IIT-JEE ADVANCE PART TEST-201831/12/2017 M.M. : 180 PART TEST – 01 Before 7 pm tomorrow (PAPER – I) TIME : 3.00 Hrs Read the following Instructions very carefully before you proceed. 1. The question paper consists of 3 parts (Part A : Physics, Part B : Chemistry, Part C : Mathematics). Each Part contains 20 questions & 3 sections (Section I, Section II , Section III). Section I contains 10 single correct type questions, Section II contains 5 one or more than one option correct type questions and Section III contains 5 Integer type questions. 2. For each question in section I, you will be awarded 2 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. For each question in section II, you will be awarded 4 marks if you darken the bubble(S) corresponding to only the correct answer(S) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. For each question in section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 3. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on the Answer Sheet. Use of pencil is strictly prohibited. 4. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room. 5. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your Test Code, Roll No. and Group properly in the space given in the ANSWER SHEET. 6. Do not fold or make any stray marks on the Answer Sheet. 7. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 8. No one will be permitted to leave the test room before the end of the test. 1 PART TEST_01 (PAPER I) PART – A (Physics) Section – I Single Correct Choice Type 1. As shown in the fig. All contact are smooth, force F is applied as show. What will be the acceleration of wedge M : F (A) M (B) Zero 2F (C) M (D) None of these 2. As shown in the figure. What will be the relation between a 1 and a2 sin sin sin sin (A) a 2 a1 (B) a1 a 2 (C) a1 a 2 (D) a 2 a1 sin tan tan sin 3. Assuming all the surfaces to be frictionless, acceleration of the block C shown in the figure is : (A) 5 m/s2 (B) 7 m/s2 (C) 3.5 m/s2 (D) 4 m/s2 4. A block of mass m is kept on an inclined plane of a lift moving down with acceleration of 2 m/s 2. What should be the coefficient of friction for the block to move down with constant velocity relative to lift : 1 (A) 3 (B) = 0.4 (C) = 0.8 (D) = 0.5 5. A particle is moved from point A(2, 4) to point B(6, 8) by the action of force F (2xyˆi x 2ˆj) N . Calculate work done by the force : (A) 200J (B) 270 J (C) 272 J (D) None of these 2 PART TEST_01 (PAPER I) 6. Potential energy of a conservative system is given by U = ax2 – bx, a, b are the constant. Its equilibrium position will be : b 2a b b (A) x , unstable (B) x . stable (C) x , stable (D) x , stable 2a b a 2a 7. A particle is projected vertically upwards from O with velocity V and a second particle is projected at the same instant from P (at a height h above O) with velocity v at an angle of projection . The time when the distance between them is minimum is : h h h h (A) (B) (C) (D) 2vsin 2vcos v 2v 8. When a man walks from point A to point B (man starts from point A and stops his motion at point B) then the direction of force of friction acting on him is (A) always in forward direction. (B) always in backward direction. A B (C) forwards for some time and backwards for some time. (D) None of these 9. A swimmer can swim in still water with a speed of 5 m/s. While crossing a river his average speed is 3 m/s. If he cross the river in the shortest possible time, what is the speed of flow of water? (A) 2 m/s (B) 4 m/s (C) 6 m/s (D) 8 m/s 10. A car starting from rest is accelerated at constant rate until it attains a constant speed v. It is then retarded at a constant rate until it comes to rest. Considering that the car moves with constant speed for half of the time of total journey, the average speed of the car for the journey is v 3v 3v (A) (B) (C) (D) Data insufficient 4 4 2 Section – II One or More Than One Option Correct Type 11. A body of mass M was slowly hauled up the rough hill by a force F which at each point was directed along tangent to the hill. Work done by the force (A) is independent of shape of trajectory F M (B) depends upon vertical component of displacement but independent of the horizontal component. (C) depends upon both the components (D) does not depend upon coefficient of friction 12. The potential energy U (in joule) of a particle of mass 1 kg moving in x-y plane obeys the law U = 3x + 4y, where (x, y) are the co-ordinates of the particle in meter. If the particle is at rest at (6, 4) at time t = 0, then : (A) the particle has constant acceleration (B) the particle has zero (C) the speed of particle when it crosses the y-axis is 10 m/s (D) coordinates of the particle at t = 1 sec are (4, 5, 2) 3 PART TEST_01 (PAPER I) 13. Two small balls A and B of mass M and 3M hang from the ceiling by strings of equal length. The ball A is drawn aside so that it is raised to a height H. It is then released and collides with ball B. Select the more options : A 2H B (A) If collision is perfectly elastic, ball B will rise to a height H/2. (B) If the collision is perfectly elastic, ball A will rise upto a height H/2. (C) If the collision is perfectly inelastic, the combined mass will rise to a height H/8. (D) If the collision is perfectly inelastic, the combined mass will rise to a height H/4. 14. A man pulls a block heavier than himself with a light rope as shown in the figure. The coefficient of friction is same between the man and the ground as well as that between the block and the ground. (A) The block will not move unless the man also moves. (B) The man can move even when the block is stationary. (C) If both moves, the acceleration of the man is greater than the acceleration of the block. (D) None of the above is assertions is correct. 15. In the system shown in the figure, all surfaces are smooth. Pulley, string and spring balance is ideal. m1 = 8 kg, m2 = 2kg and k = 1600 N/m, then (g = 10 m/s 2) which of the followings are correct at the steady state. T (A) Tension in the string T = 17.2 N0 m1 (B) Reading of the spring balance is 1.6 kg k (C) Elongation of the spring is 1 cm m2 (D) Force on the pulley is 32 N0 Section – III Integer Type 16. Two bodies A and B of each of mass 100 gm are allowed to move along a frictionless typical path as shown below. In order to have the same kinetic energy for both the bodies at M, the initial velocity that should be given to B, if A starts from rest is a 2 calculate a. 4 PART TEST_01 (PAPER I) 17. A force given by the relation F = 8t, acts on a body of mass 2kg, initially at rest, then work done by this force on the body during first 2 seconds is 8 × a. Calculate a. A B 18. A heavy string of mass m hangs between two fixed points A and B at the same level. The tangents to the string at A and B are at an angle with the horizontal as shown in the figure. The tension in the string at mg lowest point is . Find K? K tan 19. Two particles A and B are projected simultaneously in the direction shown in the figure with velocities v A = 20 m/s and v B = 10 m/s respectively. They collide in air after 1/2 sec. Then the distance x is K 3 m. Find K? vA = 20 m/s vB = 10 m/s x 20. An object of mass m is projected with momentum P at such an angle that its maximum height (H) is 1/4 th of p2 its horizontal range (R). Its minimum kinetic energy in its path will be . Find K? Km PART – B (Chemistry) Section – I Single Correct Choice Type 1. When radiations of a particular frequency incident on a sample of H atoms, the maximum no. of spectral lines obtainable in the emission spectrum is 15. Find the uppermost E level to which the e – are excited is : (A) 4 (B) 5 (C) 6 (D) 7 2. If radius of nth orbit rn is related to its energy content En (where En = total energy) by the following relation : rn En x , then find x. (A) 0 (B) –2 (C) 2 (D) –1 3. Oxidation state of nitrogen is incorrectly given for : Compound Oxidation state (A) [Co(NH3)5Cl]Cl2 –3 (B) NH2OH –1 (C) (N2H5)2 SO4 +2 (D) Mg3N2 –3 4. The equivalent weight of the salt KHC 2O4. H2C2O4. 4H2O used as reducing agent is : (A) Mol. Wt./1 (B) Mol. Wt./2 (C) Mol. Wt./3 (D) Mol. Wt./4 –5 5. Find the degree of ionization of 0.1 M HA (Ka = 10 ) by the addition of 0.1 M NaOH. (A) nearly 1 (B) 0.1 (C) 10–4 (D) 10–5 6. In saturated solution of AgCl, the following equilibrium is maintained. AgCl(s) aq Ag (aq) Cl (aq) 5 PART TEST_01 (PAPER I) Which of the following activity leads to increase of concentration of Cl – at equilibrium. (A) addition of more AgCl (B) addition of water (C) addition of AgNO3 (D) addition of concentrated NH3(aq) 7. For the reaction : 2HI(g) H2(g) + I2(g), the degree of dissociation () of HI(g) is related to equilibrium constant Kp by the expression 1 2 Kp 1 2K p 2K p 2 Kp (A) (B) (C) (D) 2 2 1 2K p 1 2 Kp 8. The value of G of gaseous mercury is 31 KJ/ mole. At what total external pressure mercury start boiling at 25C. [R = 8.3 J/K mole] (A) 10–5.44 (B) 10–12.5 (C) 10–6.52 (D) 10–3.12 9. During winters, moisture condenses in the form of dew and can be seen on plant leaves and grass. The entropy of the system in such cases decreases as liquid possess lesser disorder as compared to gases with reference to the second law, which statement is correct, for the above process ? (A) The randomness of universe decreases (B) The randomness of surrounding decreases (C) Increase in randomness of surrounding equals the decrease in randomness of system (D) The increase in randomness of the surrounding is greater as compared to the decreases in randomness of the system 10. 2.1 g of iron completely reacts with excess sulphur to form FeS. 3.77 KJ of heat is evolved in the process. What is the heat of formation of FeS? (A) – 3.77 KJ.mol-1 (B) – 2.79 KJ.mol-1 (C) – 100.5 KJ.mol-1 (D) – 47.125 KJ.mol-1 Section – II One or More Than One Option Correct Type 11. When 0.1 M arsenic acid H3AsO4 in a 10 lit buffer solution of pH = 8, which of the following hold true ? K1 = 2.5 × 10–4, K2 = 5 × 10–8 and K3 = 2 × 10–13 for arsenic acid. (A) H3 AsO4 H2 AsO4 (B) H2 AsO4 HAsO24 (C) HAsO24 H2 AsO4 (D) AsO34 HAsO24 12. If one mole of H3POx is completely neutralized by 40g of NaOH, select the correct statement(s) : (A) x = 2 and acid is monobasic (B) x = 3 and acid is dibasic (C) x = 4 and acid is tribasic (D) x = 2 and acid does not form acid salt 13. Which of the following are true (A) 3s orbital is spherically symmetrical with two nodes (B) d x 2 y2 orbitals has lobes of electron density in XY plane along X and Y axis 6 PART TEST_01 (PAPER I) (C) The radial probability curve of 1s, 3p and 5d have one, two and three regions of maximum probability (D) 3d z2 has zero electron density in XY plane. 14. Which one of these graphs for an ideal gas having a fixed amount the arrow indication is /are correctly marked. P V P Increasing P decreasing decreasing Temperature Press. decreasing Volume Temp (A) (B) (C) (D) 0 Temp in K -273 tC V 0 0 1/V 15. Which of the following graphs are correct for ideal gases? T1 < T 2 T1 < T2 1 dN 1 dN du N (A) (B) . du N T2 K T1 K T1 K T2 K u u M2 < M 1 M1 < M 2 1 dN 1 dN du N . du N (C) . (D) M2 M2 M1 M1 u u Section – III Integer Type 16. The velocity of electron in a certain Bohr’s orbit of H – atom bears the ratio 1 : 275 to the velocity of light. What is the number of orbit ? 17. The ratio of wavelength for 2nd line of Balmer series and 1st line of Lyman series is : M 18. Fe3 Cl2 , if equivalent weight of FeCl2 is given as FeCl2 , for the above change. Then value of x is x ______. 19. Find the pH of a solution prepared by mixing 100 ml, 0.1 M Na 3PO4 and 200 ml, 0.1 M H3PO4. (given : pKa1 , pKa2 and pKa3 of H3PO4 are 4, 6 and 9 respectively.) 7 PART TEST_01 (PAPER I) 20. If Kc = 7.5 × 10–9 at 1000 K for the reaction N2 (g) + O2 (g) 2NO(g), If the Kp at 1000 K for the reaction 2NO (g) N2(g) + O2 (g) is expressed as a 10b then the value of b is _______ PART – C (Mathematics) Section – I Single Correct Choice Type 1. Let each corner of a cube is represented by + 1 or -1 arbitrarily and on each of the six faces of the cube write the product of the numbers written at the four corners of that face. Let S1, S2, …. S8 are the numbers written on the corners and P1, P2, ….. P6 are the product of the numbers written at the four corners of the face, then 8 6 total number of solution of the equation Si Pi 0 is i 1 i 1 (A) 0 (B) 1 (C) 2 (D) infinite many 2. Given 6 different toys of green colour, 5 different toys of blue colour and 4 different toys of red colour. Combination of toys that can be chosen taking atleast one green and one blue toys are (A) 31258 (B) 31248 (C) 31 (D) 63 k 1 x r 0 2r 3. If k 1 is a polynomial in x, p and q are any two value of k, then the roots of the equation 3x2 + px + 5q = x r 0 r 0 can not be (A) real (B) imaginary (C) rational (D) irrational 4. Let it be known that all roots of on equation x3 + px2 + qx + r = 0 are positive. The condition on its coefficient p, q, r so that the line segments of lengths equal to the roots are the sides of a triangle (A) p3 + 4pq + 8r < 0 (B) p3 – 4pq + 8r > 0 (C) (p3 – 4pq) (qr + 4pq) > 0 (D) none of these 5. If an A.P. a7 = 9 if a1a2a7 is least, the common difference is 13 23 33 (A) (B) (C) (D) none of these 20 50 20 6. Five cards are drawn from a pack of 52 cards. The probability of getting exactly 3 diamonds and 2 queens is 12 C2 3 C1 36 C1 12 C3 3 C2 12 C2 3 C2 36 C1 12 C3 3 C2 (A) 52 (B) 52 C5 C5 12 C1 3 C2 36 C1 12 C3 3 C2 12 C1 3 C2 36 C2 12 C2 3 C3 (C) 52 (D) 52 C5 C5 H1 2 H20 3 7. If H1 , H2, ……, H20 be 20 harmonic means between 2 and 3, then = H1 2 H20 3 (A) 20 (B) 21 (C) 40 (D) 38 8. The number of functions f from the set A = {0, 1, 2} into the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that ƒ i ƒ j for i < j and i, j A is 8 PART TEST_01 (PAPER I) (A) 8 C3 (B) 8 C3 2 8 C2 (C) 9 C3 (D) 10 C3 2013 9. If 1 x 2010 x 2011 x 2012 a0 a1 x a2 x 2 ......... an x n , then value of 1 1 1 1 a0 a1 a2 a3 a4 a5 a6 ....... is : 3 3 3 3 42013 8 42013 8 42013 9 42013 9 (A) (B) (C) (D) 9 9 8 8 Coefficient of x in 2 x 1 4 x 38 x 7 .............. 2100 x 2100 1 is 99 10. 1 1 (A) 24949 99 100 (B) 24949 101 100 2 2 1 1 (C) 25050 101 100 (D) 25050 99 100 2 2 Section – II One or More Than One Option Correct Type 11. Let f(x) = x² + ax + 8, a R and f(x) = 0 has roots and . Then (A) f(x) > 0 x R , then a 4 2 , 4 2 33 (B) , 1, 5 , then a , 4 2 15 33 (C) If only one root lies in (1, 5) then a 9, 5 (D) 0 can not lies between the roots of f(x) = 0 12. Let x n be a sequence of real numbers such that x1 2, xn1 xn2 xn 1 , n = 1, 2, 3….. Let 1 1 1 1 k ........ . Then x1 x 2 x 3 x1000 1 1 (A) k<1 (B) k>1 (C) k 1 (D) k 1 10001000 10001000 13. The number of ways in which three numbers in A.P. can be selected from 1, 2, 3, ……, n is n n 2 1 n 1 , when n is odd 2 (A) , when n is even (B) 4 4 n n 2 1 n 1 , when n is odd 2 (C) , when n is even (D) 2 2 9 PART TEST_01 (PAPER I) 14. If 3 terms are chosen randomly from the set {1, 2, 2 2, …. 2n} without replacement then the probability that they are in increasing geometric progression is 3 4 (A) n odd (B) n odd 2n 3n 1 3n 2n (C) n even (D) n even 2(n 2 1) n 4 2 15. 0 < c < b < a and the roots of of the equation cx2 + bx + a = 0 are imaginary, then α β 1 1 (A) α β (B) 2 α β 1 1 (C) 2 (D) none of these α β Section – III Integer Type 16. k and d (d being variable) are the nth term and common difference of an A.P. If the multiplication of (n – k 1)th, (n + 3)th term of an A.P is maximum then find the value of . d 17. Divide the unit square into 9 equal squares by means of two pairs of lines parallel to the sides. Now remove the central square. Treat the remaining 8 squares the same way and repeat the process n times. If 2 1 represents the area of all removed squares, such that , then find the value of n. 5 2 18. If a triangle is chosen at random inscribed in a fixed circle and if the probability that the orthocenter lies 1 inside circumcircle is then x equals ____________. x 19. If f(x) = a + bx + cx², where c > 0 and b² – 4ac < 0, then the area enclosed by the coordinate axes, the line x 1 = 2 and the curve y = f(x) is given by f(0) f(1) f(2) sq. unit, then is ___________. 3 m n mn 2m 2m 2n = 20. m 0 n 0 10 PART TEST_01 (PAPER I)
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