strings are present ( a. Suppose you implement quick sort by always choosing the central element of the array as the pivot. Which one of the following is TRUE? (A) Both 2 Σ * and Σ * are countable (B) 2 Σ * is countable Σ * is uncountable (C) 2 Σ * is uncountable and Σ * is countable (D) Both 2 Σ * and Σ * are uncountable Answer: (C) Exp: 2ε* is the power set of ε * ε * is countabily infinite.CS-GATE-2014 PAPER-03| 16.gateforum. 17. Answer: (C) Exp: Intermediate code is machine independent code which makes it easy to retarget the compiler to generate code for newer and different processors. 18. (A) 1 and 2 only (B) 2 and 3 only (C) 3 and 4 only (D) 1 and 3 only Answer: (D) Exp: To implement recursion. www. activation record should be implemented by providing dynamic memory allocation. This dynamic allocation is done from runtime stack. In the context of modular software design. 4) Both heap and stack are essential to implement recursion. So 2ε* is uncountable.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 10 . One of the purposes of using intermediate code in compilers is to (A) make parsing and semantic analysis simpler. 19. which one of the following combinations is desirable? (A) High cohesion and high coupling (B) High cohesion and low coupling (C) Low cohesion and high coupling Answer: (B) (D) Low cohesion and low coupling India’s No. So statement 1 and 3 are correction. Which of the following statements are CORRECT? 1) Static allocation of all data areas by a compiler makes it impossible to implement recursion. 3) Dynamic allocation of activation records is essential to implement recursion. 2) Automatic garbage collection is essential to implement recursion.com Let Σ be a finite non-empty alphabet and let 2Σ* be the power set of Σ * . (B) improve error recovery and error reporting (C) increase the chances of reusing the machine-independent code optimizer in other compliers. Heap is essential to allocate memory for data structures at run-time. (D) improve the register allocation. not for recursion. and ε * is countable. The power set of countabily infinite set is uncountable. What is the optimized version of the relation algebra expression πA1 ( πA 2 (σF1 ( r ) ))). 6. 1. 1. So in the context of modular software design there should be high cohesion and low coupling. remaining attributes are known as non-prime or non-key tribute 23.gateforum. 7. A2 are sets of attributes in with A1 ⊂ A 2 and F1.CS-GATE-2014 PAPER-03| www. A prime attribute of a relation scheme R is an attribute that appears (A) in all candidate keys of R. What is the total number of page faults that will occur while processing the page reference string given below? 4. 6. It uses the Least Recently Used (LRU) page replacement policy. 7. A system uses 3 page frames for storing process pages in main memory. the INCORRECT pair is (A) Network layer and Routing (B) Data Link Layer and Bit synchronization (C) Transport layer and End-to-end process communication (D) Medium Access Control sub-layer and Channel sharing Answer: (B) India’s No. (C) in a foreign keys of R. 2. 6. 7. Answer: (B) Exp: A prime attribute or key attribute of a relation scheme R is an attribute that appears in any of the candidate key of R. Assume that all the page frames are initially empty. so final relation will be displaying values for attributes present in set A. In the following pairs of OSI protocol layer/sub-layer and its functionality. 7. F2 are Boolean expressions based on the attributes in r? (A) π A1 ( σ ( F1 ∧ F2 )( r ) ) (B) π A1 ( σ ( F1 ∨ F2 )( r ) ) (C) π A2 ( σ ( F1 ∧ F2 )( r ) ) (D) π A2 ( σ ( F1 ∨ F2 )( r ) ) Answer: (A) Exp: π is used to select a subset of attributes and σ p is used to select subset of tuples matching the predicate P.com Exp: Cohesion is a measure of internal strength within a module. (B) in some candidate key of R. 7. 2. ( ( ( Π A1 Π A2 σF1 σ F ( r ) 2 ))) ( = Π A1 Π A2 ( σ ( F1 ∧ F2 )( r ) ) ) and as A1 ⊂ A 2 . (D) only in the primary key of R. 1. .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 11 . 6. 7. where A1. 20. 2 2 2 Implementing LRU using 3 page frames Total page faults = 6 6 7 21. whereas coupling is a measure of inter dependency among the modules. 2 Answer: (6) Exp: Page reference string is 4 1 4. 1. ( ) Π A1 Π A2 ( σ ( F1 ∧ F2 )( r ) ) =Π A1 ( σ ( F1 ∧ F2 )( r ) ) 22. which of the following IP header field(s) may be different from that of the original datagram D? (i) TTL (ii) Checksum (iii) Fragment Offset (A) (i) only (B) (i) and (ii) only (C) (ii) and (iii) only (D) (i).1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 12 . When D reaches B. No.00/12 3 131. Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP V4 network B). (d) MAC sub layer have 3 types of protocols (Random. then the input bit-string is (A) 0111110100 (B) 0111110101 (C) 0111111101 (D) 0111111111 Answer: (B) Exp: Given 8 – bit delimiter pattern of 01111110.gateforum. Q.com (a) One of the main functionality of Network Layer is Routing. (ii) and (iii) Answer: (D) Exp: While an IP Datagram is transferring from one host to another host.0.19. So Option (a) is CORRECT.0/14 5 131. An IP router implementing Classless Inter-domain routing (CIDR) receives a packet with address 131. If the output bit-string after stuffing is 01111100101. 26 – 55 Carry Two Marks Each 26. So Option (b) is INCORRECT. India’s No. (c) End – to – End Process Communication is handled by Transport Layer. Assume that no error occurred during the transmission of D.CS-GATE-2014 PAPER-03| Exp: www. Output Bit string after stuffing is 01111100101 ⇓ StuffedBit Now. So Option (c) is CORRECT.0.16. Input String is 0111110101 25. TTL.151. A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. The router’s routing table has the following entries: Prefix Output Interface Identifier 131.22. (b) Bit Synchronization is always handled by Physical Layer of OSI model but not Data Link Layer.0. Controlled and Channelized Access). 24.76. Checksum and Fragmentation Offset will be changed.0/16 2 131.23.0/15 1 The identifier of the output interface on which this packet will be forwarded is _____.28. 22.151. After what period (in seconds) will the identifiers generated by a host wrap around? Answer: (256) Exp: Given that each host has a globally unique IPv4 Address and we have to design 50 – bit unique Id. Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup.0/16 131.0.0 Matched nd Coming to the 2 field of given Routing table ⇒ 131. The values of the relevant fields in the header of the third IP fragment generated by the router for this packet are (A) MF bit: 0. Each host needs to generate up to 1000 unique identifiers per second.0 Not matched.0. Design a 50-bit globally unique ID for this purpose.0 (∵ given mask bits = 14) ⇒ 131. Offset: 2960 India’s No. It is clearly showing that IP Address (32 – bit) followed by 18 bits. 1000 unique Ids => 1Sec 218 unique Ids => 218 / 1000 = 28 = 256 28.151.0001 0100.0/12 131.20. so output interface identifier is 1.0 (∵ given mask bits = 12) ⇒ 131.0/14 131.0. Offset: 185 (C) MF bit: 1.0.0. So.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 13 .151.0. An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP packet of size 4404 bytes with an IP header of length 20 bytes.23.0.28.0001 0111.coming to the first field of given routing table ⇒ 131.0001 0111. Assume that each host has a globally unique IPv4 address.0/15 131. Datagram Length: 1424.76 131. rd Coming to the 3 field of given Routing table Error! Not a valid link. So.0 Not matched th Coming to the 4 field of given Routing table ⇒ 131.0001 0111.0. Datagram Length: 1424.0.19. Offset: 370 (B) MF bit: 1.0 Matched st We are getting 1 and 4th entries are matched so among them we have to picked up the longest mask bit .22.0 (∵ given mask bits = 16) ⇒ 131.gateforum.76.com Answer: (1) Exp: Given address 131.16.0.0001 0111.151.23.0.0001 0000.0001 0110.151. Datagram Length: 1500.76 131.0 (∵ given mask bits = 15) ⇒ 131. 50 – bit in the sense (32 + 18). Datagram Length: 1444. 131. 27.76 131.0.0001 0111.16. Offset: 370 (D) MF bit: 0.CS-GATE-2014 PAPER-03| www.76 131. w3(Y). w1 (X) . r1 (z) . Ans: (A) Exp: Precedence graph for S1 &S2 are as follows S1 : S2 : T1 T2 T3 No cycle T3 T1 T2 cycle ∴Only S1 is conflict serializable. r3(X). r2(Z). w2(Z). r3(X). r1(Z). r2 (z) . w1(Z) Which one of the following statements about the schedules is TRUE? (A) Only S1 is conflict-serializable. r3(Y). (D) Neither S1 nor S2 is conflict-serializable. (B) Only S2 is conflict-serializable. r3 (X) . (C) Both S1 and S2 are conflict-serializable. w1(X). w1(X). w3(Y). T2. and T3 and the schedules S1 and S2 given below.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 14 .com Router 4404 bytes M 1500 bytes MTU DataLength 29. India’s No. w3 (Y) S1: r1(X). r2(Y). r2(Z). 1480 1480 1444 + + HeaderLength 20 20 MF 1 1 0 Consider the transactions T1. w2(Z). w2 (z) T3 : r3 (X) . r3(Y). T1 : r1 (X) .gateforum. w1 (z) T2 : r2 (X) . w1(Z) S2: r1(X).CS-GATE-2014 PAPER-03| Answer: (A) Exp: www. r1(Z). r2(Y). Answer: (7) Exp: Maximum Allocate Need Available 2 1 1 P1 -3 P2 -3 2 1 P3 -3 2 1 With the above given data. www. empName. So answer is 7 tape units. Consider the following set of processes with their arrival times and CPU burst times (in milliseconds): P4 Process P1 Arrival Time 0 Burst Time 12 P2 2 4 P3 3 6 8 5 The average waiting time (in milliseconds) of the processes is _________. India’s No. depAge) Consider the following relational algebra query Π empId ( employee ) −Π emp Id ( employee ( empId = eID ) ∧ ( emp Age ≤ depAge )dependent ) The above query evaluates to the set of empIds of employees whose age is greater than that of (A) some dependent. Now when set of empIds of all employees minus set of empIds obtained from part A is done. eId. ( employee empId.com Consider the relational schema given below. Q.32 An operating system uses shortest remaining time first scheduling algorithm for pre-emptive scheduling of processes. (B) all dependents. 31. where eId of the relation dependentis a foreign key referring to empId of the relation employee. with 1 available unit any of the 3 process can be satisfied in such a way. Assume that every employee has at least one associated dependent in the dependent relation. that No dead lock will be there.gateforum.CS-GATE-2014 PAPER-03| 30. (C) some of his/her dependents. empAge ) dependent (depId. A system contains three programs and each requires three tape units for its operation.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15 . then we get the set of empIds of employees whose age is greater than that of all of his/her dependents. depName. The minimum number of tape units which the system must have such that deadlocks never arise is _________. (D) all of his/her dependents Answer: (D) A Exp: ∏ ( employee ) − ∏ ( employee empId empId dependent ) ( empId = eID ) ∧ ( empAge ≤ depAge ) B Part A of the above given relational algebra query will give the set of empIds of those employees whose age is less than or equal to the age of some of his/her dependents. after allocating 2 units of tape to each process. Consider a paging hardware with a TLB. So the final basic block can be written as follows: India’s No.5 4 4 33. Assume that the entire page table and all the pages are in the physical memory.CS-GATE-2014 PAPER-03| www. a =b+c c=a+d d=b+c e=d−b a =e+b The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are (A) 6 and 6 (B) 8 and 10 (C) 9 and 12 (D) 4 and 4 Answer: (A) Exp: The given basic block can be rewritten as a =b+c a =b+c c=a+d c=b+c+d d=b+c ⇒ d = b + b + c + d = 2b + c + d e=d−b a =e+b e= b +b+c+d− b =b+c+d a = b + b + c + d = 2b + c + d From above simplification it is visible that e is same as c and final value of a is same as d. Consider the basic block given below. If the TLB hit ratio is 0.6 )( 10 + 2 × 80 ) Tave = 0.6 Tave = 0. the effective memory access time (in milliseconds) is _________.com Answer: (5. Answer: (122) Exp: Tave = H1 × ( TTLB + TM ) + (1 − H1 ) × ( TTLB + 2 × TM ) TTLB = time to search in TLB = 10ms TM=time to access physical memory = 30ms H1 = TLB hit ratio = 0.gateforum.6 × 90 ms + 0.6 × (10 + 80 ) + (1 − 0.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 16 .6.5) Exp: The Gantt chart for SRTF scheduling algorithm is as follows: P P 1 0 2 P 2 Average waiting time = P 3 6 1 2 P 4 1 1 7 2 7 15 + 0 + 3 + 4 22 = = 5.4 (170 ) ms Tave = 54 ms + 68ms =122 ms 34. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. com a =b+c c=a+d d = 2b + c + d e=c a=d The DAG generated for the above basic block in as + d.1. Which one of the following problems is undecidable? (A) Deciding if a given context-free grammar is ambiguous.CS-GATE-2014 PAPER-03| www. but for L3 only non-deterministic PDA possible. so they are DCFL’s. But there is no algorithm for ambiguity of CFG.1} *} = { ww | w ∈ {0.1} *} L1 = 0n1n | n ≥ 0 L2 L3 r r Here wr is the reverse of the string w. a c.gateforum.c} { } = { wcw | w ∈{ 0. so it is undecidable.6 ) 35. (B) Deciding if a given string is generated by a given context-free grammar. India’s No. There were algorithms to find the membership of CFG (using CYK algorithm) and finiteness of CFG (using CNF graph) and emptiness. Which of these languages are deterministic Contextfree languages? (A) None of the languages (B) Only L1 (C) Only L1 and L2 (D) All the three languages Answer: (C) Exp: For the languages L1 and L2 we can have deterministic push down automata.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 17 . (C) Deciding if the language generated by a given context-free grammar is empty. Answer: (A) Exp: 36. Consider the following languages over the alphabet Σ = { 0. e + a + c d b Maximum number of modes and edges in above DAG is ( 6. (D) Deciding if the language generated by a given context-free grammar is finite. So the language L3 is not a deterministic CFL. From 9 to z ⇒ There are only two such values-one is the simple one step on number line i.e. and in particular from 9 there is a shortcut to 15. In each step. j if you are at position i on the number line. T()z) = 1+min (Dist. T(9) = Dist. (C) solvable in constant time since any input instance is satisfiable. 39. T(9) = 1+min (T(y). ( ) India’s No. The decision problem 2CNFSAT is (A) NP-Complete. but not NP-complete. Given a shortcut i. 15.j with i < j. from 9 to y/Dist. y ) ∈ E iff there is a clause in ϕ that is equivalent to x → y (all the clauses are converted to equivalent implications and the graph built is called as implication graph) 3. (D) NP-hard. From 9 to 100 As given.e. Then the value of the product yz is_______. you either move right by a unit distance or you take a shortcut. (B) solvable in polynomial time by reduction to directed graph reachability. ⇒ Therefore. Let ϕ be CNF with clauses of length 2 and let P be the set of propositional variables(literals) in ϕ 2.E) with V= P ∪ {¬p|p ∈ P} and ( x. suppose further that there is at most 1 shortcut involving any number. Suppose T(k) denotes the smallest number of steps needed to move from k to 100. Observe that ϕ is unsatisfiable iff there is a p ∈ P such that there is both a path from p to to ¬p and from ¬p to p in G. Answer 38. Dist.com 37. T(z)). Build a graph G=(V. from y to 100. If the tightest upper bound on the time to compute the sum is O n a log b n + m c log d n . φ = ( x1 v x 2 ) ∧ x1v x 3 ∧ ( x 2 v x 4 ) is a Boolean formula and it is in 2CNFSAT. This condition can be tested by running the reachability algorithm several times. the value of a + 10b + 100c + 1000d is _______.gateforum. and the other is the shortcut associated with 9 i. 10. This we can prove by reducing 2 SAT to directed graph reachability problem which is known to be in P. Suppose you want to move from 0 to 100 on the number line. Consider the decision problem 2CNFSAT defined as follows: { φ | φ is a satisfiable propositional formula in CNF with at most two literal per clause} ( ) For example. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 18 . Answer: (B) Exp: 2 SAT is in P. Answer: (150) Exp: By definition. Let y and z be such that T(9) = 1 + min(T(y). Suppose we have a balanced binary search tree T holding n numbers. Suppose there are m such numbers in T. From z to 100) ⇒1=Dist. you may directly move to j. Procedure for reducing 2 SAT to reachability problem: 1. y and z are 10 and 15 (in any order) ⇒ Product yz = 150. A shortcut is simply a pre-specified pair of integers i.CS-GATE-2014 PAPER-03| www. Assuming simple uniform hashing. n1 is the smallest number greater than or equal to L and there is no predecessor n’1 of n1 such that n’1 is equal to n1. it takes ‘m’ time to add all elements between n1 and n2. 2. so second insertion can be done at same index as first index ] = 97 C1 97 = 100C1 100 [∵ Third insertion can be done at same index as first or second index ] B P(second insertion in such a way that first 3 slots are unfilled) C P(Third insertion in such a way that first 3 slots are unfilled) So Total prob. The function Dosomething () takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. what is the probability that the first 3 slots are unfilled after the first 3 insertions? (A) (97 × 97 × 97)/1003 (B) (99 × 98 × 97)/1003 (C) (97 × 96 × 95)/1003 (D) (97 × 96 × 95)/(3! × 1003) Answer: (A) Exp:A P(First insertion in such a way that first 3 slots are unfilled) = 97 C1 97 = 100C1 100 = 97 C1 97 = 100C1 100 [∵ chaining is used to resolve collision. b = 1.CS-GATE-2014 PAPER-03| www. India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 19 . Collisions are resolved using chaining. P ( A ) × P ( B ) × P ( C ) = 41.gateforum. n2 is the largest number less than or equal to H and there is no successor of n’2 of n2 such that is equal to n2. ( 97 × 97 × 97 ) 97 97 97 × × = 100 100 100 1003 Consider the pseudocode given below. Each node of the tree is of type treeNode. c = 1 and d =0 40. So time complexity is O (log n + m) So the given expression becomes O (no log’ n + m’ logo n) And a+ 10b+ 100c+1000d = 0 + 10*1 + 100*1 + 1000*1 = 10 + 100 = 110 Because a = 0. Consider a hash table with 100 slots. Since there are m elements between n1 and n2.com Answer: (110) Exp: It takes (log n ) time to determine numbers n1 and n2 in balanced binary search tree T such that 1. gateforum. int n) India’s No. if (tree ! = NULL) { If (tree -> leftMostchild = = NULL) else value = Dosomething (tree->leftMostchild). } When the pointer to the root of a tree is passed as the argument to DoSomething. sored in ascending order. ⇒ The function recursively counts.CS-GATE-2014 PAPER-03| www. int ProcessArray (int * listA. } return (value). there is no child at all). Int Dosomething (treeptr tree) { int value =0. Here.com typedef struct treeNode* treeptr. (D) number of leaf nodes in the tree. Struct treeNode { Treeptr leftMostchild. whenever a leaf node is encountered. int x. ⇒ Which means the node under consideration is a leaf node. Assume that the array listA contains n (> 0) elements. ⇒ The function returns the number of leaf nodes in the tree. }. rightSibiling. 42. (B) height of the tree. Answer: (D) Exp: The key to solving such questions is to understand or detect where/by what condition the value (or the counter) is getting incremented each time. value = value + Dosometing (tree->rightsibiling). that condition is if (tree→leftMostchild == Null) ⇒ Which means if there is no left most child of the tree (or the sub-tree or the current nodeas called in recursion) ⇒ Which means there is no child to that particular node (since if there is no left most child. Consider the C function given below. (C) number of nodes without a right sibling in the tree. the value returned by the function corresponds to the (A) number of internal nodes in the tree. and adds to value.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 20 . if (x < = listA [k]) j = k – 1. 2 ns. Let us now check for options A and D. So option A is wrong. D is also wrong. RF2) each of latency 2. the EX stage is split into two stages (EX1. To gain in terms of frequency. So option C is clearly eliminated. The execution times of this program on the old and the new design are P and Q nanoseconds.CS-GATE-2014 PAPER-03| www. instruction decode and register fetch (ID/RF). (D) It will return – 1 even when x is present in listA. else return -1. 2. RF1. Running iterations of the algorithm would indicate that the loop exits when the x is not present. Answer: (B) Exp: By the logic of the algorithm it is clear that it is an attempted implementation of Binary Search. }while (1 < = j).gateforum. Correct answer is B. All instructions other than the branch instruction have an average CPI of one in both the designs. EX2) each of latency 1 ns. It is a correct implementation of Binary Search. i = 0. 43. respectively. and register write back (WB) with stage latencies 1 ns.2/3 ns. One may make any array of choice. the correct index is indeed returned.com { Int 1. memory access (MEM). when x is present. namely. Also. j. j = n – 1. The value of P/Q is __________ India’s No. An instruction pipeline has five stages. 1 ns. The IF stage stalls after fetching a branch instruction until the next instruction pointer is computed. instruction fetch (IF). (B) It is an implementation of binary search (C) It will always find the maximum element in listA. respectively (ns stands for nanoseconds). A program has 20% branch instructions which execute in the EX stage and produce the next instruction pointer at the end of the EX stage in the old design and at the end of the EX2 stage in the new design. k. } Which one of the following statements about the function ProcessArray is CORRECT? (A) It will run into an infinite loop when x is not in listA.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 21 . If (listA [k] = = x) return (k) . do { k = (i + j) /2. and 0. Also. A good way to do this is to create small dummy examples (arrays) and implement the algorithm as it is. instruction execution (EX).75 ns. the designers have decided to split the ID/RF stage into three stages (ID. The new design has a total of eight pipeline stages.2 ns. If (listA [k] < = x) i = k+1. 2ns P New design 8 5 20% 1 ns Q P = 80% (1clock ) + 20% ( 1 completion + 2 stall clock ) ×T c−p P = (.54 Q 2 ns 44.2 ns = 3.08 ns Q = 80% (1clock ) + 20% ( 1 completion + 5 stall clock ) × T c− p P = (.6 ) × 2.8 + .68) 60 memory 100 instruction 40 memory Exp: Total instruction = + operand read + fetch operation operand write op operation = 200 instructions ( operations ) Time taken for fetching 100 instructions (equivalent to read) = 90 *1ns + 10 *5ns = 140 ns Memory operand Read operations = 90% ( 60 ) *1ns + 10% ( 60 ) × 5ns = 54 ns + 30 ns = 84 ms Memory operands write operation time = 90% ( 40 ) * 2 ns + 10% ( 40 ) *10 ns = 72 ns + 40 ns = 112 ns Total time taken for executing 200 instructions = 140 + 84 + 112 = 336 ns ∴ Average memory access time = 336 ns = 1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 22 . 60 memory operand read operations and 40 memory operand write operations.8 + .54 ) Exp: No. 2 nanoseconds for a write operation with a hit in cache and 10 nanoseconds for a write operation with a miss in cache. of stages Stall cycle Stall frequency Clock period Avg. The cache hit-ratio is 0. Answer: (1. The average memory access time (in nanoseconds) in executing the sequence of instructions is __________. 5 nanoseconds for a read operation with a miss in cache.CS-GATE-2014 PAPER-03| www.12 ) ×1ns = 2 ns So the value of P 3.9.68 ns 200 India’s No.gateforum. access time Old design 5 2 20% 2.com Answer: ( 1. The memory access time is 1 nanosecond for a read operation with a hit in cache.08ns = = 1. Execution of a sequence of instructions involves 100 instruction fetch operations. FFinputs Q2 Q1 Q0 J2 K2 N.5625 1 y0 y1 y2 y3 y4 India’s No. b =1 let n = 4 b−a 1− 0 ⇒ h= = = 0. 110. 0 0 1 0 0 0 0 1 1 0 0 0 0 2 2 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 b With respect to the numerical evaluation of the definite integral. (A) I only Answer: ( C ) (B) II only (C) Both I and II (D) Neither I nor II b Exp: ∫x 2 dx a let a = 0. 110. 010.com 45. J C > K Q2 Q1 J C > K Q2 J C > K Q1 Q0 Q0 The above synchronous sequential circuit built using JK flip-flops is initialized with Q 2Q1Q0 = 000.625 0.25 0. 001 Answer: (C) Exp: P.gateforum.75 1 y = x2 0 0.S. 101 (C) 100. 011 (B) 111.CS-GATE-2014 PAPER-03| www. J1 K1 J0 Q 2 + Q1+ Q0 + K0 (Q ) (Q ) (Q ) (Q ) (Q ) (Q ) 1 0 1 1 46. which of the following statements is/are TRUE? (I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.5 0. 011. (II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral. where a and b a are given.25 0.S. 111 (D) 100.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 23 .25 n 4 x 0 0. The state sequence for this circuit for the next 3 clock cycles is (A) 001. K = ∫ x 2dx. 25 1 ( 0 + 1) + 2 ( 0.25 + 0.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 24 . If P (.) denotes the probability of the event.34375 2 II. www.gateforum.25 ( 0 + 1) + 2 ( 0.P (A)] =? Let P ( A ) = X Let f ( x ) = x (1 − x ) = x − x 2 India’s No. the maximum value of P(A)P(B) is ______ Answer: (0.com 0 1 3 The value of the integral given below is ∫ π 0 (A) −2π x 2 cos xdx (B) π (C) −π (D) 2π Answer: ( A) π Exp: ∫x 2 cos x dx = x 2 ( sin x ) − 2x ( − cos x ) + 2 ( − sin x ) 0 48.25) Exp: Given A ∪ B =S ⇒ P ( A ∪ B ) = P (S) = 1 ⇒ P ( A ) + P ( B) = 1 (∵ A & B are mutually exclusive) ⇒ P ( B ) =1 − P(A) Maximum value of P ( A ) P ( B ) = ? Maximum value of P (A) [1. By Trapezoidal rule 1 ∫x 2 0 = h dx = ( y 0 + y 4 ) + 2 ( y1 + y 2 + y3 ) 2 0.5625 ) = 3 3 1 x3 Exact value ∫ x dx = 3 0 1 = 2 47. By Simpson’s 1 ∫ x dx 2 = 0 = 1 rule 3 h ( y0 + y 4 ) + 2 ( y 2 ) + 4 ( y1 + y3 ) 3 0. π 0 = ( π2 sin π + 2π cos π − 2sin π ) − ( 0 + 0 + 0 ) = − 2π Let S be a sample space and two mutually exclusive events A and B be such that A ∪ B = S.0625 + 0.5625 ) = 0.CS-GATE-2014 PAPER-03| I.25 ) + 4 ( 0.0625 + 0. Which one of the following is CORRECT? (A) P.f(i) = i. = = 0.f ( 3) = 2..com 1 2 1 f "( x ) = − 2.. There are two elements x.. The maximum number of elements in such a group is _________________.. It is known that x * x = y*y = x*y*x*y = y*x*y*x = e where e is the identity element. f ( 2013) = 2012 and f ( 2014 ) = 2014 Clearly f ( f ( i ) ) = i for 0 ≤ i ≤ 2014 Here f ( i ) ≠ i for every i and f ( i ) = i for some i Also f is onto Hence.2014} → { 0.f ( 2 ) = 3. f " < 0 2 ∴ f ( x ) has max imum 1 and maximum value 2 1 1 1 1 1 1 = f = 1 − = .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 25 .25 2 2 2 2 2 4 At x = 49.. f(i) = i.. For each such function it must be the case that for every i.*) such that every element in the group can be written as a product of some number of x’s and y’s in some order. Consider the following statements.1. Q and R are true (B) Only Q and R are true (C) Only P and Q are true (D) Only R is true Answer: (B) Exp: Let us consider a function (counter example) as f ( 0 ) = 1.f ( 2012 ) = 2013.f (1) = 0. for 0 ≤ i ≤ 2014 . Consider the set of all functions f : {0...y in a group (G.CS-GATE-2014 PAPER-03| for f ( x ) max imum ⇒ f ' ( x ) = 0 ⇒ 1 − 2x = 0 ⇒ x = www. Each such function must be onto. For each such function it must be the case that for some i.gateforum. only Q and R are true 50..2014} such that f ( f ( i ) ) = i.. Q. P..1. Answer: (4) Exp: x×x = e ⇒ x is its own inverse India’s No. R... If G is a forest with n vertices and k connected components..CS-GATE-2014 PAPER-03| y× y = e www.. For all planar graphs on n vertices with δ ≥ 3... + n k = n (number of vertices in G) Hence.. n 2 .....1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 26 . the number of faces is less than n +2 2 (C) There is a planar embedding in which the number of faces is less than (D) There is a planar embedding in which the number of faces is at most n +2 2 n δ +1 Answer: (A) India’s No. how many edges does G have? (A) [ n / k ] Answer: Exp: (B) [ n / k ] (C) n − k (D) n − k + 1 (C) Let n1 ... n 2 − 1.. number of edges in G = number of edges in K connected components = ( n1 − 1) + ( n 2 − 1) + . Let δ denote the minimum degree of a vertex in a graph..gateforum..*) to be group any element should have only one inverse element (unique) This process x × y = y × x (is one element) So the elements of such group are 4 which are {x..com ⇒ y is its own inverse ( x × y ) × ( x × y ) = e ⇒ ( x × y ) is its own inverse ( y × x ) × ( y × x ) = e ⇒ ( y × x ) is its own inverse also x × x × e = e × e can be rewritten as follows x × y × y × x = e × y × y × e = e [∵ y × y = e ] ( x × y ) × ( y × x ) = e shows that ( x × y ) and ( y × x ) Are each other’s inverse and we already know that ( x × y ) and ( y × x ) are inverse of its own. As per ( G....n k be the number of vertices respectively in K connected components of a forest G.e. x × y} 51. y. n k − 1 be the number of edges respectively in K connected components and n1 + n 2 + .. which one of the following is TRUE? (A) In any planar embedding. then n1 − 1. the number of faces is at least n +2 2 (B) In any planar embedding.. + ( n k − 1) = n − k 52. rating ) SalesRepId is a foreign key referring to empId of the employee relation. “not all rainy days are cold” is (A) ∀d ( Rainy ( d ) ∧ ∼ Cold ( d ) ) (B) ∀d ( ∼ Rainy ( d ) → Cold ( d ) ) (C) ∃d ( ∼ Rainy ( d ) → Cold ( d ) ) (D) ∃d ( Rainy ( d ) ∧ ∼ Cold ( d ) ) Answer: (D) Exp: Given statement is ~ ∀d r ( d ) → c ( d ) ≡ ~ ∀d ~ r ( d ) ∨ c ( d ) ≡ ∃d r ( d ) ∧ ~ c ( d ) (Sin ce p → q ≡∼ p ∨ q and let r(d) be rainy day.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 27 .. What does the following query return? SELECT empName FROM employee E WHERE NOT EXISTS (SELECT custId FROM customer C WHERE C.com We know that v + r = e + 2 ⇒ e = n + r − 2 . (1) Where V = n ( number of vertices ) . empDept Customer ) ( custId. Assume that each employee makes a sale to at least one customer. sales Re pId. empName.CS-GATE-2014 PAPER-03| Exp: www. rating < > ‘GOOD’) India’s No.r = number of faces and e = number of edges Given. salesRepId = E. n +2 2 The CORECT formula for the sentence. c(d) be cold day) 54.. δ ≥ 3 then 3n ≤ 2e ⇒e≥ 3n 2 ⇒n+r−2≥ ⇒r≥ 3n ( u sin g (1) ) 2 3n n −n +2⇒ r ≥ +2 2 2 ∴Νumber of faces is atleast 53.custName. empId AND C.gateforum. Consider the following relational schema: ( Employee empId. Q ) = ( (1 ⊕ P ) ⊕ ( P ⊕ Q ) ) ⊕ ( ( P ⊕ Q ) ⊕ ( Q ⊕ 0 ) ) ( ) ( = P ⊕ ( PQ + PQ ) ⊕ ( PQ + PQ ) ⊕ Q ) = P ( PQ + P Q ) + P ( PQ + PQ ) ⊕ ( PQ + PQ ) Q + ( PQ + PQ ) Q = ( PQ + PQ ) ⊕ ( PQ + PQ ) =Q⊕P = PQ + PQ = P ⊕ Q India’s No. Such an employee should not be selected in the output of outer query. F ( P.Q ) = ( (1 ⊕ P ) ⊕ ( P ⊕ Q ) ) ⊕ ( ( P ⊕ Q ) ⊕ ( Q ⊕ 0 ) ) The equivalent expression for F is (A) P + Q (B) P + Q (C) P ⊕ Q (D) P ⊕ Q Answer: (D) Exp: F ( P. if rating of customer is NOT good.com (A) Names of all the employees with at least one of their customers having a ‘GOOD’ rating. only if inner query for that tuple will return no tuple (usage of NOT EXISTS). Let ⊕ denote the Exclusive OR (XOR) operation. So the query will return the names of all those employees whose all customers have GOOD rating. Answer: (D) Exp: The outer query will return the value (names of employees) for a tuple in relation E. (B) Names of all the employees with at most one of their customers having a ‘GOOD’ rating. (C) Names of all the employees with none of their customers having a ‘GOOD’ rating. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q. 55. (D) Names of all the employees with all their customers having a ‘GOOD’ rating.CS-GATE-2014 PAPER-03| www.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28 .gateforum. The inner query will run for every tuple of outer query. It selects cust-id for an employee e. CS-Paper Code-B GATE 2011 www. 1 – 25 Carry One Mark Each 1.(D) Exp: . 1 . (P + Q + R ) . No. No part of this document may be reproduced or utilized in any form without the written permission. (P + Q + R ) ( ) ( = P QR + P QR + P QR = P Q R + R + P QR = P Q + P QR =P Q + QR ) = P ( Q + R) = P + Q R 2. Discuss GATE 2011 question paper at www. (P + Q + R ) . P + Q + R . In relation to this.com Q. The simplified SOP (Sum of Product) P + Q + R .(B) Exp: QR 00 P 0 01 11 10 1 1 1 ( )( f = P+R P+Q ) = P + QR 1 Alternate method (P + Q + R ) .2n ≥ 258 ⇒ n = 9 4.(A) Exp: .com.gateforum. P + Q + R is ( )( (A) (PQ + R ) )( ) ( (B) P + QR ) form ( (C) PQ + R of the ) Boolean expression (D) (PQ + R ) Answer: .All options except option ‘D’ gives EX-NOR gates 3. which of the followings is TRUE? © All rights reserved by Gateforum Educational Services Pvt.gatementor. Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate? (A) (B) (C) (D) Answer: . (P + Q + R ) = (P + Q + R ) . Ltd. The minimum number of D flip-flops needed to design a mod-258 counter is (A) 9 (B) 8 (C) 512 (D) 258 Answer: . A thread is usually defined as a ‘light weight process’ because an operating system (OS) maintains smaller data structures for a thread than for a process. Ltd. Discuss GATE 2011 question paper at www.CS-Paper Code-B GATE 2011 www. the OS maintains only CPU register state (B) The OS does not maintain a separate stack for each thread (C) On per-thread basis. No part of this document may be reproduced or utilized in any form without the written permission. If the difference between the expectation of the square of random variable E X2 and the square of the expectation of the random variable E X2 is ( ) ( ) denoted by R then (A) R = 0 (B) R<0 (C) R ≥ 0 (D) R>0 Answer: . 2 . The lexical analysis for a modern computer language such as Java needs the power of which one of the following machine models in a necessary and sufficient sense? (A) Finite state automata (B) Deterministic pushdown automata (C) Non-Deterministic pushdown automata © All rights reserved by Gateforum Educational Services Pvt.com.(B) Exp: - Q3 K4 ∴ Both K4 and Q3 are planar 6.(A) 5. the OS does not maintain virtual memory state (D) On per thread basis.gateforum.com (A) On per-thread basis. K4 and Q3 are graphs with the following structures K4 Q3 Which one of the following statements is TRUE in relation to these graphs? (A) K4 is planar while Q3 is not (B) Both K4 and Q3 are planar (C) Q3 is planar while K4 is not (D) Neither K4 not Q3 is planar Answer: .(C) 7.gatementor. the OS maintains only scheduling and accounting information Answer: . 20(R2). What does the following fragment of C-program print? char c = "GATE2011". Let the page fault service time be 10ms in a computer with average memory access time being 20ns.com. No part of this document may be reproduced or utilized in any form without the written permission.gateforum.(B) Exp: .Here 20 will act as base and content of R2 will be index 10. which during execution reads a 32-bit word from memory and stores it in a 32-bit register R1. 3 .P = page fault rate EA = p × page fault service time + (1 − p ) × Memory access time = 9. Ltd.9 ns Consider a hypothetical processor with an instruction of type LW R1.(D) Exp: .(C) © All rights reserved by Gateforum Educational Services Pvt.gatementor. char *p =c. 1 1 × 10 × 106 + 1 − 6 106 10 × 20 ≅ 29. The effective address of the memory location is obtained by the addition of constant 20 and the contents of register R2.(A) Exp: . If one page fault is generated for every 106 memory accesses.com (D) Turing machine Answer: . Discuss GATE 2011 question paper at www. p+p 3 − p 1) . what is the effective access time for the memory? (A) 21ns (B) 30ns (C) 23ns (D) 35ns Answer: . printf ( "%s".CS-Paper Code-B GATE 2011 www.Lexical Analysis is implemented by finite automata 8. (A) GATE2011 (B) E2011 (C) 2011 (D) 011 Answer: . Which of the following best reflects the addressing mode implemented by this instruction for the operand in memory? (A) Immediate Addressing (B) Register Addressing (C) Register Indirect Scaled Addressing (D) Base Indexed Addressing Answer: . Discuss GATE 2011 question paper at www. GATE 2011 www.com A max-heap is a heap where the value of each parent is greater than or equal to the value of its children.gatementor. Answer: . Let P be a regular language and Q be a context free language such that Q ⊆ P..Ln−1 ) .(B) Exp: Heap is a complete binary tree 12. Ltd. Let Li denote the length of the longest monotonically increasing sequence starting at index i in the array Initialize Ln-1 =1 For all i such that 0 ≤ i ≤ n − 2 Li = { 1 + L i + 1 if A [i] < A [i + 1] 1 Otherwise Finally the length of the longest monotonically increasing Max (L 0 .(A) 13. Which of the following statements is TRUE? sequence is (A) The algorithm uses dynamic programming paradigm (B) The algorithm has a linear complexity and uses branch and bound paradigm (C) The algorithm has a non-linear polynomial complexity and uses branch and bound paradigm (D) The algorithm uses divide and conquer paradigm. Then which of the following is ALWAYS regular? { (A) P ∩ Q } (B) P − Q (C) ∑ * − P (D) ∑ * − Q © All rights reserved by Gateforum Educational Services Pvt. let P be the language represented by the regular expression p*q* and Q be pnqn | n ∈ N ). Which of the following is a max-heap? 10 (A) 10 (B) 8 8 6 4 5 2 4 6 5 1 2 1 10 5 (C) (D) 5 6 8 4 2 8 2 1 1 4 6 10 Answer: .com. 4 .CS-Paper Code-B 11.gateforum.L1 .. An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array A 0 : n − 1 is given below. (For example.. No part of this document may be reproduced or utilized in any form without the written permission.. keywords of a language are recognized during (A) parsing of the program (B) the code generation (C) the lexical analysis of the program (D) dataflow analysis Answer: . checking email in a web browser is done through HTTP © All rights reserved by Gateforum Educational Services Pvt.Σ* − P is the complement of P so it is always regular.Sample space = {HH.(C) Exp: . 5 .(C) Exp: . TH} Required probability = 1 3 17.(C) Exp: .(A) Exp: .com Answer: .com.gateforum. No part of this document may be reproduced or utilized in any form without the written permission. Discuss GATE 2011 question paper at www. If two fair coins are flipped and at least one of the outcomes is known to be a head.(A) Exp: .gatementor. what is the probability that both outcomes are heads? (A) 1/3 (B) 1/4 (C) 1/2 (D) 2/3 Answer: . Consider different activities related to email. In a compiler.Since it is a layer 4 firewall it cannot block application layer protocol like HTTP. m1: Send an email from a mail client to a mail server m2: Download an email from mailbox server to a mail client m3: Checking email in a web browser Which is the application level protocol used in each activity? (A) m1:HTTP m2:SMTP m3:POP (B) m1:SMTP m2:FTP m3:HTTP (C) m1: SMTP m2: POP m3: HTTP (D) m1: POP m2: SMTP m3:IMAP Answer: .Any identifier is also a token so it is recognized in lexical Analysis 15. A layer-4 firewall (a device that can look at all protocol headers up to the transport layer) CANNOT (A) block entire HTTP traffic during 9:00PM and 5:00AM (B) block all ICMP traffic (C) stop incoming traffic from a specific IP address but allow outgoing traffic to the same IP address (D) block TCP traffic from a specific user on a multi-user system during 9:00PM and 5:00AM Answer: . since regular languages are closed under complementation 14.CS-Paper Code-B GATE 2011 www.Sending an email will be done through user agent and message transfer agent by SMTP. downloading an email from mail box is done through POP. 16.HT. Ltd. 00.000 Maintenance time 5 years 5 years Cost of maintenance per year Rs. Which of the following is TRUE? (A) t1 > t2 (B) t1 = t2 (C) t1 < t2 (D) Nothing can be said about the relation between t1 and t2 Answer: .gatementor. The number of lines of code (LOC) developed using L2 is estimated to be twice the LOC developed with L1.000 Rs. A company needs to develop digital signal processing software for one of its newest inventions.8 for the software development on embedded systems.(C) Exp: . Let the time taken to switch between user and kernel modes of execution be t1 while the time taken to switch between two processes be t2. Parameter Language L1 Language L2 Man years needed for development LOC / 10000 LOC / 10000 Development Cost per year Rs.LOC L1 = x L 2 = 2x Total cost of project x 2x × 1000000 + 5 × 100000 = × 750000 + 50000 × 5 10000 10000 100x + 500000 = 150x + 250000 ⇒ 50x = 500000 − 250000 250000 ∴ x= ⇒ x = 5000 50 19. Various parameters for the company are given in the table below.000 Rs. Ltd. GATE 2011 www. 1.Process switching also involves mode changing.(B) Exp: .com A company needs to develop a strategy for software product development for which it has a choice of two programming languages L1 and L2. The multiplicative factor for this model is given as 2. What is the estimated effort in personmonths? © All rights reserved by Gateforum Educational Services Pvt. The company needs to determine the effort in person-months needed to develop this software using the basic COCOMO model. while the exponentiation factor is given as 1. 6 . 50. The software is expected to have 40000 lines of code.00.com. 10. Discuss GATE 2011 question paper at www.50. No part of this document may be reproduced or utilized in any form without the written permission.000 Total cost of the project includes cost of development and maintenance.20. 20. 7. What is the LOC for L1 for which the cost of the project using L1 is equal to the cost of the project using L2? (A) 4000 (B) 5000 (C) 4333 (D) 4667 Answer: . the product will have to be maintained for five years.CS-Paper Code-B 18.gateforum. CS-Paper Code-B (A) 234.com.80 www.com (D) 122. Hence answer is (B) 22. Discuss GATE 2011 question paper at www.20 = 2.8 × ( 40 ) 1.gateforum.(B) Exp: .40 = α. 7 . (kDSI) B KDSI = Kilo LOC = 2. A computer handles several interrupt sources of which the following are relevant for this question.(D) 23.50 Answer: . Which of the following pairs have DIFFERENT expressive power? (A) Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA) (B) Deterministic push down automata (DPDA) and Non-deterministic push down automata (NPDA) (C) Deterministic single-tape Turing machine and Non-deterministic single tape Turing machine (D) Single-tape Turing machine and multi-tape Turing machine Answer: .25 (B) 932. Which one of the following actions is NOT supported by pure HTML (without any server or client side scripting) pages? (A) Embed web objects from different sites into the same page (B) Refresh the page automatically after a specified interval (C) Automatically redirect to another page upon download (D) Display the client time as part of the page Answer: .(D) 24.8 × 83. HTML (Hyper Text Markup Language) has language elements which permit certain actions other than describing the structure of the web document.6511 = 234. Ltd.gatementor.(A) Exp: .NPDA is more powerful than DPDA. No part of this document may be reproduced or utilized in any form without the written permission.Effort person per month GATE 2011 (C) 287.22 person per month 21. Which of the following is NOT desired in a good Software Requirement Specifications (SRS) document? (A) Functional Requirements (B) Non Functional Requirements (C) Goals of Implementation (D) Algorithms for Software Implementation Answer: . Interrupt from CPU temperature sensor Interrupt from Mouse © All rights reserved by Gateforum Educational Services Pvt. f3. This attributes stores the primary account number 4.(D) 25.gatementor.(A) Let n = 1024 (B) f3. A student can have multiple accounts or joint accounts. Name: Name of the Student 5. 1.(A) Exp: . f3. unique at the national level for each citizen 3.f2. 26 – 51 Carry Two Marks Each 26. No. f2 (n) = n3 / 2.com (B) Interrupt from Mouse (D) Interrupt from CPU temp sensor Consider a relational table with a single record for each registered student with the following attributes. f2. Ltd. Registration_Number: Unique registration number for each registered student 2.f1 f1 (n) = 21024 f2 (n) = 215 f3 (n) = 10 × 210 f4 (n) = 102410 = 2100 ∴ f3 .f4 (C) f2. Q. f4 . UID: Unique Identity number.f4 (D) f2. f4. f1. No part of this document may be reproduced or utilized in any form without the written permission. BankAccount_Number: Unique account number at the bank. f4. 8 . f2 . Which of the given options provides the increasing order of asymptotic complexityoffunctionsf1. Discuss GATE 2011 question paper at www. Hostel_Room: Room number of the hostel Which of the following options is INCORRECT? (A) BankAccount_Number is a candidate key (B) Registration_Number can be a primary key (C) UID is a candidate key if all students are from the same country (D) If S is a superkey such that S ∩ UID is NULL then S ∪ UID is also a superkey Answer: . f3 (n) = nlog2 n.CS-Paper Code-B Interrupt from Keyboard Interrupt from Hard Disk (A) Interrupt from Hard Disk (C) Interrupt from Keyboard Answer: . GATE 2011 www.f1 Answer: . f2. f1.f3andf4? f1 (n) = 2n. f1 is the rquired increa sin g order © All rights reserved by Gateforum Educational Services Pvt.gateforum.com.In case two students hold joint account then BankAccount_Num will not uniquely determine other attributes. f4 (n) = nlog2 n (A) f3. but not on Q2 (D) Hashing will outperform ordered indexing on Q2.7. When multiplied as ( (M1 × M2 ) × M3 ) × M4 .. 4. GATE 2011 www.2.3 (B) 3.An c1 ≤ AP ≤c2 (r ) ) where c1 and c2 are constants The database can be configured to do ordered indexing on Ap or hashing on Ap. but not on Q1.3 (C) 7. then the minimum number of scalar multiplications needed is (A) 248000 Answer: . Consider the matrix as given below. M2.An σAP =c (r ) where c is a const Q2: πA1.4.. q=100.com Four matrices M1.3 Answer: . A2. q × r.Given matrix is upper triangular matrix and its diagonal elements are its eigen values = 1.gateforum. For example When multiplied as ( (M1 × M2 ) × (M3 × M4 ) ) the total number of scalar multiplications is pqr+rst+prt. the total number of scalar multiplications is pqr+prs+pst. Consider a relational table r with sufficient number of records. 9 . M3 and M4 are dimensions p × q. An and let 1 ≤ p ≤ n. s=5 and t=80.. having attributes A1. Two queries Q1 and Q2 are given below.….. No part of this document may be reproduced or utilized in any form without the written permission.(C) (B) 44000 (C) 19000 (D) 25000 Exp: .3. r=20. Ltd.(A) Exp: . ( (σ ) Q1 : πA1.Multiply as (M1 × (M2 × M3 ) ) × M4 The total number of scalar multiplication is = qrs + pqs + pst = 10000 + 5000 + 4000 = 19000 28. Discuss GATE 2011 question paper at www.2 (D) 1. r × s and s × t respectively can be multiplied in several ways with different number of total scalar multiplications. 3 © All rights reserved by Gateforum Educational Services Pvt.com. ( ) If p=10. Answer: .(C) 29.CS-Paper Code-B 27. Which of the following statements is TRUE? (A) Ordered indexing will always outperform hashing for both queries (B) Hashing will always outperform ordered indexing for both queries (C) Hashing will outperform ordered indexing on Q1. 1 2 3 0 4 7 0 0 3 Which one of the following provides the CORRECT values of eigenvalues of the matrix? (A) 1.gatementor. Discuss GATE 2011 question paper at www.1 (D) 3. The pipeline registers are required between each stage and at the end of the last stage.gatementor. 10 .5 (C) 1.(B) Exp: . The processor generates 32-bit addresses. each of size 32-bytes. Definition of a language L with alphabet {a} is given as following = 30 = 2. GATE 2011 www.com. Ltd.0 Answer: .(D) (B) 6144bits (C) 6656bits (D) 5376bits © All rights reserved by Gateforum Educational Services Pvt.5 12 { } L = ank | k > 0.gateforum. What is the total size of memory needed at the cache controller to store metadata (tags) for the cache? (A) 4864 bits Answer: . Delays for the stages and for the pipeline registers are as given in the figure. 1 Valid bit 1 Modified bit As many bits as the minimum needed to identify the memory block mapped in the cache. S3 and S4) each with combinational circuit only.CS-Paper Code-B 30. Pipeline Reg Delay 1ns State S1 Delay 5ns State S2 Delay 6ns Pipeline Reg Delay 1ns State S3 Delay 11ns Pipeline Reg Delay 1ns State S4 Delay 8ns Pipeline Reg Delay 1ns What is the approximate speed up of the pipeline in steady state under ideal conditions when compared to the corresponding non-pipeline implementation? (A) 4.0 (B) 2. S2. The cache controller maintains the tag information for each cache block comprising of the following. No part of this document may be reproduced or utilized in any form without the written permission. and n is a positive integer constant What is the minimum number of states needed in a DFA to recognize L? (A) k+1 (C) 2n+1 (B) n+1 (D) 2k+1 Answer: .Let n = 3 and k=1 q0 (n + 1) 32.(B) Exp: - (5 + 6 + 11 + 8 ) (11 + 1) 31. a q1 a q2 a q3 a states An 8KB direct mapped write-back cache is organized as multiple blocks.com Consider an instruction pipeline with four stages (S1. 5 sec 34.gatementor. No part of this document may be reproduced or utilized in any form without the written permission.25s (D) 1.(B) Exp: . The seek time of the disk to a random location is given as 10ms.b q a r a.6000 rotations ________ 60 sec 1 ∴ (C) 1.gateforum. A deterministic finite automation (DFA ) D with alphabet ∑ = {a. how long does it take to load all libraries? (The time to transfer data from the disk block once the head has been positioned at the start of the block may be neglected) (A) 0. 11 .50s Answer: . Discuss GATE 2011 question paper at www. An application loads 100 libraries at startup. Loading each library requires exactly one disk access.b r (B) b a p s a.00s rotation ________ 10 ms Rotational latency = 5ms Time for one disk access = 15 ms Time to load all libraries = 15 × 100 = 1500 ms = 1. Rotational speed of disk is 6000rpm. Ltd. If all 100 libraries are loaded from random locations on the disk.50s (B) 1.com.CS-Paper Code-B Exp: - 19 + 2 Byte offset = 25 block offset = www.b a a.b} is given below p b q a.com 5 8 TAG GATE 2011 213 = 28 25 Required answer = 256 × (19 + 2 ) = 5376 bits 33.b s a.b a.b a b r a.b © All rights reserved by Gateforum Educational Services Pvt.b s t Which of the following finite state machines is a valid minimal DFA which accepts the same language as D? (A) p b a q b a. 0 0. float c.T6 (D) T2.0 1. 12 . The following is comment written for a C function /* This function computes the roots of a quadratic equation a.com.0 0.(C) © All rights reserved by Gateforum Educational Services Pvt.b p a.0 -1.0 0 T4 4.0 -1.x+c=0.T5.0 3.0 -2. He comes up with the following test cases.0 9.T2.0 7. The function stores two real roots in *root1 and *root2 and returns the status of validity of roots.gateforum.5 1.T3.0 0.0 0 T6 1.0 0. Otherwise 0 is stored in the roots.gatementor.0 4.0 2.0 1. float *root1.0 0. float *root2 ) . many of which are redundant.b Exp: . */ A software test engineer is assigned the job of doing black box testing.T4.T6 (B) T1.b b r b a q a s Answer: .T3.0 1. No part of this document may be reproduced or utilized in any form without the written permission.0 0.T4. (i) When coefficient a is zero irrespective of discriminant (ii) When discriminant is positive (iii) When discrimanant is zero (iv ) When discrimanant is negative Only in cases (ii) and (iii) .com b (C) (D) a.0 0. So the minimized DFA is option A 35.CS-Paper Code-B GATE 2011 www.0 -3. the stored roots are valid. Discuss GATE 2011 question paper at www.0 -12.0 -1 T2 0. Ltd.0 -1.x^2+b.5 0 T5 1.0 1.0 3. the function returns 0 when the roots are valid and -1 otherwise.T5 (C) T2.0 -1 Which one of the following options provide the set of non-redundant tests using equivalence class partitioning approach from input perspective for black box testing? (A) T1. int get_QuadRoots ( float a.T5 Answer: . It handles four different kinds of cases. The functin also ensures root1>=root2. Input set Test Case Expected Output set a b C Root1 Root2 Return Value T1 0. float b.0 -1 T3 1.(A) a.Options B and C will accept the string b Option – D will accept the string “bba” Both are invalid strings.b q p a.T4.T3. the output would be Borrower Bank_Manager Load_Amount Ramesh Sunderajan 10000.com Exp: . Ltd.(C) Exp: - S T Borrower Bank _ Manager Bank _ Manager Loan _ Amount Ramesh Sunderajan Sunderajan 10000. 13 .00 Mahesh Sunderajan 7000.00 Ramesh Sunderajan 7000.00 © All rights reserved by Gateforum Educational Services Pvt.gatementor.00 What is the output of the following SQL query? SELECT count(*) FROM( (SELECT Borrower. Discuss GATE 2011 question paper at www. No part of this document may be reproduced or utilized in any form without the written permission.T1 and T2 checking same condition a = 0 hence.00 Mahesh Sunderjan Sunderjan 7000. (A) 3 (B) 9 (C) 5 (D) 6 Answer: . T3. Borrower Bank_Manager Loan_ Amount Ramesh Sunderajan 10000.00 After executing the given query. Hence any one of it is redundant.00 Mahesh Sunderajan 7000. T5 : D>0 T6 : D<0 36. any one of T1 and T2 is redundant.00 Mahesh Sunderajan 10000. Loan_Amount FROM Loan_Records) AS T ).00 Suresh Ramgopal 5000.00 Suresh Ramgopal 5000.com.00 Suresh Ramgqpal Ramgopal 5000. Bank_Manager FROM Loan_Records) AS S NATURAL JOIN (SELECT Bank_Manager.CS-Paper Code-B GATE 2011 www. Database table by name Loan_Records is given below. T4: in both case discriminant (D)= b2 − 4ac = 0 .gateforum. ) ) ↓ 2 as ↓ is left associative Consider the languages L1. 14 . L2 and L3 as given below { } L2 = {0 1 | p.com Consider two binary operators ' ↑ ' and ' ↓ ' with the precedence of operator ↓ being lower than that of the operator ↑ . is left associative. No part of this document may be reproduced or utilized in any form without the written permission. Discuss GATE 2011 question paper at www. Which one of the following represents the parse tree for expression ( 7 ↓ 3 ↑ 4 ↑ 3 ↓ 2 ) ? (A) (B) 2 7 7 3 3 4 4 3 3 2 (C) (D) 7 2 2 3 3 3 4 4 7 3 Answer: . q.7 ↓ 3 ↑ 4 ↑ 3 ↓ 2 ⇒ 7 ↓ 3 ↑ ( 4 ↑ 3) ↓ 2 as ↑ is right associative ( ( ⇒7↓ 3↑ 4↑3 )) ↓ 2 ( ( ⇒ 7 ↓ 3 ↑ ( 4 ↑ 3) 38. Ltd.gateforum. Operator ↑ is right associative while operator ↓. GATE 2011 www. q ∈ N and p = q} and L3 = {0 1 0 | p.(B) Exp: .CS-Paper Code-B 37. q ∈ N p q p q r Which of the following statements is NOT TRUE? (A) Push Down Automata (PDA) can be used to recognize L1 and L2 (B) L1 is a regular language (C) All the three languages are context free (D) Turing machines can be used to recognize all the languages © All rights reserved by Gateforum Educational Services Pvt.r ∈ N and p = q = r} L1 = 0p1q | p.com.gatementor. Ltd.No. Initialize the address register Initialize the count to 500 LOOP: Load a byte from device Store in memory at address given by address register Increment the address register Decrement the count If count != 0 go to LOOP Assume that each statement in this program is equivalent to a machine instruction which takes one clock cycle to execute if it is a non-load/store instruction.4 (C) 5.1 (D) 6.7 Answer: . What is the approximate speedup when the DMA controller based design is used in place of the interrupt driven program based input-output? (A) 3. The designer of the system also has an alternate approach of using the DMA controller to implement the same transfer. and a predicate P ( x ) = ¬ ( x = 1) ∧ ∀y ( ∃z ( x = y * z ) ⇒ ( y = x ) ∨ ( y = 1) ) (A) P(x) being true means that x is a prime number © All rights reserved by Gateforum Educational Services Pvt. In how many ways can we populate the tree with the given set so that it becomes a binary search tree? (A) 0 (B) 1 (C) n! (D) 1 2n . y and z.(C) Exp: . which is a part of the interrupt service routine. Each DMA transfer cycle takes two clock cycles to transfer one byte of data from the device to the memory. Cn n+1 Answer: .gateforum.gatementor.com Answer: .4 (B) 4.L1: regular language L2: context free language L3: context sensitive language 39. 3502 = 3.(D) 41. No part of this document may be reproduced or utilized in any form without the written permission. of clock cycles required by using load-store approach = 2 + 500 × 7 = 3502 and that of by using DMA = 20 + 500 × 2 = 1020 Required speed up = 40. The load-store instructions take two clock cycles to execute. a program segment. is given to transfer 500 bytes from an I/O device to memory. The DMA controller requires 20 clock cycles for initialization and other overheads.com.(A) Exp: . 15 . On a non-pipelined sequential processor.CS-Paper Code-B GATE 2011 www.4 1020 We are given a set of n distinct elements and an unlabeled binary tree with n nodes. Discuss GATE 2011 question paper at www. Which one of the following options is CORRECT given three positive integers x. It may be noted that each time after the insertion.(D) Exp: .com.∫ π 2 0 e2ix = 2i 43. (A) 127 (B) 255 (C) 129 (D) 257 Answer: . 16 .(A) Exp: X Y 1 1 2 3 3 7 4 15 5 31 6 63 7 127 © All rights reserved by Gateforum Educational Services Pvt. values of MX and MY change. 2*MY+1 respectively. Y=l) is inserted in the table.gatementor. eix e −ix dx = π ∫0 2 e 2ix dx π 2 1 1 1 −2 −1 i −i eiπ − 1 = = × = = i cos π + i sin π − 1 = −1 + 0 − 1 = = 2i 2i 2i 2i i i −1 0 Consider a database table T containing two columns X and Y each of type integer. what will be the evaluation of the definite integral cos x + i sin x dx ? cos x − i sin x (A) 0 (B) 2 (C) –i (D) i Answer: .com (B) P(x) being true means that x is a number other than 1 (C) P(x) is always true irrespective of the value of x (D) P(x) being true means that x has exactly two factors other than 1 and x Answer: . Using MX and MY. new records are inserted in the table 128 times with X and Y values being MX+1.CS-Paper Code-B GATE 2011 www.gateforum. one record (X= 1. After the creation of the table. What will be the output of the following SQL query after the steps mentioned above are carried out? SELECT Y FROM T WHERE X=7. Let MX and MY denote the respective maximum values of X and Y among all records in the table at any point in time.(A) 42. i= Given π /2 ∫ 0 −1. No part of this document may be reproduced or utilized in any form without the written permission. Discuss GATE 2011 question paper at www. Ltd. 4) Required probability = 46. Which one of the following statements is INCORRECT? (A) Index position of mode of X in X is the same as the index position of mode of Y in Y.com Consider a finite sequence of random values X = x1 .33 ms (C) 6.3). (4. (3..33 ms (D) 7. where a and b are positive constants.. 4 4 1 = = 5 × 4 20 5 Consider the following table of arrival time and burst time for three processes P0. 17 . No part of this document may be reproduced or utilized in any form without the written permission.(D) 45. (B) Index position of median of X in X is the same as the index position of median of Y in Y.2). What is the average waiting time for the three processes? (A) 5.gateforum. Ltd.gatementor. Let µ y be the mean and σy be the standard deviation of this sequence. Discuss GATE 2011 question paper at www. x2 . What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card? (A) 1/5 (B) 4/25 (C) 1/4 (D) 2/5 Answer: . GATE 2011 www. P1 and P2.Let another finite sequence Y of equal length be derived from this as yi = a * xi + b.com. Scheduling is carried out only at arrival or completion of processes. A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly.0 ms (B) 4. (C) µ y = aµx + b (D) σy = aσx + b Answer: .xn .33 ms Answer: . Let µx be the mean and σx be the standard deviation of X .(A) © All rights reserved by Gateforum Educational Services Pvt. Process Arrival time Burst Time P0 0 ms 9 ms P1 1 ms 4ms P2 2 ms 9ms The pre-emptive shortest job first scheduling algorithm is used.(A) Exp: .1).CS-Paper Code-B 44.(2.. Two cards are then removed one at a time from the deck. (5. If no intermediate results can be stored in memory. R3 . c .gateforum.R2 . R2 ← M b Sub R1 .com.(D) Exp: . a .com P2 22 13 4 + 11 = 5 ms 3 Consider evaluating the following expression tree on a machine with load-store architecture in which memory can be accessed only through load and store instructions. d . No part of this document may be reproduced or utilized in any form without the written permission. e . R3 ← M d Add R2 .R2 : R3 ← R 3 − R2 Add R1. b.CS-Paper Code-B Exp: - P1 P0 0 P0 5 1 Average waiting time = 47.R3 .Load R1 . c. R2 ← M c Load R 3 . The variables a.gatementor. 18 . R1 ← R1 − R 2 Load R 2 . The binary operators used in this expression tree can be evaluated by the machine only when the operands are in registers. R1 ← M a Load R 2 . Ltd. GATE 2011 www. what is the minimum number of registers needed to evaluate this expression? + − a − b + e c (A) 2 (B) 9 (C) 5 d (D) 3 Answer: .b . Discuss GATE 2011 question paper at www. R1 ← R1 + R 3 Total 3 Registers are required minimum © All rights reserved by Gateforum Educational Services Pvt. The instructions produce result only in a register. R3 ← M e Sub R 3 . d and e are initially stored in memory. R 2 ← R 2 + R 3 Load R 3 . No part of this document may be reproduced or utilized in any form without the written permission.10 ) 4 + f ( 3. 19 .2 ) + 0 f ( 2. 2 ) Exp: - f ( 256.2 ) + 0 0 1 +1 = 2 f ( 4.2 ) + 1 f (128. unsigned int r ) { if (n > 0 ) return (n%r ) + foo (n / r. 2)? (A) 9 (B) 8 (C) 5 (D) 2 Answer: .com. } 48. r )). What is the return value of the function foo when it is called as foo (513. Ltd. else return 0.2 ) + 0 f (16. (A) 345 (B) 12 (C) 5 10) ? (D) 3 Answer: . Discuss GATE 2011 question paper at www.(D) f (513.2 ) 0 + 0 f ( 32.2 ) What is the return value of the function foo when it is called as foo (345.2 ) + 0 + 0 f ( 64.CS-Paper Code-B GATE 2011 www.10 ) © All rights reserved by Gateforum Educational Services Pvt.com Common Data Questions: 48 & 49 Consider the following recursive C function that takes two arguments unsigned int foo (unsigned int n.10 ) 3 + 5 + 4 + 3 = 12 f ( 0.2 ) + f (1.2 ) 1 49 + f ( 0.2 ) + f ( 8.gateforum.10 ) Exp: 5 + f ( 34.gatementor.(B) f ( 345. D P Q Clock Q D Clock Q D Clock 50. 1 and 0 respectively. Q Q R Q Q If all the flip-flops were reset to 0 at power on.com Common Data Questions: 50 & 51 Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. No part of this document may be reproduced or utilized in any form without the written permission. 20 .gateforum. Q and R have a value 0.CS-Paper Code-B GATE 2011 www.com. Ltd. what shall be the value of PQR after the clock edge? (A) 000 (B) 001 (C) 010 (D) 011 © All rights reserved by Gateforum Educational Services Pvt. what is the total number of distinct outputs (states) represented by PQR generated by the counter? (A) 3 (B) 4 (C) 5 (D) 6 Answer: .(B) Exp: CLOCK Inputs Outputs D1 = R D2 = (P + R ) D3 = Q R P Q R 1 0 1 0 0 1 0 2 0 1 1 0 1 1 3 1 0 0 1 0 0 4 0 0 0 0 0 0 So Total number of distinct outputs is 4 51. P. If at some instance prior to the occurrence of the clock edge.gatementor. Discuss GATE 2011 question paper at www. (B) 53. The length of the path from v5 to v6 in the MST of previous question with n = 10 is (A) 11 (B) 25 (C) 31 (D) 41 Answer: . A sample graph with n = 4 is shown below V3 4 V1 52. v j are connected if and only if 0 < i − j ≤ 2. v2 . Two nodes vi .CS-Paper Code-B GATE 2011 www.vn. 21 .52 to Q. Each edge (v .. if first state is 010 next State is 011 Linked Answer Questions: Q.(D) Exp: -From the Table Shown in the explanation of question 50.E) contains n ( n > 2 ) nodes named v1 . v ) i j is assigned a weight i + j.gatementor.com.. Ltd. 7 5 3 V4 6 V2 What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes? (A) ( 1 11n2 − 5n 12 ) (B) n2 − n + 1 (D) 2n + 1 (C) 6n − 11 Answer: .(C) Exp: 12 v7 v6 v5 10 8 v4 v3 6 4 v1 3 v2 12 + 8 + 4 + 3 + 6 + 10 = 31 © All rights reserved by Gateforum Educational Services Pvt..com Answer: .. Discuss GATE 2011 question paper at www. No part of this document may be reproduced or utilized in any form without the written permission.gateforum.55 Carry Two Marks Each Statement for Linked Answer Questions: 52 & 53 An undirected graph G(V. 6 ) N4 : ( 8. 8. 0. 2. Discuss GATE 2011 question paper at www. N3 N1 3 N2 2 N3 0 N4 2 N5 5 1+2 2+3 After the update in the previous question. 2.com. In between two rounds. 0. 2. what will be the cost to N1 in the distance vector of N3? (A) 3 (B) 9 (C) 10 (D) ∞ © All rights reserved by Gateforum Educational Services Pvt. 3. 6. as shown below N1 N5 3 4 N4 N2 6 2 N3 The net work uses a Distance Vector Routing protocol. the distance vectors at different nodes are as following N1 : ( 0. 4 ) N5 : ( 4. N2 will reflect this change immediately in its distance vector as cost.2. ∞ . 2. No part of this document may be reproduced or utilized in any form without the written permission. 7. 0. 0. 6) (C) (7. 2. 3 ) N3 : ( 7. 0. 2. where the distance to itself is 0. 4 ) N2 : (1. 5) (B) (3.1. any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors 54. 0 ) Each distance vector is the distance of the best known path at that instance to nodes. all nodes exchange their distance vectors with their respective neighbors. 0. all links are symmetric and the cost is identical in both directions. 5) (D) (7. The cost of link N2-N3 reduces to 2 in (both directions). 2. Ltd. 22 . Then all nodes update their distance vectors. 0. 6. 6) Answer: .gatementor. the link N1-N2 goes down. 7. In each round. Also. what will be the new distance vector at node.gateforum. N1 to N5. Once the routes have stabilized. After the NEXT ROUND of update. 2.7. N1 to N5. After the next round of updates.com Statement for Linked Answer Questions: 54 & 55 Consider a network with five nodes. 4. 6. 2. N3? (A) (3.(A) Exp: - 55.CS-Paper Code-B GATE 2011 www. (B) © All rights reserved by Gateforum Educational Services Pvt. 56 – 60 Carry One Mark Each 56.The tone of the sentence clearly indicates a word that is similar to understated is needed for the blank. 59. you cannot do so by being understated. 23 .com Answer: .CS-Paper Code-B GATE 2011 www.gatementor.logP = log Q = log (R ) = k 2 3 ∴ P = bk . I contemplated________Singapore for my vacation but decided against it.(C) Exp: . If you are trying to make a strong impression on your audience.(B) Exp: .(C) Exp: . Alternatively. No part of this document may be reproduced or utilized in any form without the written permission. Q2 = b4k = b3k bk = PR 57. (A) Hyperbolic (B) Restrained (C) Argumentative (D) Indifferent Answer: . Ltd. Choose the most appropriate word from the options given below to complete the following sentence.R = b3k Now. (A) To visit (B) having to visit (C) visiting (D)for a visit Answer: . Discuss GATE 2011 question paper at www.N3 has neighbors N2 and N4 N2 has made entry ∞ N4 has the distance of 8 to N1 N3 has the distance of 2 to N4 So 2 + 8 = 10 Q.Contemplate is a transitive verb and hence is followed by a gerund Hence the correct usage of contemplate is verb+ ing form. Choose the most appropriate word(s) from the options given below to complete the following sentence. 58.gateforum. the best choice is restrained which means controlled/reserved/timid.(B) 1 1 Exp:.com. Choose the word from the options given below that is most nearly opposite in meaning to the given word: Amalgamate (A) Merge (B) Split (C) Collect (D) Separate Answer: . No. Therefore. tentative or_____________. then which of the following options is TRUE? (A) P2 = Q3R 2 (B) Q2 = PR (C) Q2 = R 3P (D) R = P2Q2 Answer: . the word should be antonym of strong (fail to make strong impression). If Log (P) = (1/2)Log (Q) = (1/3) Log (R). Q = b2k . Amalgamate means combine or unite to form one organization or structure. Which microbe should the company target in its first attempt? (A) P (B) Q (C) R (D) S © All rights reserved by Gateforum Educational Services Pvt. 60.com Exp: .CS-Paper Code-B GATE 2011 www. No part of this document may be reproduced or utilized in any form without the written permission. Q.6 Potency 0. So the best synonym here is incomprehensible. Q. potency and growth attributed to a microbe shown in the figure below Toxicity 61.4 0. it is too general to be the best antonym in the given question while Merge is the synonym.gateforum.gatementor. that cannot be explained. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. or accounted for. understood.(A) Exp: . Collect is not related. Discuss GATE 2011 question paper at www. Ltd.com.8 1 (Probability that microbe will overcome human immunity system) A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. 61 – 65 Carry Two Marks Each 1000 P (50 mm ) 800 mass in kilograms) (milligrams of microbe required to destroy half of the body P. So the best option here is split. The danger to human beings varies proportionately with the toxicity. Separate on the other hand.2 0. 24 .Inexplicable means not explicable. 600 400 Q ( 40 mm ) S (20 mm ) R ( 30 mm ) 200 0 0. R and S are four types of dangerous microbes recently found in a human habitat. No. although a close synonym. Which of the following options is the closest in the meaning to the word below: Inexplicable (A) Incomprehensible (B) Indelible (C) Inextricable (D) Infallible Answer: . 100 8000 + 3 3 8500 17 ⇒ x > 5 3 Minimum possible = 6 64.(C) Exp: .4 0.CS-Paper Code-B GATE 2011 www.5 0.gateforum. Currently. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. (V+F). How much spirit is now left in the container? (A) 7. A container originally contains 10 litres of pure spirit. Option A gives the minimum cost. 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time.(D) Exp: .e. he has some pending orders (backlog) to be shipped.84 litres (C) 7 litres (D) 7. A transporter receives the same number of orders each day.58 litres (B) 7. then all the orders are cleared at the end of the 10th day. No part of this document may be reproduced or utilized in any form without the written permission.29 litres © All rights reserved by Gateforum Educational Services Pvt. 25 . From this container 1 litre of spirit is replaced with 1 litre of water. P Q R S Requirement 800 600 300 200 Potency 0. If he uses 7 trucks. Alternatively. where q is the quantity produced. if he uses only 3 trucks.8 The variable cost (V) of manufacturing a product varies according to the equation V= 4q. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day? (A) 4 (B) 5 (C) 6 (D) 7 Answer: .com. Ltd. Discuss GATE 2011 question paper at www.gatementor.e = 3 3 5days ⇒ 500x = ⇒ 500x = 5. Subsequently. 63.By observation of the table.Let each truck carry 100 units. we can say S 62. 2800 = 4n + e n = normal 3000 = 10n + e e = excess/pending ∴n = 100 8000 .com Answer: .Checking with all options in formula: (4q+100/q) i. How many units should be produced to minimize the total cost (V+F)? (A) 5 (B) 4 (C) 7 (D) 6 Answer: (A) Exp: . then at the end of the 4th day he can clear all the orders.4 0. CS-Paper Code-B GATE 2011 www. Based on the above passage which topic would not be included in a unit on bereavement? (A) how to write a letter of condolence (B) what emotional stages are passed through in the healing process (C) what the leading causes of death are (D) how to give support to a grieving friend Answer: .(C) Exp: . Rest all are important in dealing with grief. and yet all students at some point in their lives suffer from losses through death and parting. Discuss GATE 2011 question paper at www. No part of this document may be reproduced or utilized in any form without the written permission.gatementor.(D) 3 3 729 10 − 1 9 Exp:. irrespective of the causes of death. Therefore. © All rights reserved by Gateforum Educational Services Pvt. a school student rarely gets into details of causes—which is beyond the scope of the context. 729 × 1 = 7. 26 .The given passage clearly deals with how to deal with bereavement and grief and so after the tragedy occurs and not about precautions.gateforum.com.29 litres 1000 Few school curricula include a unit on how to deal with bereavement and grief.com Answer: .10 = 10 = 10 10 1000 ∴ 65. Ltd. In the IPv4 addressing format.|CS-GATE-2012 PAPER| Q. But first 3 bits are fixed as 110. is L also context-free? 3) If L is regular language. Regular and recursive languages are closed under complementation. Which of the following transport layer protocols is used to support electronic mail? (A) SMTP (B) IP (C) TCP (D) UDP Answer:-(C) Exp:. 5. baa}. then. baa} Let S1 = ab . No. is L also recursive? (A) 1.4 Answer:.4 (D) 3. Which of the following problems are decidable? 1) Does a given program ever produce an output? 2) If L is context-free language. The values of the cumulative distribution function F(x) at x = -1 and +1 are (A) 0 and 0. application layer protocol which intern uses TCP transport layer protocol.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 .2.E-mail uses SMTP.3.3 and 4 (C) 1. aa.5 (B) 0 and 1 India’s No.2 (C) 2.(D) Exp:. Consider a random variable X that takes values + 1 and -1 with probability 0. Given the language L-{ab. aa. which of the following strings are in L*? 1) abaabaaabaa 2) aaaabaaaa 3) baaaaabaaaab 4) baaaaabaa (A) 1.2 and 3 (B) 2. size of network field is 24 bits. the number of networks allowed under Class C addresses is (A) 214 (B) 27 (C) 221 (B) 224 Answer:-(C) Exp:.3. S2 = aa and S3 =baa abaabaaabaa can be written as S1S2S3S1S2 aaaabaaaa can be written as S1S1S3S1 baaaaabaa can be written as S3S2S1S2 3.CFL’s are not closed under complementation. then. hence total number of networks possible is 221 4.For class C address.4 (B) 1. 2.3 and 4 Answer:-(C) Exp:- L = {ab. then.5 each. 1 – 25 Carry One Mark Each 1.2 and 4 (D) 1. is L also regular? 4) If L is recursive language. Let W(n) and A(n) denote respectively. the worst case and average case running time of an algorithm executed on an input of size n. So the amount of ROM needed is 28 × 8 bits = 2Kbits.5 F ( +1) = P ( X ≤ +1) = P ( X = −1) + P ( X = +1) = 0.We have the relation V-E+F=2. Bubble Sort and merge sort). Output will contain 8 bits.25 and 0.The average case time can be lesser than or even equal to the worst case. The amount of ROM needed to implement a 4 bit multiplier is (A) 64 bits (B) 128 bits (C) 1 Kbits Answer:-(D) Exp:- (D) 2 Kbits For a 4 bit multiplier there are 2 4 × 24 = 28 = 256 combinations.The cumulative distribution function (D) 0.75 F(x) = P(X ≤ x) F ( −1) = P ( X ≤ −1) = P ( X = −1) = 0.5 + 0. ∴A ( n ) = O ( W ( n )) 9.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 . 7.Register renaming is done to eliminate WAR/WAW hazards. So A(n) would be upper bounded by W(n) and it will not be strict upper bound as it can even be same (e.|CS-GATE-2012 PAPER| (C) 0. by this we will get the total number of faces. Which of the following is ALWAYS TRUE? (A) A ( n ) = Ω ( W ( n ) ) (B) A ( n ) = Θ ( W ( n ) ) (C) A ( n ) = O ( W ( n ) ) (D) A ( n ) = o ( W ( n ) ) Answer:-(C) Exp:.5 = 1 6. 8. India’s No.g.5 and 1 Answer:-(C) Exp:. Register renaming is done is pipelined processors (A) as an alternative to register allocation at compile time (B) for efficient access to function parameters and local variables (C) to handle certain kinds of hazards (D) as part of address translation Answer:-(C) Exp:. If G is a connected graph. Let G be a simple undirected planar graph on 10 vertices with 15edges. then the number of bounded faces in any embedding of G on the plane is equal to (A) 3 (B) 4 (C) 5 (D) 6 Answer:-(D) Exp:. The recurrence relation capturing the optimal execution time of the Towers of Hanoi problem with n discs is (A) T ( n ) = 2T ( n − 2 ) + 2 (B) T ( n ) = 2T ( n − 1) + n (C) T ( n ) = 2T ( n / 2 ) + 1 (D) T ( n ) = 2T ( n − 1) + 1 Answer:-(D) Exp:. Out of 7 faces one is an unbounded face.T(n-1) 2. the goal is to move n pegs from A to C using peg B The following sequence of steps are executed recursively 1. Id Name 1 Ramesh 2 Ramesh 3 Rajesh 4 Suresh Select count (*) From student Group by Name Output will be Count (*) 2 1 India’s No.move n−1 discs from A to B. Which of the following statements are TRUE about an SQL query? P : An SQL query can contain a HAVING clause even if it does not have a GROUP BY clause Q : An SQL query can contain a HAVING clause only if it has GROUP BY clause R : All attributes used in the GROUP BY clause must appear in the SELECT clause S : Not all attributes used in the GROUP BY clause need to appear in the SELECT clause (A) P and R (B) P and S (C) Q and R (D) Q and S Answer:-(B) Exp:. option P is true and Q is false.B and C.T(n-1) So.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 . F = 7. T(n) = 2T(n-1) +1 11. In other words. So.|CS-GATE-2012 PAPER| 10. the HAVING condition applies to all rows that satisfy the search condition.move n−1 discs from B to C so they sit on disc n----.Let the three pegs be A.If we use a HAVING clause without a GROUP BY clause. all rows that satisfy the search condition make up a single group. so total 6 bounded faces. This leaves disc n alone on peg A --. S is also true as an example consider the following table and query.move disc n from A to C---------1 3. (B) Exp:. Option D: There exists some number which is not rational or which is real. which of the following is INCORRECT? (A) An attribute of an entity can have more than one value (B) An attribute of an entity can be composite (C) In a row of a relational table. 13. 15. so complement of this language is {є} 14. Option B: All real numbers are rational Option C: There exists a real number which is rational.Language accepted by NFA is a+.Option A: There exists x which is either real or rational and can be both. ε} Answer:. As multivalued attributes are not allowed in relational databases. in a row of a relational (table). Options A and B both are true since ER model supports both multivalued and composite attributes. an attribute can have exactly one value or a NULL value Answer:-(C) Exp:.(C) Exp:. an attribute can have more than one value (D) In a row of a relational table. Given the basic ER and relational models. Let A be the 2 x 2 matrix with elements a11 = a12 = a21= + 1 and a22 =-1. What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” (A) ∃x ( real ( x ) v rational ( x ) ) (B) ∀x ( real ( x ) → rational ( x ) ) (C) ∃x ( real ( x ) ∧ rational ( x ) ) (D) ∃x ( rational ( x ) → real ( x ) ) Answer:. What is the complement of the language accepted by the NFA show below? Assume Σ = {a} and ε is the empty string.The term ‘entity’ belongs to ER model and the term ‘relational table’ belongs to relational model.|CS-GATE-2012 PAPER| 1 12.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 . ε a ε (A) ∅ (B) {ε} (C) a * (D) {a. Then the eigen values of the matrix A19 are (A) 1024 and -1024 (B) 1024 2 and − 1024 2 India’s No. an attribute cannot have more than one value. Network layer . The total number of child processes created is (A) 3 (B) 4 (C) 7 Answer:. and a minimum value of –1 at and at all angles 2 2 conterminal with them. at π / 2 (C) Two. at 3π / 2 (A) One. The graph of f ( x ) = sin x is 3π π 7π ∴ In the int erval . Transport layer and Application layer are frame. The number and location (s) of the local minima of this function are (B) One.7π / 4] . datagram. fork (). at π / 2 and 3π / 2 (D) Two. Consider the function f(x) = sin(x) in the interval x ∈ [ π / 4. 17. The protocol data unit (PDU) for the application layer in the Internet stack is (A) Segment (B) Datagram (C) Message (D) Frame Answer:-(C) Exp:.(C) (D) 8 India’s No. A process executes the code fork ().Characteristic equation of A is |A − λI |= 0 where λ is the eigen value 1− λ 1 = 0 ⇒ λ2 − 2 = 0 ⇒ λ2 = ± 2 1 −1− λ Every matrix satisfies its characteristic equation Therefore A 2 − 2I = 0 ⇒ A 2 = 2I A19 = A18 × A = ( A 2 ) × A = ( 2I ) × A = 512 × A 9 9 Hence eigen values of A19 are ± 512 2 16. . it has one local minimum at x = 4 4 2 18. at π / 4and 3π / 2 Answer:-(B) Exp:- Sin x has a maximum value of 1 at π 3π . segment and message respectively.|CS-GATE-2012 PAPER| (C) 4 2 and − 4 2 (D) 512 2 and − 512 2 Answer:-(D) Exp:.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 . fork ().The PDU for Datalink layer. India’s No. So. Assuming P ≠ NP. The worst case running time to search for an element in a balanced binary search tree with n2n elements is (A) Θ ( n log n ) ( ) (B) Θ n2n (C) Θ ( n ) (D) Θ ( log n ) Answer:-(C) Exp:- The worst case search time in a balanced BST on ‘x’ nodes is logx.0)2 × 2−1 So.(A) Exp:- XY '+ XY = X ( Y'+ Y ) = X 21. there will be total 2n running processes including the parent process.|CS-GATE-2012 PAPER| Exp:..000 20. So. 19. which of the following is TRUE? (A) NP-complete = NP (B) NP-complete ∩ P = ∅ (C) NP-hard = NP (D) P = NP-complete Answer:-(B) Exp:- If P!=NP.5)10 = (1. The decimal value 0. then it implies that no NP-Complete problem can be solved in polynomialtime which implies that the set P and the set NPC are disjoint.5 in IEEE single precision floating point representation has (A) fraction bits of 000…000 and exponent value of 0 (B) fraction bits of 000…000 and exponent value of -1 (C) fraction bits of 100…000 and exponent value of 0 (D) no exact representation Answer:-(B) Exp:- ( 0. there will be 2n-1 child processes. exponent = -1 and fraction is 000 . then log(n2n) = logn + log(2n) = logn + n = θ(n) 22. if x = n2n.If fork is called n times.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 . The truth table X Y f(X.Y) 0 0 0 0 1 0 1 0 1 1 1 1 represents the Boolean function (A) X (B) X + Y (C) X ⊕ Y (D) Y Answer:.. Inference: The cricket match was played. The cricket match was played. What will be the output of the following C program segment? Char inChar = ‘A’ . } (A) No choice (B) Choice A (C) Choice A Choice B No choice (D) Program gives no output as it is erroneous Answer:-(C) Exp:. India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 . Inference: There was no rain. switch (inChar ) { case ‘A’ : printf (“Choice A\ n”). the program executes all the subsequent case statements after printing “choice A” 24. I2 : If it rains then the cricket match will not be played. since if a relation is in BCNF it will always be in 3NF. case ‘D’ : case ‘E’ : default : printf (“No Choice”) . It did not rain. Which of the following is TRUE? (A) Every relation is 3NF is also in BCNF (B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R (C) Every relation in BCNF is also in 3NF (D) No relation can be in both BCNF and 3NF Answer:-(C) Exp:. 25. since for a relation to be in BCNF it needs to be in 3NF. case ‘B’ : case ‘C’ : print f(“Choice B”). Option D is false.|CS-GATE-2012 PAPER| 23.Option A is false since BCNF is stricter than 3NF (it needs LHS of all FDs should be candidate key for 3NF condition) Option B is false since the definition given here is of 2NF Option C is true.Since there is no ‘break’ statement . Consider the following logical inferences. every relation in BCNF satisfies all the properties of 3NF. I1 : If it rains then the cricket match will not be played. Consider the set of strings on {0. 26 – 51 Carry Two Marks Each 26.1} in which. but 100010 is not.1 10 1 11 1 India’s No. All strings of length less than 3 are also in the language.(B) Exp:I1 : R →~ C ≈ ~RV~C C ______ ( there was no rain ) ~R ______ I2 : R →~ C ≈ ~Rv~C ~R ~R ______ ~ RvC ______ ( I1 is correct and I2 is not correct inference ) Q. every substring of 3 symbols has at most two zeros. No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 8 . A partially completed DFA that accepts this language is shown below. 00 0 0 0 1 0 1 0 ε 1 1 0 q 0. For example.|CS-GATE-2012 PAPER| Which of the following is TRUE? (A) Both I1 and I2 are correct inferences (B) I1 is correct but I2 is not a correct inference (C) I1 is not correct but I2 is a correct inference (D) Both I1 and I2 are not correct inferences Answer:. 001110 and 011001 are in the language. The complete DFA is 00 0 1 1 0 0 0 01 0 1 0 ε 1 q 0. The function shown in the pseudocode below is invoked as height (root) to compute the height of a binary tree rooted at the tree pointer root.|CS-GATE-2012 PAPER| The missing arcs in the DFA are (A) (B) 00 00 01 1 0 10 11 1 01 10 01 00 1 01 1 10 11 0 01 1 (D) q 10 1 01 10 0 11 q 1 0 1 01 10 q 0 00 0 11 0 00 0 10 11 00 11 0 00 01 10 0 11 (C) 00 q 0 0 11 Answer:-(D) Exp:. if ( n → left == NULL ) India’s No.1 0 1 10 0 1 1 11 1 27.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 9 . int height (treeptr n) { if (n== NULL) return -1. The height of a tree is defined as the number of edges on the longest path in the tree. return */ else return (1+height ( n → right ) ). → / * First Find the height of left sub tree for node ‘n’ */ If ( n → right == NULL ) return (1 + h1) . // Box 2 } } } The appropriate expressions for the two boxes B1 and B2 are (A) B1: (1 + height ( n → right ) ) (B) B1: ( height ( n → right ) ) B2 : (1 + max ( h1. return -1 */ if ( n → left == NULL ) → / * If there is no left child for node 'n ' * / if ( n → right == NULL ) return O. → / *If no left child & no right child for 'n '. h2 ) B2 : max ( h1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 10 . India’s No. but there is a right child. h2 ) Answer:-(A) Exp:.int height (treeptr n) { if (n = = nu11) return – 1. → /* If no left child. Therefore total height is 1+ height ( n → right ) */ else { → / * If there exist left child node for node ‘n’ */ h1 = height ( n → left ) . then compute height for right sub tree. → /* If there is no node. else return BI . // Box 1 else {h1 = height (n → left). if ( n → right == NULL ) return (1 + h1) . return B2 .|CS-GATE-2012 PAPER| if ( n → right == NULL ) return 0.h2 ) ) (D) B1: (1 + height ( n → right ) ) B2 : max ( h1.h2 ) ) (C) B1: height ( n → right ) B2 : (1 + max ( h1. else {h2 = height (n → right). → /* If there exist right child also. → /* Total height for node ‘n’= 1 + Max (Left Subtree height. Find the congestion window size at the end of the tenth transmission. h 2 ) ) . h2) */ } } 28. Right sub tree height) = 1 + Max (h1. (A) 8MSS (B) 14MSS (C) 7MSS (D) 12MSS Answer:-(C) 11 Exp:10 Time out 9 8 7 6 congestion 5 window size ↑ 4 3 2 1 O 1 2 3 4 5 6 7 8 9 10 11 Time → India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 11 . then compute height of right sub tree for a node ‘n’ */ return (1 + max ( h1 . Assume that a timeout occurs during the fifth transmission. then total height = height from (n to n → left ) + left sub tree height =1 + height ( n → left ) = 1 + h1 */ else {h2 = height ( n → right ) .|CS-GATE-2012 PAPER| → / * If there exist left child and no right child and no right child for a node ‘n’. Consider an instance of TCP’s Additive Increase Multiplicative decrease (AIMD) algorithm where the window size at the start of the slow start phase is 2 MSS and the threshold at the start of the first transmission is 8 MSS. during 1st transmission. Find the total sum of transmission and propagation delays in transmitting the file from S to D? (A) 1005ms (B) 1010ms (C) 3000ms (D) 3003ms Answer:. L2 connects R1 to R2. congestion window size = 8 (Threshold meet) Time = 4. Consider a source computer (S) transmitting a file of size 106 bits to a destination computer (D) over a network of two routers (R1 and R2) and three links (L1. transmits 5 (threshold is 5) Time = 9. congestion window size = 9. Let the file be broken down into 1000 packets each of size 1000 bits. L1 connects S to R1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 12 . transmits 10 MSS. Let r1 and r2 be the corresponding relation instances. which of the following is ALWAYS TRUE? (A) Π B ( r1 ) − Π C ( r2 ) =∅ (B) Π C ( r2 ) − Π B ( r1 ) =∅ (C) Π B ( r1 ) = Π C ( r2 ) (D) Π B ( r1 ) − Π C ( r2 ) ≠∅ Answer:-(A) India’s No. L2 and L3 for one packet is 1ms Therefore the sum of transmission delay and propagation delay on each link for one packet is 2ms. transmits 4 Time = 8. it transmits 7 segments hence at the end of the tenth transmission the size of congestion window is 7 MSS. D ) are two relation schemas. R1 and R2 will take 1ms Propagation delay on each link L1. but time out occurs congestion window size = 10 Hence threshold = (Congestion window size)/2 = 10 = 5 2 Time = 6. transmits 7 ∴ During 10th transmission. of acknowledgments) Time = 3.|CS-GATE-2012 PAPER| Given. and L3). Suppose R1 ( A.Congestion window size = 2 (slow start phase) Time = 2.(A) L1 L2 L3 Exp:29. congestion window size = 4 (double the no. transmits 6. L2. and L3 connects R2 to D. B) and R2 ( C. S R1 R2 D Transmission delay for 1 packet from each of S. initial threshold = 8 Time = 1. The first packet reaches the destination at 6thms The second packet reaches the destination at 7thms So inductively we can say that 1000th packet reaches the destination at 1005th ms 30. transmits 2 Time = 7. Assume signals travel over each line at a speed of 108 meters per second. after threshold (increase by one Additive increase) Time = 10. Assume that the link bandwidth on each link is 1Mbps. Let each link be of length 100km. B is a foreign key that refers to C in R2. after threshold (increase by one Additive increase) Time = 5. If data in r1 and r2 satisfy referential integrity constrains. 4.|CS-GATE-2012 PAPER| Exp:- Since B is a foreign key referring C.1.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 13 . Then (A) OPTIMAL < LRU < FIFO (B) OPTIMAL < FIFO < LRU (C) OPTIMAL = LRU (D) OPTIMAL = FIFO Answer:. 1 indirect block address and 1 doubly indirect block address.1 on a demand paged virtual memory system running on a computer system that has main memory size of 3 page frames which are initially empty. FIFO and OPTIMAL denote the number of page faults under the corresponding page replacement policy.3. The maximum possible file size in this file system is (A) 3 KBytes (C) 280 KBytes Answer:-(B) Exp:.4.values under B will be subset of values under C ( Π B ( r1 ) ⊆ Π C ( r2 ) ⇒ Π B ( r1 ) − Π C ( r2 ) =∅ ) 31. A file system with 300 GByte disk uses a file descriptor with 8 direct block addresses.2.FIFO 1 1 1 4 4 4 2 2 2 1 1 → (6) faults 3 3 3 2 Optimal 1 1 1 1 1 2 2 4 4 → (5) faults 3 3 2 LRU 1 1 1 4 4 4 2 2 2 2 2 2 2 3 3 3 1 3 3 1 1 1 → (9) faults 4 4 Optimal < FIFO < LRU 32. The size of each disk block is 128 Bytes and the size of each disk block address is 8 Bytes.2. Consider the virtual page reference string 1. Let LRU.(B) Exp:.3.Each block size = 128 Bytes Disk block address = 8 Bytes (B) 35 KBytes (D) dependent on the size of the disk 128 = 16 addresses 8 Size due to 8 direct block addresses: 8 x 128 Size due to 1 indirect block address: 16 x 128 Size due to 1 doubly indirect block address: 16 x 16 x 128 ∴ Each disk can contain = Size due to 1 doubly indirect block address: 16 x 16 x 128 India’s No.2. the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.|CS-GATE-2012 PAPER| So. D. − − − −. E. 2 C 2 E 1 G 1 1 A 4 3 4 3 3 7 D S 4 3 5 5 T 3 B F (A) SDT (B) SBDT (C) SACDT Answer:. W = φ We will use the following procedure Repeat until Q is empty { 1 u = choose a vertex from Q with minimum d[u] value 2. in any iteration. A.(D) Exp:. d[A] = ∞ . W = W U{u} } d[S] = 0. update all the adjacent vertices of u 4. There are multiple shortest paths between vertices S and T. B.T} .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 14 . Consider the directed graph shown in the figure below. d[T] = ∞ Iteration 1 India’s No.F. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that.………. Q = Q − u 3.d [ T ] = ∞ And let P[v] represent the predecessor of v in the shortest path from ‘S’ to ‘v’ and let P[v]=-1 denote that currently predecessor of ‘v’ has not been computed → Let Q be the set of vertices for which shortest path distance has not been computed → Let W be the set of vertices for which shortest path distance has not been computed → So initially. d[B] = ∞ . Q = {S.G.C. maximum possible file size: = 8 × 128 + 16 × 128 + 16 × 16 × 128 =1024 + 2048 + 32768 = 35840 Bytes = 35KBytes 33.Let d[v] represent the shortest path distance computed from ‘S’ (D) SACET Initially d[S]=0. d [ B] = ∞. d[A] = ∞ . P [ T ] = −1 Step 4 : W = {S} Iteration 2: Step 1: u = B Step 2 : Q = {A. d [ E ] = ∞ − −−. P [ B] = S.d [ T ] = ∞ P [ A ] = S. E. B.d [ C] = ∞.T} step 3 : final values after adjustment d [S] = 0.T} step 3 : final values after adjustment d [S] = 0.G.P [ E ] = −1 − −−.d [ E ] = 6.C} Iteration 5: India’s No.d [ D] = 7. A. A} Iteration 4: Step 1: u = C Step 2 : Q = {D. E. d [ B] = 3. d [ B] = 3.G. P [ E ] = C.d [ E ] = ∞ − −−. P [ E ] = −1 − −−.d [ E ] = ∞ − −−.P [ C] = −1. P [ D ] = S.|CS-GATE-2012 PAPER| Step 1 : u = S Step 2 : Q = {A. B} Iteration 3: Step 1: u = A Step 2 : Q = {C. B.d [ T ] = ∞ P [ A ] = S. P [ C] = A. B. − − −.E. D. F.d [ T ] = ∞ P [ A ] = S.C.P [ D] = S.d [ A ] = 4. P [ T ] = −1 Step 4 : W = {S. P [ D ] = S. − − −. F. F.d [ A ] = 4. P [ T ] = −1 Step 4 : W = {S. F.D.d [ D ] = 7.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15 .G.d [ D ] = 7. d [ C] = 5.d [ T ] = ∞ P [ A ] = S. P [ T ] = −1 Step 4 : W = {S. d [ B] = 3. P [ D ] = S.T} Step 3: final values after adjustment d [S] = 0. P [ B] = S.d [ C] = 5. P [ C] = A. d [ A ] = 4. P [ B] = S. E.G.d [ A ] = 4. P [ E ] = −1 − −−. D. d [ B] = 3. P [ B] = S. P [ C ] = −1.d [ C ] = ∞.d [ D ] = 7.C.T} step 3 : final values after adjustment d [S] = 0. Var . .C. P [ T ] = E Step 4 : W = {S. P [ B] = S. B.No option matching (marks to all) Exp:. Consider the program given below. A. is sorted into lexicographic order using the merge-sort algorithm. 37.Total number of functions is 2n.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 16 . If vertices of G are labeled.(C) Exp:.The height of the recursion tree using merge sort is logn and n2 comparisons are done at each level. P [ C] = A. P[C]=A . E} After iteration 5.d [ D ] = 7. P [ D ] = S. Let G be a complete undirected graph on 6 vertices. P[A]=S. out of which there will be exactly two functions where all elements map to exactly one element. d [ B] = 3. A list of n strings.T} step 3 : final values after adjustment d [S] = 0. each of length n. P [ F] = −1.|CS-GATE-2012 PAPER| Step 1: u = E Step 2 : Q = {D. Var ….3!)/2 = 45.G. Number of cycles of length 4 that can be formed from those selected vertices is (4-1)!/2 (left or right/ up or down does not matter). P[E]=C . P [ E ] = C. Procedure A1.d [ F] = ∞.2 (D) 2(2n -2) Answer:. then the number of distinct cycles of length 4 in G is equal to (A) 15 (B) 30 (C) 90 (D) 360 Answer:. in a block-structured pseudo-language with lexical scoping and nesting of procedures permitted. so total number of 4 length cycles are (6c4.4 vertices from 6 vertices can be chosen in in 6c4. Program main.d [ E ] = 6. P [ G ] = E.d [ T ] = 10 P [ A ] = S. so total number of onto functions is 2n-2 36. F.d [ C] = 5. we can observe that P[T]=E . How many onto (or surjective) functions are there from an n-element ( n ≥ 2) set to a 2element set? (A) 2n (B) 2n -1 (C) 2n . So the shortest path from S to T is SACET 34. India’s No. The worst case running time of this computation is (A) O ( n log n ) ( (C) O n 2 + log n ( ) (D) O ( n ) (B) O n 2 log n ) 2 Answer:-(B) Exp:. .d [ G ] = 8. So the worst case running time is O ( n 2 log n ) 35.d [ A ] = 4. where at most n pairs of strings are compared at each level and n comparisons are required to compare any two strings. Consider the calling chain: Main → A1 → A2 → A21 → A1 The correct set of activation records along with their access links is given by (A) FRAME POINTER (B) Main Main A1 A1 A2 A2 A21 A21 A1 ACCESS FRAME POINTER A1 ACCESS LINKS LINKS (D) (C) Main Main A1 FRAME POINTER A1 A2 A2 A21 A21 ACCESS LINKS FRAME POINTER A1 ACCESS LINK Answer:-(D) India’s No. Call A1. End A1 Procedure A2. End A21 Call A21. End A2 Call A1.|CS-GATE-2012 PAPER| Call A2. End main. .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 17 . Var . Var . . . Procedure A21. . 0/21 Answer:. respectively. − − − − − − −2 −1 India’s No. at this point the condition empty above is satisfied. so this condition is also false The counter example for the condition empty : (REAR+1)mod n = FRONT is Initially when the Queue is empty REAR=FRONT=0 and let n=2.0/21 and 245.248. but the queue of capacity n-1 is full here 39. and a quarter to Organization B.248.248.136.248. at this point the condition empty above is satisfied. at this point the condition full above is satisfied. Assume that the insertion and deletion operations are carried out using REAR and FRONT as array index variables.136.248.132. while retaining the remaining with itself.0/20. but still there is place for one more element in Queue.132. so after inserting one element REAR=1 and FRONT=0.0/21 and 245.A2 and A21 are main . 11111000. The ISP wants to give half of this chunk of addresses to Organization A. Initially.(A) Exp:- Network part host part 11110101. REAR = FRONT = 0.132. main and A2 38. Which of the following is a valid allocation of address to A and B? (A) 245.1000 12 − −13− −.0/21 (D) 245.128. but the queue of capacity n-1 is full here The counter example for the condition empty : (FRONT+1)mod n =REAR is Initially when the Queue is empty REAR=FRONT=0 and let n=2. so the closest enclosing blocks respectively for A1 .0/22 (C) 245.(A) Exp:- The counter example for the condition full : REAR = FRONT is Initially when the Queue is empty REAR=FRONT=0 by which the above full condition is satisfied which is false The counter example for the condition full : (FRONT+1)mod n =REAR is Initially when the Queue is empty REAR=FRONT=0 and let n=3.Access link is defined as link to activation record of closest lexically enclosing block in program text.128.|CS-GATE-2012 PAPER| Exp:.0/22 and 245. Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. The conditions to detect queue full and queue empty are (A) full: (REAR+1) mod n==FRONT (B) full:(REAR+1)mod n==FRONT empty: REAR ==FRONT empty: (FRONT+1)mod n==REAR (C) full: REAR==FRONT empty: (REAR+1) mod n ==FRONT (D) full:(FRONT+1)mod n==REAR empty: REAR ==FRONT Answer:.248.248. An Internet Service Provider (ISP) has the following chunk of CIDR-based IP addresses available with it: 245.128.0/24 and 245. so after inserting one element REAR=1 and FRONT=0.248.128. so after inserting one element REAR=1 and FRONT=0.248.0/22 (B) 245.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 18 . 0/22 40. } Release Lock(L){ L = 0.(B) Exp:- (B) 5/12 (C) 2/3 5 Toss a coin 6 1 1 6 1 6 6 4 1 6 1 1 6 1 6 4 6 5 5 2 6 3 3 4 5 6 (D) 1/6 2 probability = 6 3 probability = 6 4 probability = 6 1 2 1 3 1 4 1 15 5 ∴ Re quired probability = × + × + × + = = 6 6 6 6 6 6 6 36 12 41. It is used in the pseudocode shown below to implement a busy-wait lock.1)) L = 1. 2. so the valid allocation of addresses to A is 245. 12th bit is set to ‘0’ but since we need only half of 2048 addresses. If the value on the die is 1. The value of 0 corresponds to lock being available. i) is an atomic Read-Modify-Write instruction that reads the value of memory location X. What is the probability that the sum total of values that turn up is at least 6? (A) 10/21 Answer:. the die is rolled a second time.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 19 . Fetch_And_Add (X. while any nonzero value corresponds to the lock being not available. AcquireLock(L){ While (Fetch_And_Add(L.0/21 Now for organization B. we can set 12th bit to 1 and include that bit into network part of organization A. Suppose a fair six-sided die is rolled once.|CS-GATE-2012 PAPER| Since half of 4096 host addresses must be given to organization A.248.136.128. L is an unsigned integer shared variable initialized to 0. and returns the old value of X.248. increments it by the value i. or 3. } This implementation (A) fails as L can overflow (B) fails as L can take on a non-zero value when the lock is actually available India’s No. 13th bit can be set to ‘0’ and include that bit into network part of organization B so the valid allocation of addresses to B is 245. P3.P3.P1.5.P2. P3.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 20 . P3. While (Fetch_And_Add(L.2. } Let P and Q be two concurrent processes in the system currently executing as follows P executes 1. Release Lock (L) { 5. P2 RR2: P1. P1. Process Arrival time Time units Required P1 0 5 P2 1 7 P3 3 4 The completion order of the 3 processes under the policies FCFS and RR2 (round robin scheduling with CPU quantum of 2 time units) are (A) FCFS: P1.P2 This RQ itself shows the order of execution on CPU(Using Gantt Chart) and here it gives the completion order as P1. P2 RR2: P1. by which all the processes could starve. Consider the 3 process. P2. 1)) 3.(B) Exp:. 42.P1. P3 Answer:-(C) Exp:.P3 Next For RR with time quantum=2.|CS-GATE-2012 PAPER| (C) works correctly but may starve some processes (D) works correctly without starvation Answer:.3 then Q executes 1 and 2 then P executes 4. L = 1. Acquire lock (L) { 2.P2. P3 RR2: P1. P2 and P3 shown in the table. P2.the arrangement of Ready Queue will be as follows: RQ: P1.P2. P3 RR2: P1. L = 0.6 then L=0 now Q executes 3 by which L will be set to 1 and thereafter no process can set L to zero. P2 (D) FCFS: P1. 6. P3. P2.For FCFS Execution order will be order of Arrival time so it is P1. P3. India’s No. P2.1. P3 (B) FCFS: P1. } 4.P2 in Round Robin algorithm. P2 (C) FCFS: P1.P3. |CS-GATE-2012 PAPER| 43. Let G be a weighted graph with edge weights greater than one and G’ be the graph constructed by squaring the weights of edges in G. with total weights t and t’. What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term. Which of the following statements is TRUE? (A) T’ = T with total weight t’ = t2 (B) T’ = T with total weight t’ < t2 (C) T’ ≠ T but total weight t’ = t2 (D) None of these Answer:-(D) Exp:2 3 2 G G1 Graph G is counter example for options (B) and (C) and Graph G1 is counter example for option (A) India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 21 . Let T and T’ be the minimum spanning trees of G and G’ respectively.(B) Exp:- ab cd 00 01 00 01 1 X 11 10 1 1 X 11 10 1 X X d 'b '+ c 'b ' 44. ab 00 01 1 X 11 10 X 1 cd 00 01 1 X 11 1 10 X (A) bd (B) b d + b c (C) bd + abcd (D) b d + b c + c d Answer:. (A) 1 (B) 3 (C) 5 (D) 7 Answer:. The method converges to a solution after ______ iterations.(B) Exp:45.9]. f ( x ) = x 4 − x3 − x 2 − 4 f (1) < 0 and f ( 9 ) > 0 ∴ x 0 = 1+ 9 =5 2 f ( 5 ) > 0 ∴ root lies in [1.x2 – 4 in the interval [1.The graph in option (A) has a 3 length cycle whereas the original graph does not have a 3 length cycle The graph in option (C) has vertex with degree 3 whereas the original graph does not have a vertex with degree 3 India’s No. Which of the following graph is isomorphic to (A) (B) (C) (D) Answer:-(B) Exp:.5] x1 = 1+ 5 =3 2 f ( 3) > 0 ∴ root lies in [1.3] x2 = 1+ 3 =2 2 f ( 2 ) = 0 ∴ root is 2 46.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 22 .|CS-GATE-2012 PAPER| The bisection method is applied to compute a zero of the function f(x) = x4 -x3 . write (Q). so the precedence graph for S has an edge from T1 to T2. the precedence graph for S also contains an edge from T2 to T1. In a similar way we can show that if T2 is the earliest transaction then also the schedule is not conflict serializable. Consider the following transactions with data items P and Q initialized to zero: T1 : read (P) . Any non-serial interleaving of T1 and T2 for concurrent execution leads to (A) a serializable schedule (B) a schedule that is not conflict serializable (C) a conflict serializable schedule (D) a schedule for which precedence graph cannot be drawn Answer:-(B) Exp:.|CS-GATE-2012 PAPER| The graph in option (D) has a 4 length cycle whereas the original graph does not have a 4 length cycle 47. T2 : read (Q) . Common Data Questions: 48 & 49 Consider the following relations A.Let S be a non-serial schedule. if P = 0 then Q : = Q + 1 . read (P) if Q = 0 then P : = P + 1 . read (Q) .1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 23 . The first instruction of T1 is read(P) and the last instruction of T2 is write(P). B and C: A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 India’s No. So we will have a cycle in the precedence graph which implies that any non serial schedule with T1 as the earliest transaction will not be conflict serializable. without loss of generality assume that T1 has started earlier than T2. now since S is a non-serial schedule the first instruction of T2(read(Q)) should be executed before last instruction of T1(write(Q)) and since read and write are conflicting operations. write (P). Id <15 C (A) 7 Answer:-(A) Exp:.Age FROM B WHERE B. ‘>ALL’ comparison is true . void prtFun(void).Id Phone Area 12 Arun 60 10 2200 02 15 Shreya 24 10 2200 02 25 Hari 40 10 2200 02 98 Rohit 20 10 2200 02 98 Rohit 20 99 2100 01 99 Rohit 11 10 2200 02 99 Rohit 11 99 2100 01 Common Data Questions: 50 & 51 Consider the following C code segment: int a.Id > 40 v C. b. How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A ∪ B is the same as that of A.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 24 .|CS-GATE-2012 PAPER| 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 220 02 99 2100 01 48. c = 0.As the result of subquery is an empty table. How many tuples does the result of the following SQL query contain? SELECT A.Age > ALL(SELECT B.The final table is (B) 4 (C) 5 (D) 9 AUB . Therefore. ( A ∪ B ) A. India’s No.Id FROM A WHERE A. Id Name Age C.Name = ‘Arun’) (A) 4 (B) 3 (C) 0 (D) 1 Answer:-(B) Exp:. 49. all the three row id’s of A will be selected from table A. int b=1. (A) (B) (C) (D) 3 4 1 1 4 6 2 1 4 6 2 2 4 4 2 2 4 2 6 1 2 0 2 0 Answer:-(D) Exp:- Static local variables: Scope is limited to function/block but life time is entire program. 0 → 1 b 2 2 1 pr int s : 4 2 → (1) pr int s : 4 2 → ( 2) b (3 ) India’s No. a. a 0 b 0 c 0 main ( a ) (1) 1 2 2 4 a 4 (2 ) 4 a pr in t s : 2. b). /* Line 1 */ /* Line 2 */ What output will be generated by the given code segment if: Line 1 is replaced by auto int a = 1. a+=++b.|CS-GATE-2012 PAPER| main( ) { static int a = 1. printf(“\n %d %d “. Register variables: Same as automatic variables except that the register variables will not have addresses Hence may not take the address of a register variable. prtFun( ). } 50. } void prtFun(void) { static int a=2. Automatic local variables: Storage allocated on function entry and automatically deleted or freed when the function is exited. a + = 1. Line 2 is replaced by register int a = 2. a.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 25 . b). prtFun( ) printf(“\n %d %d “. |CS-GATE-2012 PAPER| 51. 1 modified bit and 1 replacement bit. The number of bits in the tag field of an address is (A) 11 (B) 14 (C) 16 Answer:. Each cache tag directory entry contains.52 to Q. 2 valid bits.(C) Exp:main ( a 0 b 0 c 0 a 4 ) (1) pr int s : 4 2 → (1) a 2 1 2 b 1 2 a 4 b 1 (2 ) pr int s : 2. 52.2 → (2) Linked Answer Questions: Q. 4-way set associative. number of sets = 213 = 211 22 32 bits TAG 16 SET offset 11 Byte offset 5 India’s No. 0 4 2 6 2 2 0 static (keeps old value ) 6 2 pr int : 6.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 26 . The processor sends 32 bit addresses to the cache controller. What output will be generated by the given code segment? (A) (B) (C) (D) 3 4 1 1 4 6 2 1 4 6 2 2 3 5 1 2 4 2 6 1 2 0 5 2 Answer:.55 Carry Two Marks Each Statement for Linked Answer Questions: 52 & 53 A computer has a 256 KByte.(C) Exp:- Number of blocks = (D) 27 256 KB 218 = 5 = 213 blocks 32 Bytes 2 As it is 4–way set associative. write back data cache with block size of 32 Bytes. in addition to address tag. b} Follow ( A ) = First ( bB ) ∪ First ( aB ) = {a.a. b.a. S → a AbB bAa B ε A→S B→S a b $ S E1 E2 S→ ε A A→S A→S error B B→S B→S E3 54. and | separates alternate right hand sides of productions. b} FOLLOW(B) ={$} (C) FIRST(A) = {a. E2.|CS-GATE-2012 PAPER| 53.b} India’s No.} = FIRST(B) FIRST(A) = {a. b. b. b} FOLLOW(B) = {a.b} Follow ( B ) = Follow ( S) = {$} ∪ Follow ( A ) = {$. b. ε is the empty string. b. b. The size of the cache tag directory is (A) 160 Kbits (B) 136 Kbits (C) 40 Kbits Answer:-(A) Exp:. a partial LL(1) parsing table is also presented along with the grammar. b} Answer:. ε } = FIRST (B) FOLLOW(A) = {a.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 27 .TAG controller maintains 16 + 4 = 20 bits for every block (D) 32 Kbits Hence. ε } = FIRST(B) FIRST(A) = {a. a. b} FOLLOW(B) = ∅ (D) FIRST(A) = {a. $ indicates end of input. The First and Follow sets for the non-terminals A and B are (A) FIRST(A) = {a. ε } FOLLOW(A) = {a. b} FOLLOW(B) ={a.(A) Exp:- First ( A ) = First ( S) = First ( aAbB ) ∪ First ( bAaB ) ∪ First (∈) = {a} ∪ {b} ∪ {∈} = {∈. and E3.b} First ( B ) = First ( S) = {∈. $} FIRST(B) = {a. Entries that need to be filled are indicated as E1. $} (B) FIRST(A) = {a. size of cache tag directory = 20 × 213 bits = 160 K bits Statement for Linked Answer Questions: 54 & 55 For the grammar below. where q is the amount of production.a. (A) that (B) which (C) who (D) whom Answer:. S → ε E2: S → bAaB. S → ε E2: B → S. b} . Follow ( B ) = {$. q = 5 Else check with options 57. 56 – 60 Carry One Mark Each 56.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28 . Follow ( S) = {$. B → S E2: S → bAaB.a. S → ε E3: B → S E3: S → ε (C) E1: S → aAbB. The number of units to be produced by the firm such that the profit is maximized is (A) 5 (B) 10 (C) 15 (D) 25 Answer:. <0 dq dq 2 ∴ p is max imum at 50 − 10q = 0 or. No. b} a b $ S S → aAbB S → bAaB S →∈ S →∈ S →∈ B → S to be placed in LL(1) Parsing table as follows:- First ( S) = {∈.(A) India’s No.(C) Exp:First ( S) = {∈.|CS-GATE-2012 PAPER| 55. Choose the most appropriate alternative from the options given below to complete the following sentence: Suresh’s dog is the one ________ was hurt in the stampede. The appropriate entries for E1.a. S → ε (D) E1: A → S. E2.a. S → ε (A) E1: S → aAbB. and E3 are (B) E1: S → aAbB. b} .(A) Exp:P = 50q − 5q 2 dp d2p = 50 − 10q. S → ε E3: B → S E3: B → S Answer:. b} a b $ B B→S B→S B→S Q.50 per unit. A → S E2: S → bAaB. The cost function for a product in a firm is given by 5q 2 . The firm can sell the product at a market price of Rs. Wanted Temporary. Choose the most appropriate alternative from the options given below to complete the following sentence: Despite several __________ the mission succeeded in its attempt to resolve the conflict.Gender is not mentioned in the advertisement and (B) clearly eliminated 62. (C) The committee initially asked for a funding of Fifty Lakh rupees. Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. (D) This country's expenditure on educational reforms is very less Answer:-(D) 59. +5 JP . OV +6 Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list India’s No. Evening and Saturday work.(A) +2 +4 +3 Exp:- AD . AD CG FK JP. Choose the grammatically INCORRECT sentence: (A) They gave us the money back less the service charges of Three Hundred rupees. Transportation paid. Requirements: High School-pass.|CS-GATE-2012 PAPER| 58. must be available for Day. expenses reimbursed. Given the sequence of terms. Which one of the following is the best inference from the above advertisement? (A) Gender-discriminatory (B) Xenophobic (C) Not designed to make the post attractive (D) Not gender-discriminatory Answer:.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 29 . (A) attempts (B) setbacks (C) meetings (D) delegations Answer:. Which one of the following options is the closest in meaning to the word given below? Mitigate (A) Diminish (B) Divulge (C) Dedicate (D) Denote Answer:. CG . 61 – 65 Carry Two Marks Each 61. the next term is (A) OV (B) OW (C) PV Answer:.(C) Exp:. +3 63.(B) Q. (B) This country's expenditure is not less than that of Bangladesh. +4 (D) PW +5 FK . No. but later settled for a lesser sum.(A) 60. 3.P and R always hold true Else consider a sample set {1.334 (C) 0.1x 2 where y is the height of the arch in meters. 72% are reliable.Supply 60% 40% Reliable 96% 72% Overall 0.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 30 .334 0. S Answer:-(C) Exp:. Q (B) Q. A political party orders an arch for the entrance to the ground in which the annual convention is being held. 2. All shock absorbers are subjected to a quality test.|CS-GATE-2012 PAPER| S: Doubling each entry in a list leaves the standard deviation of the list unchanged (A) P. The profile of the arch follows the equation y = 2x − 0. 4} and check accordingly 64.288 0. Of Y's shock absorbers.288 ∴ P(x) = = 0. is made by Y is (A) 0.576 0. R (C) P.2x dx d2 y < 0 ∴ y max imises at 2 − 0. which is found to be reliable. X supplies 60% and Y supplies 40% of the shock absorbers. 96% are reliable.2x = 0 dx 2 ⇒ x = 10 ∴ y = 20 − 10 = 10 m India’s No.288 65. The probability that a randomly chosen shock absorber. The maximum possible height of the arch is (A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters Answer:-(B) Exp:y = 2x − 0. The ones that pass the quality test are considered reliable Of X's shock absorbers.288 (B) 0. R (D) R.720 Answer:-(B) x y Exp:.667 (D) 0. An automobile plant contracted to buy shock absorbers from two suppliers X and Y.1x 2 dy = 2 − 0.576 + 0.
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