GATE Solved Question Papers for Production & Industrial Engineering [PI] by AglaSem.Com

SOLVED PAPERSGATE PRODUCTION AND INDUSTRIAL ENGINEERING (PI) aglaem .com A comprehensive study guide for GATE CONTENTS • Introduction • Question Paper Pattern • Design of Questions • Marking Scheme • Syllabus • Previous Year Solved Papers o Solved Question Paper 2014 o Answer Key 2014 o Solved Question Paper 2013 o Answer Key 2013 o Solved Question Paper 2012 o Answer Key 2012 Introduction The Graduate Aptitude Test in Engineering (GATE) is the all India level examination conducted by the Indian Institute of Science and seven Indian Institutes of Technology (IITs). A crucial part of GATE preparation is to solve and practice using previous year GATE papers. Solving previous year GATE papers help the candidate in understanding the exam pattern, knowing the level of difficulty of questions, and analyzing preparation. While attempting to solve any previous year GATE paper, it is advisable that it is done in a simulated test environment. This means, that the candidate sets a timer to countdown to test time, makes sure there is no other distraction, and then sits down to take the test as if he / she is in the exam hall. After attempting the paper, check how many questions you could get right in the first attempt. Analyse the strong and weak areas of preparation, and accordingly devise a study schedule or revision pattern. After going through those areas where in the first attempt could not do well, try the next paper. Almost all of the engineering colleges in India take admission in M.Tech courses on the basis of GATE scores. Apart from that, PSUs also recruit students directly on this basis. To score high in this elite examination is tough, but quite achievable. GATE Previous Year Solved Papers by _________________________________________________________ Question Paper Pattern In all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10 questions carrying a total of 15 marks are in General Aptitude (GA). In the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI, TF and XE, the Engineering Mathematics will carry around 13% of the total marks, the General Aptitude section will carry 15% of the total marks and the remaining percentage of the total marks is devoted to the subject of the paper. In the papers bearing the codes AR, CY, EY, GG, MA, PH and XL, the General Aptitude section will carry 15% of the total marks and the remaining 85% of the total marks is devoted to the subject of the paper. GATE would contain questions of two different types in various papers: (i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers and sections. These questions are objective in nature, and each will have a choice of four answers, out of which the candidate has to mark the correct answer(s). (ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. For these questions the answer is a real number, to be entered by the candidate using the virtual keypad. No choices will be shown for this type of questions. GATE Previous Year Solved Papers by ________________________________________________________ Design of Questions The questions in a paper may be designed to test the following abilities: (i) Recall: These are based on facts, principles, formulae or laws of the discipline of the paper. The candidate is expected to be able to obtain the answer either from his/her memory of the subject or at most from a one-line computation. (ii) Comprehension: These questions will test the candidate's understanding of the basics of his/her field, by requiring him/her to draw simple conclusions from fundamental ideas. (iii) Application: In these questions, the candidate is expected to apply his/her knowledge either through computation or by logical reasoning. (iv) Analysis and Synthesis: In these questions, the candidate is presented with data, diagrams, images etc. that require analysis before a question can be answered. A Synthesis question might require the candidate to compare two or more pieces of information. Questions in this category could, for example, involve candidates in recognising unstated assumptions, or separating useful information from irrelevant information. GATE Previous Year Solved Papers by __________________________________________________________ Marking Scheme For 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer. Likewise, for2-marks multiple-choice questions, 2/3 marks will be deducted for a wrong answer. There is no negative marking for numerical answer type questions. General Aptitude (GA) Questions In all papers, GA questions carry a total of 15 marks. The GA section includes 5 questions carrying 1 mark each (sub-total 5 marks) and 5 questions carrying 2 marks each (sub-total 10 marks). Question Papers other than GG, XE and XL These papers would contain 25 questions carrying 1 mark each (sub-total 25 marks) and 30 questions carrying 2 marks each (sub-total 60 marks). The question paper will consist of questions of multiple choice and numerical answer type. For numerical answer questions, choices will not be given. Candidates have to enter the answer (which will be a real number, signed or unsigned, e.g. 25.06, -25.06, 25, -25 etc.) using a virtual keypad. An appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors. GG (Geology and Geophysics) Paper Apart from the General Aptitude (GA) section, the GG question paper consists of two parts: Part A and Part B. Part A is common for all candidates. Part B contains two sections: Section 1 (Geology) and Section 2 (Geo-physics). Candidates will have to attempt questions in Part A and either Section 1 or Section 2 in Part B. Part A consists of 25 multiple-choice questions carrying 1-mark each (sub-total 25 marks and some of these may be numerical answer type questions). Each section in Part B (Section 1 and Section 2) consists of 30 multiple choice questions carrying 2 marks each (sub-total 60 marks and some of these may be numerical answer type questions). XE Paper (Engineering Sciences) GATE Previous Year Solved Papers by _________________________________________________________ In XE paper, Engineering Mathematics section (Section A) is compulsory. This section contains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each (sub- total 7 marks), and 4 questions carrying 2 marks each (sub-total 8 marks). Some questions may be of numerical answer type questions. Each of the other sections of the XE paper (Sections B through G) contains 22 questions carrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13 questions carrying 2 marks each (sub-total 26 marks). Some questions may be of numerical answer type. XL Paper (Life Sciences) In XL paper, Chemistry section (Section H) is compulsory. This section contains 15 questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks) and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be of numerical answer type. Each of the other sections of the XL paper (Sections I through M) contains 20 questions carrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10 questions carrying 2 marks each (sub-total 20 marks). Some questions may be of numerical answer type. Note on Negative Marking for Wrong Answers For a wrong answer chosen for the multiple choice questions, there would be negative marking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wrong answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a wrong answer. However, there is no negative marking for a wrong answer in numerical answer type questions. GATE Previous Year Solved Papers by _________________________________________________________ Syllabus for General Aptitude (GA) Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation. Syllabus for Production and Industrial Engineering (PI) ENGINEERING MATHEMATICS Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation. Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson,Normal and Binomial distributions. Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations. GENERAL ENGINEERING Engineering Materials: Structure and properties of engineering materials and their applications; effect of strain, strain rate and temperature on mechanical properties of GATE Previous Year Solved Papers by __________________________________________________________ metals and alloys; heat treatment of metals and alloys, its influence on mechanical properties. Applied Mechanics: Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium; strength of materials – stress, strain and their relationship, Mohr’s circle, deflection of beams, bending and shear stress, Euler’s theory of columns. Theory of Machines and Design: Analysis of planar mechanisms, cams and followers; governers and fly wheels; design of elements – failure theories; design of bolted, riveted and welded joints; design of shafts, keys, spur gears, belt drives, brakes and clutches. Thermal Engineering: Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, equations of continuity and momentum; thermodynamics – zeroth, first and second law of thermodynamics, thermodynamic system and processes, calculation of work and heat for systems and control volumes; air standard cycles; basics of internal combustion engines and steam turbines; heat transfer – fundamentals of conduction, convection and radiation, heat exchangers. PRODUCTION ENGINEERING Metal Casting: Casting processes – types and applications; patterns – types and materials; allowances; moulds and cores – materials, making, and testing; casting techniques of cast iron, steels and nonferrous metals and alloys; solidification; design of casting, gating and risering; casting inspection, defects and remedies. Metal Forming: Stress-strain relations in elastic and plastic deformation; concept of flow stress, deformation mechanisms; hot and cold working – forging, rolling, extrusion, wire and tube drawing; sheet metal working processes such as blanking, piercing, bending, deep drawing, coining and embossing; analysis of rolling, forging, extrusion and wire /rod drawing; metal working defects. Metal Joining Processes: Welding processes – manual metal arc, MIG, TIG, plasma arc, submerged arc, electroslag, thermit, resistance, forge, friction, and explosive welding;other joining processes – soldering, brazing, braze welding; inspection of welded joints, defects and remedies; introduction to advanced welding processes – ultrasonic, electron beam, laser beam; thermal cutting. GATE Previous Year Solved Papers by _________________________________________________________ Machining and Machine Tool Operations: Basic machine tools; machining processes- turning, drilling, boring, milling, shaping, planing, gear cutting, thread production, broaching, grinding, lapping, honing, super finishing; mechanics of machining – geometry of cutting tools, chip formation, cutting forces and power requirements, Merchant’s analysis; selection of machining parameters; tool materials, tool wear and tool life, economics of machining, thermal aspects of machining, cutting fluids, machinability; principles and applications of nontraditional machining processes – USM, AJM, WJM, EDM and Wire cut EDM, LBM, EBM, PAM, CHM, ECM. Tool Engineering: Jigs and fixtures – principles, applications, and design; press tools – configuration, design of die and punch; principles of forging die design. Metrology and Inspection: Limits, fits, and tolerances, interchangeability, selective assembly; linear and angular measurements by mechanical and optical methods, comparators; design of limit gauges; interferometry; measurement of straightness, flatness, roundness, squareness and symmetry; surface finish measurement; inspection of screw threads and gears; alignment testing of machine tools. Powder Metallurgy: Production of metal powders, compaction and sintering. Polymers and Composites: Introduction to polymers and composites; plastic processing – injection, compression and blow molding, extrusion, calendaring and thermoforming; molding of composites. Manufacturing Analysis: Sources of errors in manufacturing; process capability; tolerance analysis in manufacturing and assembly; process planning; parameter selection and comparison of production alternatives; time and cost analysis; manufacturing technologies – strategies and selection. Computer Integrated Manufacturing: Basic concepts of CAD,CAM, CAPP, cellular manufacturing, NC, CNC, DNC, Robotics, FMS, and CIM. INDUSTRIAL ENGINEERING Product Design and Development: Principles of good product design, tolerance design; quality and cost considerations;product life cycle; standardization, simplification, diversification, value engineering and analysis, concurrent engineering. Engineering Economy and Costing: Elementary cost accounting and methods of depreciation; break-even analysis, techniques for evaluation of capital investments, financial statements. GATE Previous Year Solved Papers by _________________________________________________________ Work System Design: Taylor’s scientific management, Gilbreths’s contributions; productivity – concepts and measurements;methodstudy, micro-motion study, principles of motion economy; work measurement – stop watch time study, work sampling, standard data, PMTS; ergonomics; job evaluation, merit rating, incentive schemes, and wage administration; business process reengineering. Facility Design: Facility location factors and evaluation of alternate locations; types of plant layout and their evaluation; computer aided layout design techniques; assembly line balancing; materials handling systems. Production Planning and Inventory Control: Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; aggregate production planning; master production scheduling; MRP and MRP-II; order control and flow control; routing, scheduling and priority dispatching; push and pull production systems, concept of JIT manufacturing system; logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic and probabilistic inventory models, quantity discount; perpetual and periodic inventory control systems. Operation Research: Linear programming – problem formulation, simplex method, duality and sensitivity analysis; transportation and assignment models; network flow models, constrained optimization and Lagrange multipliers; simple queuing models; dynamic programming; simulation – manufacturing applications; PERT and CPM, time- cost trade-off, resource leveling. Quality Management: Quality – concept and costs, quality circles, quality assurance; statistical quality control, acceptance sampling, zero defects, six sigma; total quality management; ISO 9000; design of experiments – Taguchi method. Reliability and Maintenance: Reliability, availability and maintainability; distribution of failure and repair times; determination of MTBF and MTTR, reliability models; system reliability determination; preventive maintenance and replacement, total productive maintenance – concept and applications. Management Information System: Value of information; information storage and retrieval system– database and data structures; knowledge based systems. Intellectual Property System: Definition ofintellectual property, importance of IPR; TRIPS and its implications, patent, copyright, industrial design and trademark. GATE Previous Year Solved Papers by _________________________________________________________ GATE Previous Year Solved Papers Production & Industrial Engineering - PI 2012 - 14 GATE Previous Year Solved Papers by ___________________________________________________________ Duration: 180 minutes Maximum Marks: 100 Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: “I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition”. GATE Previous Year Solved Papers by _________________________________________________________ GATE 2014 Solved Paper Product ion & Indust rial Engineering - PI Q. 1 – Q. 5 carry one mark each. Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease short-term memory loss. (A) experienced (B) has experienced (C) is experiencing (D) experiences Q.2 Choose the most appropriate word from the options given below to complete the following sentence. ____________ is the key to their happiness; they are satisfied with what they have. (A) Contentment (B) Ambition (C) Perseverance (D) Hunger Q.3 Which of the following options is the closest in meaning to the sentence below? “As a woman, I have no country.” (A) Women have no country. (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries. (D) Women of all countries have equal legal rights. Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ____ years. Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate? (A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years Q. 6 – Q. 10 carry two marks each. Q.6 In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the group. Which of the following statements is/are required to find the eldest child in the group? Statements 1. Shiv is younger to Riaz. 2. Shiv is elder to Som. (A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statements 1 and 2 are both required to determine the eldest child. (D) Statements 1 and 2 are not sufficient to determine the eldest child. GATE 2014 General Aptitude - GA GATE Previous Year Solved Papers by Q.7 Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is: (A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below. The pie chart for exports shows the quantity of each item as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram? (A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1 Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? (A) 1 (B) √2 (C) √3 (D) 2 Q.10 10% of the population in a town is HIV + . A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV + individuals 95% of the time, and HIV − individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _______ END OF THE QUESTION PAPER Item 1 11% Item 2 20% Item 3 19% Item 4 22% Item 5 12% Item 6 16% Exports Item 1 12% Item 2 20% Item 3 23% Item 4 6% Item 5 20% Item 6 19% Revenues GATE 2014 General Aptitude - GA GATE Previous Year Solved Papers by Q. 1 – Q. 25 carry one mark each. Q.1 The system of equations, given below, has x+2y+4z=2 4x+3y+z=5 3x+2y+3z=1 (A) a unique solution (B) two solutions (C) no solution (D) more than two solutions Q.2 Directional derivative of 2 2xz y ϕ = − , at the point (1, 3, 2), becomes maximum in the direction of (A) 4 2 3 i j k + − (B) 4 6 2 i j k − + (C) 2 6 2 i j k − + (D) 4 6 2 i j k − − Q.3 A metallic sphere of 0.1 m diameter has a thermal conductivity of 10 W/m-K. If the fluid flowing around it has a heat transfer coefficient of 10 W/m 2 -K and thermal conductivity of 0.4 W/m-K, the value of Biot number is ______ Q.4 A quantitative measure of maintainability is (A) Downtime (B) Mean Time Between Failure (C) Mean Time To Repair (D) System availability Q.5 Which one of the following techniques is used to analyze the cause and effect of product failure? (A) Quality Function Deployment (B) Fault Tree Analysis (C) Value Analysis (D) Failure Mode and Effect Analysis Q.6 As the product passes through different stages of product life cycle, the product variety (A) increases (B) decreases and then increases (C) remains the same (D) decreases GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.7 A machine has been purchased for Rs.100,000 and its useful life is estimated to be 10 years. Its scrap value at the end of 10 years is estimated as Rs.20,000. If the depreciation is determined using the declining balance method, the value of depreciation (in Rs.) during the first year is _______ Q.8 A company wants to determine the proportion of time workers are idle. In a pilot study, the proportion of idle time was found to be 0.16. If the company wants to be 95% confident (z-value = 1.96) that the estimated value is within 0.03 of the true proportion, the number of observations required in the study should be _______ Q.9 A manufacturing plant, working in 2 shifts of 8 hrs each, produces 30,000 switch boards using a set of 7 workstations in series. The cycle time, in seconds, is _______ Q.10 A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12, respectively. The standard error of mean is _______ Q.11 The diameter of a shaft must be within a tolerance of 0.02 of the nominal diameter. Which control chart is useful to determine that the process is in statistical control? (A) p chart (B) c chart (C) X and R chart (D) U chart Q.12 Which one of the following is not a characteristic of JIT manufacturing system? (A) Reduction of lot sizes (B) Efficient use of buffer inventory (C) Small but frequent deliveries (D) Higher productivity Q.13 Relationship between Young’s Modulus (E), Shear Modulus (G), and Poisson’s Ratio (μ), for a material obeying the Hooke’s Law, is (A) = (2+μ) (B) = 2 (1+μ) (C) (1 ) E G µ = + (D) 2 (1 ) E G µ = + GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.14 For a metal alloy, which one of the following descriptions relates to the stress-relief annealing process? (A) Heating the workpiece material above its recrystallization temperature, soaking and then cooling in still air (B) Heating the workpiece material below its recrystallization temperature, holding for some time and then furnace cooling (C) Heating the workpiece material up to its recrystallization temperature and then rapid cooling (D) Heating the workpiece up to its recrystallization temperature and cooling to room temperature alternately for a few cycles Q.15 Generative Approach of Computer Aided Process Planning is NOT based on (i) part coding using Group Technology (ii) part feature recognition and extraction (iii) database of standard process plans for part families (iv) geometric modelling of part (A) (i) and (ii) (B) (i) and (iii) (C) (i),(ii) and (iii) (D) (i), (ii) and (iv) Q.16 Which one of the following methods is NOT used for producing metal powders? (A) Atomization (B) Compaction (C) Machining and grinding (D) Electrolysis Q.17 In an open loop, point-to-point controlled CNC drilling machine, a stepper motor, producing 200 angular steps per revolution, drives the table of a drilling machine by one angular step per each pulse generated by a pulse generator (shown in figure). Each angular step moves the table by one Basic Length Unit (BLU) along X axis with a lead screw having a pitch of 4 mm. If the frequency of pulse generator is doubled, the BLU will (A) become double of previous value (B) become half of previous value (C) remain the same (D) become zero Pulse generator pulses Driver Stepper motor CNC drill table X axis GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.18 A spindle speed of 300 rpm and a feed of 0.3 mm/revolution are chosen for longitudinal turning operation on an engine lathe. In finishing pass, roughness on the work surface can be reduced by (A) reducing the spindle speed (B) increasing the spindle speed (C) reducing the feed of tool (D) increasing the feed of tool Q.19 Chills are used in casting moulds to (A) achieve directional solidification (B) reduce the roughness of top surface of the cast product (C) increase the solidification time (D) reserve excess molten metal Q.20 A moving mandrel is used in (A) wire drawing (B) forging (C) tube drawing (D) bending Q.21 Brazing and Soldering are (A) plastic joining methods (B) homogeneous joining methods (C) autogenous joining methods (D) heterogeneous joining methods Q.22 Match the following: Group I (Mechanism) Group II (Machines) P Quick return 1 Lathe Q Apron 2 Shaping R Intermittent indexing 3 Gear hobbing S Differential mechanism 4 Milling (A) P1-Q2-R4-S3 (B) P2-Q1-R4-S3 (C) P4-Q1-R2-S3 (D) P2-Q3-R1-S4 GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.23 Reaming is a process used for (A) creating a circular hole in metals (B) cutting a slot on the existing hole surface (C) finishing an existing hole surface (D) making non-circular holes in metals Q.24 Find the correct combination of manufacturing processes to produce the part, shown in figure, from a blank (holes shown are with square and circular cross-sections). (A) Drilling and milling on column and knee type universal milling machine (B) Die-sinking and CNC Wire-cut EDM process (C) Die-sinking and CNC drilling (D) CNC Wire-cut EDM process only Q.25 In an open die forging, a circular disc is gradually compressed between two flat platens. The exponential decay of normal stress on the flat face of the disc, from the center of the disc towards its periphery, indicates that (A) there is no sticking friction anywhere on the flat face of the disc (B) sticking friction and sliding friction co-exist on the flat face of the disc (C) the flat face of the disc is frictionless (D) there is only sticking friction on the flat face of the disc GATE 2014 Production - PI GATE Previous Year Solved Papers by Q. 26 – Q. 55 carry two marks each. Q.26 If 3 2 4 2x y z ϕ = then 2 ϕ ∇ is (A) 2 4 2 4 3 2 3 12 4 20 xy z x z x y z + + (B) 2 2 3 4 3 2 2 2 4 24 x y z x z x y z + + (C) 2 4 3 4 3 2 2 12 4 24 xy z x z x y z + + (D) 2 2 4 3 2 2 4 4 24 xy z x z x y z + + Q.27 Using the Simpson’s 1/3 rd rule, the value of ydx ∫ computed, for the data given below, is _______ x 1 3 5 y 2 6 4 Q.28 If the equation sin() = 2 is solved by Newton Raphson’s method with the initial guess of x=1, then the value of x after 2 iterations would be _______ Q.29 If 2 kg mass of water, with a specific heat of 4.18 kJ/kg-K, is heated from 20°C to 40°C in an open container, then the change in entropy of water, in kJ/K, is ______ Q.30 A gas at a pressure of 500 kPa and volume of 0.75 m 3 is contained in a cylinder-piston assembly. When the piston moves slowly in the cylinder, the pressure inside the cylinder varies as V – 1.2 . If the final volume of gas becomes doubled, then the work done by the gas, in kJ, is _______ Q.31 Two geometrically identical metallic bars are joined end to end (as shown in Fig.). Bars P and Q have thermal conductivities of 5 W/m-K and 10 W/m-K respectively. The free end of the Bar P is kept at 40°C, while that of Bar Q is at 10°C. The junction temperature (in °C) for steady state heat flow is _______ Q.32 A metallic sphere of 1 kg mass, with surface area of 0.0314 m 2 , is maintained at an initial temperature of 50°C. The fluid circulating around the sphere is maintained at a temperature of 10°C. Specific heat of metallic sphere is 314 J/kg-K and the heat transfer coefficient between the fluid and the sphere is 10 W/m 2 -K. The time taken (in seconds) for the sphere to cool down to 20°C is ________ GATE 2014 Production - PI GATE Previous Year Solved Papers by PI 7/12 Q.33 An element, shown below, is subjected to stresses: σ x = 5 kN/mm 2 , σ y = 3 kN/mm 2 and τ = 1 kN/mm 2 . The magnitudes and direction of principal stresses σ 1 , σ 2 (in kN/mm 2 ) and φ (in degrees) are (A) 5.41, 2.58, –22.5 (B) 5.41, 2.58, –45 (C) 5.0, 3.0, –22.5 (D) 4.0, 4.0, –22.5 Q.34 Each axis of NC machine is driven by a stepper motor drive with a lead screw. The pitch of lead screw is p mm. The step angle of stepper motor per pulse input is α degrees/pulse. The ratio of gear drive in stepper motor drive is g (number of turns of the motor for each single turn of the lead screw). The number of pulses required to achieve a linear movement of x mm is (A) 360 g x p α (B) 360g x p (C) 360 g x p (D) 360g x pα Q.35 A uniformly distributed load (q) of 1500 N/m is applied on a simply supported beam LMN with an overhang of 0.5 m. Which one of the following statements is FALSE? (A) Reaction forces at L and M are 1 kN and 2 kN (B) Bending moment is zero at the points L, N and at a point in between L and M (C) The bending moment is zero at points L and N only (D) The shear force is zero at points L, N and at a point in between L and M GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.36 A CNC instruction G91G01X30Y40F100 commands the movement of tool along the path at a feed rate of 100 mm/min (G91- incremental format and G01- linear interpolation). The feed rate of the tool (in mm/min) along the X axis will be _______ Q.37 Elastic moduli of a fibre reinforced plastic composite and fibres are 200 GPa and 400 GPa, respectively. The longitudinal fibres are taking up 50% of the load. Assuming the area fraction equal to the volume fraction, the volume fraction of the fibres will be _______ Q.38 The processing times and the due dates of 4 independent jobs processed by a single machine in a shop are given in the table. The average lateness of the jobs (in days) following the Shortest Processing Time (SPT) rule is _______ Job Processing Time (in days) Due Date (in days) 1 4 6 2 7 9 3 2 18 4 8 15 Q.39 The annual requirement of a raw material item is 10,000 units. The holding cost of inventory for the item is 80 paise per unit per year and the ordering cost is Rs. 40 per order. The order quantity presently is 800 units per order. Assume that there are no other costs. Which one of the following observations is CORRECT? (A) The order quantity is optimal and total ordering cost is equal to total holding cost. (B) The order quantity is optimal and total ordering cost is more than total holding cost. (C) The order quantity is not optimal and total ordering cost is equal to total holding cost. (D) The order quantity is not optimal and total ordering cost is more than total holding cost. Q.40 In a single-server queuing system, arrivals are Poisson distributed with a mean of 16 per hour and the exponential service time is 3 minutes per person on the average. What would be the expected number of persons in the queue (Lq) for the queue disciplines of First-come-first-serve (FCFS) and Last-come-first serve (LCFS)? (A) 4.0, 4.0 (B) 4.0, 3.2 (C) 3.2, 4.0 (D) 3.2, 3.2 GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.41 A project consisting of five activities needs crashing. The details of crashing that was carried out are given in the table. If the overhead cost of the project is Rs. 200 per day, then the net change in project cost (in Rs.) because of crashing is _______ Activity Normal Time (days) Shortest Time (days) Cost in Rs. for Reduction/day Actually Crashed by (days) 1-2 6 4 100 1 day 1-3 7 5 100 2 days 1-4 10 7 100 1 day 2-4 4 3 200 Not Crashed 3-4 5 4 200 1 day Q.42 Two systems, P and Q, contain 3 components each. Reliability of the components is measured for 1000 hours operations and time-to-failure distributions for all the components are found to be exponential. System P components are connected in a series parallel structure with each component having a reliability of 0.8. System Q components, on the other hand, are connected in series with each component having a reliability of 0.9. See the configuration of the systems below. The reliabilities of System P and System Q will be respectively (A) 0.768, 0.729 (B) 0.512, 0.729 (C) 0.5, 0.271 (D) 0.232, 0.271 Q.43 Marks obtained by 100 students in an examination are given in the table. Sl. No. Marks Obtained Number of Students 1. 25 20 2. 30 20 3. 35 40 4. 40 20 What would be the mean, median, and mode of the marks obtained by the students? (A) Mean 33; Median 35; Mode 40 (B) Mean 35; Median 32.5; Mode 40 (C) Mean 33; Median 35; Mode 35 (D) Mean 35; Median 32.5; Mode 35 0.8 0.8 0.8 System P System Q 0.9 0.9 0.9 GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.44 In a given day in the rainy season, it may rain 70% of the time. If it rains, chance that a village fair will make a loss on that day is 80%. However, if it does not rain, chance that the fair will make a loss on that day is only 10%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day? (A) 3/10 (B) 9/11 (C) 14/17 (D) 27/41 Q.45 For the linear programming problem given below, find the number of feasible corner point solutions. Is the optimal solution degenerate? Maximize z = 2x 1 + 3x 2 Subject to: x 1 + 2x 2 ≤ 60; 2x 1 + x 2 ≤ 30; x 1 – x 2 ≥ – 10; x 1 ≥ 0; x 2 ≥ 0 (A) 4; No (B) 4; Yes (C) 5; No (D) 5; Yes Q.46 A manufacturing company must select a process for its new product, VS-5, from among two alternatives. The following cost data have been gathered. Cost Process X Process Y Fixed Rs. 10,000 Rs. 40,000 Variable Rs. 5/unit Rs. 2/unit If the objective is to select a process with the least total cost for a given demand, which one of the following is the most appropriate choice? (A) Below 10,000 units, Process X; Above 10,000 units, Process Y (B) Below 10,000 units, Process Y; Above 10,000 units, Process X (C) Below 20,000 units, Process X; Above 20,000 units, Process Y (D) Below 20,000 units, Process Y; Above 20,000 units, Process X Q.47 The following data refers to a manufacturing plant. Current Year Previous Year Revenue generated (in Rs.) 200,000 220,000 Number of units produced 1000 1200 Piece rate of workers (in Rs.) 22 18 Assuming the previous year to be the base year, the labor productivity index for this plant is _______ GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.48 A manufacturing company producing ball bearings has conducted a time study for 10 cycles of a job consisting of three elements. The details are shown in the table below. Job elements Average elemental time (in minutes) Performance rating factor 1 0.12 0.8 2 0.34 1.1 3 0.48 1.2 If the permissible allowance is 15%, then the standard time (in minutes) is _______ Q.49 A control chart for number of non-conformities per unit is to be constructed for a manufacturing process. Sixteen non-conformities were recorded while inspecting 30 units. How should the Upper Control Limit (UCL) and the Lower Control Limit (LCL) be set for this control chart? (A) UCL = 1.81, LCL = 0.70 (B) UCL = 2.71, LCL = 0.00 (C) UCL = 0.533, LCL = – 0.533 (D) UCL = 3.10, LCL = – 1.46 Q.50 For a given volume of a riser, if the solidification time of the molten metal in riser needs to be quadrupled, the surface area of the riser should be made (A) one-fourth (B) half (C) double (D) four times Q.51 A 80 mm thick steel plate with 400 mm width is rolled to 40 mm thickness in 4 passes with equal reduction in each pass, by using rolls of 800 mm diameter. Assuming the plane-strain deformation, what is the minimum coefficient of friction required for unaided rolling to be possible? (A) 0.111 (B) 0.158 (C) 0.223 (D) 0.316 Q.52 In an arc welding operation, carried out with a power source maintained at 40 volts and 400 amperes, the consumable electrode melts and just fills the gap between the metal plates to be butt-welded. The heat transfer efficiency for the process is 0.8, melting efficiency is 0.3 and the heat required to melt the electrode is 20 J/mm 3 . If the travel speed of the electrode is 4 mm/s, the cross-sectional area, in mm 2 , of the weld joint is _______ Q.53 A hard ceramic marble, having density (ρ) of 3000 kg/m 3 and diameter (d) of 0.025 m, is dropped accidentally from a static weather balloon at a height of 1 km above the roof of a greenhouse. The flow stress of roof material (σ) is 2.5 GPa. The marble hits and creates an indentation on the roof. Assume that the principle of creation of indentation is the same as that in case of abrasive jet machining (AJM). The acceleration due to gravity (g) is 10 m/s 2 . If V is the velocity, in m/s, of the marble at the time it hits the greenhouse, the indentation depth ( 1000 6 d V ρ δ σ = × × × ), in mm, is _______ GATE 2014 Production - PI GATE Previous Year Solved Papers by Q.54 An HSS drill of 20 mm diameter with 5 mm cone height is used to drill a through hole in a steel work-piece of 50 mm thickness. Cutting speed of 10 m/min and feed rate of 0.3 mm/rev are used. The drilling time, in seconds, neglecting the approach and over travel, is _______ Q.55 The alignment test “Spindle square with base plate” is applied to the radial drilling machine. A dial indicator is fixed to the cylindrical spindle and the spindle is rotated to make the indicator touch the base plate at different points. This test inspects whether the (A) spindle vertical feed axis is perpendicular to the base plate (B) axis of symmetry of the cylindrical spindle is perpendicular to the base plate (C) axis of symmetry, the rotational axis and the vertical feed axis of the spindle are all coincident (D) spindle rotational axis is perpendicular to the base plate END OF THE QUESTION PAPER GATE 2014 Production - PI GATE Previous Year Solved Papers by GATE 2014 - Answer Keys General Aptitude– GA Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range 1 D 5 A 9 C 2 A 6 A 10 0.48 to 0.49 3 C 7 C 4 25 to 25 8 D Production & Industrial Engineering Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range 1 A 20 C 39 D 2 B 21 D 40 D 3 0.1 to 0.1 22 B 41 0 to 0 4 C 23 C 42 A 5 D 24 B 43 C 6 D 25 A 44 D 7 14800 to 15000 26 C 45 A 8 574 to 574 27 20 to 20 46 A 9 1.9 to 2.0 28 0.86 to 0.88 47 0.89 to 0.90 10 1.2 to 1.2 29 0.54 to 0.56 48 1.20 to 1.21 11 C 30 240 to 250 49 B 12 B 31 20 to 20 50 B 13 D 32 1382 to 1390 51 B 14 B 33 A 52 48 to 48 15 B 34 D 53 1.56 to 1.60 16 B 35 C 54 68 to 70 17 C 36 60 to 60 55 D 18 C 37 0.30 to 0.34 19 A 38 2.5 to 2.5 GATE Previous Year Solved Papers by __________________________________________________________ Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not PI, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 16 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number PI GATE Previous Year Solved Papers by GATE 2013 Solved Paper Product ion & Indust rial Engineering - PI Q.1 to Q.25 carry one mark each. Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, respectively. The demand for the item is 500 units. To break even, the unit price of the items in Rs. should be (A) 50 (B) 75 (C) 90 (D) 100 Q.2 Therbligs refer to the (A) basic types of fixtures used in machining. (B) fundamental motions used in manual work. (C) basic types of waste in manufacturing process. (D) fundamental types of material handling systems. Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is (A) 3 (B) 4 (C) 5 (D) 6 Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The shear strength of aluminum is 80 MPa. The minimum punching force required in kN is (A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is (A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 Q.6 Match the CORRECT pairs. Processes Characteristics / Applications P. Friction Welding 1. Non-consumable electrode Q. Gas Metal Arc Welding 2. Joining of thick plates R. Tungsten Inert Gas Welding 3. Consumable electrode wire S. Electroslag Welding 4. Joining of cylindrical dissimilar materials (A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 (C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3 Q.7 In a rolling process, the state of stress of the material undergoing deformation is (A) pure compression (B) pure shear (C) compression and shear (D) tension and shear Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 ≤ x ≤ L), through a plane wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement. (A) The direction of heat transfer will be from the surface at 100°C to the surface at 0°C. (B) The maximum temperature inside the wall must be greater than 100°C. (C) The temperature distribution is linear within the wall. (D) The temperature distribution is symmetric about the mid-plane of the wall. Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.9 A cylinder contains 5 m 3 of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is (A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2 Q.10 A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker- rocker) mechanism is (A) PQ (B) QR (C) RS (D) SP Q.11 Let X be a normal random variable with mean 1 and variance 4. The probability P{X<0} is (A) 0.5 (B) greater than zero and less than 0.5 (C) greater than 0.5 and less than 1.0 (D) 1.0 Q.12 Choose the CORRECT set of functions, which are linearly dependent. (A) x sin , 2 sin x and 2 cos x (B) cos x , x sin and x tan (C) cos 2x , 2 sin x and 2 cos x (D) cos 2x , x sin and x cos Q.13 The eigenvalues of a symmetric matrix are all (A) complex with non-zero positive imaginary part (B) complex with non-zero negative imaginary part (C) real (D) pure imaginary Q.14 The partial differential equation 2 2 x u x u u t u ∂ ∂ = ∂ ∂ + ∂ ∂ is a (A) linear equation of order 2 (B) non-linear equation of order 1 (C) linear equation of order 1 (D) non-linear equation of order 2 Q.15 Match the CORRECT pairs. Numerical Integration Scheme Order of Fitting Polynomial P. Simpson’s 3/8 Rule 1. First Q. Trapezoidal Rule 2. Second R. Simpson’s 1/3 Rule 3. Third (A) P-2, Q-1, R-3 (B) P-3, Q-2, R-1 (C) P-1, Q-2, R-3 (D) P-3, Q-1, R-2 Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.16 A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from 1 E to 2 E along the length of the rod, the normal stress developed at the section-SS is (A) A P (B) ( ) ( ) 2 1 2 1 E E A E E P + − (C) 1 2 AE PE (D) 2 1 AE PE Q.17 For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop p ∆ over a length L and the wall shear stress w τ are related by (A) L D p w 4 ∆ = τ (B) 2 2 4L D p w ∆ = τ (C) L D p w 2 ∆ = τ (D) D L p w ∆ = 4 τ Q.18 For a ductile material, toughness is a measure of (A) resistance to scratching (B) ability to absorb energy upto fracture (C) ability to absorb energy till elastic limit (D) resistance to indentation Q.19 A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same material, which is 8 times heavier than the original casting, will be (A) 10 (B) 20 (C) 24 (D) 40 Q.20 A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm 3 /s is (A) 160 (B) 167.6 (C) 1600 (D) 1675.5 Q.21 In the 3-2-1 principle of fixture design, 3 refers to the number of (A) clamps required (B) locators on the primary datum face (C) degrees of freedom of the workpiece (D) operations carried out on the primary datum face Q.22 In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to (A) −1 (B) zero (C) 0.5 (D) 1 S P P S L L/2 E 1 E 2 Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.23 A company manufactures 1000 toys every day. On an average, 10% of the toys are defective and 40% of the defective toys can be reworked into defect-free ones. The average number of defect-free toys manufactured daily is (A) 900 (B) 920 (C) 940 (D) 960 Q.24 The type of control chart used to monitor the amount of dispersion in a sample is (A) c-chart (B) p-chart (C) x -chart (D) R-chart Q.25 Which one of the following is modeled based on adaptation capabilities of biological systems? (A) Relational database (B) Fuzzy system (C) Simulated annealing algorithm (D) Genetic algorithm Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.26 to Q.55 carry two marks each. Q.26 A company plans to purchase a machine whose uptime needs to be atleast 95%. They have shortlisted two models of the machine with the following operational characteristics: Machine MTBF (hr) MTTR (hr) Model M 60 4 Model N 48 2 The company should buy (A) only Model M (B) only Model N (C) either Model M or N (D) neither Model M nor N Q.27 A manufacturer produces bars designed to be of 10 mm diameter with a tolerance of ±0.1 mm. Historical data indicates that manufactured bars have an average diameter of 9.98 mm with a standard deviation of 0.15 mm. The process capability index is (A) 0.08 (B) 0.12 (C) 0.18 (D) 0.27 Q.28 Let (P) denote the linear programming formulation of a transportation problem with m sources and n destinations. Then, the dual linear program of (P) has (A) n m× variables and n m× constraints (B) n m× variables and n m+ constraints (C) n m+ variables and n m+ constraints (D) n m+ variables and n m× constraints Q.29 Following data refers to an automat and a center lathe, which are being compared to machine a batch of parts in a manufacturing shop. Automat Center Lathe Machine Set-up Time in min 120 30 Machine Set-up Cost in Rs./min 800 150 Machining Time per piece in min 2 25 Machining Cost in Rs./min 500 100 Automat will be economical if the batch size exceeds (A) 28 (B) 32 (C) 61 (D) 75 Q.30 Cylindrical pins of 020 . 0 010 . 0 25 + + mm diameter are electroplated in a shop. Thickness of the plating is 0 . 2 30 ± micron. Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is (A) 25.042 (B) 25.052 (C) 25.074 (D) 25.084 Q.31 During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be (A) 0.11 (B) 0.23 (C) 0.30 (D) 0.52 Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.32 Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Specific enthalpy (kJ/kg) Velocity (m/s) Inlet steam condition 3250 180 Exit steam condition 2360 5 The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potential energy of steam, the power developed in kW by the steam turbine per kg of steam flow rate, is (A) 901.2 (B) 911.2 (C) 17072.5 (D) 17082.5 Q.33 A simply supported beam of length L is subjected to a varying distributed load sin (3π x/L) Nm −1 , where the distance is measured from the left support. The magnitude of the vertical reaction force in N at the left support is (A) zero (B) π 3 L (C) π L (D) π L 2 Q.34 The probability that a student knows the correct answer to a multiple choice question is 3 2 . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 4 1 . Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is (A) 3 2 (B) 4 3 (C) 6 5 (D) 9 8 Q.35 The solution to the differential equation 0 2 2 = − dx du k dx u d where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is (A) L x U u = (B)         − − = kL kx e e U u 1 1 (C)         − − = − − kL kx e e U u 1 1 (D)         + + = kL kx e e U u 1 1 Q.36 The value of the definite integral 1 e x ∫ ( ) dx x ln is (A) 9 2 9 4 3 + e (B) 9 4 9 2 3 − e (C) 9 4 9 2 3 + e (D) 9 2 9 4 3 − e Q.37 The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors. dA S ) . ( 4 1 ∫∫ n F where S is the sphere, 1 2 2 2 = + + z y x and n is the outward unit normal vector to the sphere. The value of the surface integral is (A) π (B) 2π (C) 4 3π (D) 4π Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.38 The function ( ) t f satisfies the differential equation 0 2 2 = + f dt f d and the auxiliary conditions, 4 ) 0 ( , 0 ) 0 ( = = dt df f . The Laplace transform of ) (t f is given by (A) 1 2 + s (B) 1 4 + s (C) 1 4 2 + s (D) 1 2 4 + s Q.39 A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg-m 2 is (A) 25 (B) 50 (C) 100 (D) 125 Q.40 A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is (A) 83 (B) 125 (C) 167 (D) 501 Q.41 Two cutting tools are being compared for a machining operation. The tool life equations are: Carbide tool: 3000 6 . 1 = VT HSS tool: 200 6 . 0 = VT where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher tool life if the cutting speed in m/min exceeds (A) 15.0 (B) 39.4 (C) 49.3 (D) 60.0 Q.42 In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be (A) (7.5, 5) (B) (10, 5) (C) (7.5, −5) (D) (10, −5) plate width w = 200 mm plate thickness t = 5 mm number of rivets n = 3 rivet diameter d r = 10 mm rivet hole diameter d h = 11 mm allowable tensile stress of plate σ p = 200 MPa allowable bearing stress of rivet σ c = 150 MPa P t t w w P Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.43 In water jet machining, the water jet is issued through a 0.3 mm diameter orifice at a pressure of 400 MPa. The density of water is 1000 kg/m 3 . The coefficient of discharge is 1.0. Neglecting all losses during water jet formation through the orifice, the power of the water jet in kW is (A) 25.3 (B) 50.6 (C) 75.9 (D) 101.2 Q.44 A linear programming problem is shown below. Maximize 3x + 7y Subject to 3x + 7y ≤ 10 4x + 6y ≤ 8 x, y ≥ 0 It has (A) an unbounded objective function (B) exactly one optimal solution (C) exactly two optimal solutions (D) infinitely many optimal solutions Q.45 Consider a two machine flow shop where jobs are first processed in Machine X and then in Machine Y, in the same sequence. The processing times of four jobs (1, 2, 3 and 4) on the machines are: Job Processing time (in min) Machine X Machine Y 1 6 5 2 3 4 3 7 6 4 5 4 The sequence of jobs on the machines that minimizes make span is (A) 2−3−1−4 (B) 1−2−3−4 (C) 2−1−3−4 (D) 3−1−4−2 Q.46 Match the CORRECT pairs. Group I Group II P. Man-machine chart 1. Determines standard time of jobs Q. Learning curve 2. Finds the preferred method of doing work R. Time study 3. Measures work improvement S. Motion study 4. Shows idle times (A) P-2, Q-3, R-4, S-1 (B) P-3, Q-2, R-4, S-1 (C) P-4, Q-1, R-3, S-2 (D) P-4, Q-3, R-1, S-2 Q.47 A firm produces 120 units of product in every 8 hour shift. Four operations as given below are needed to manufacture each unit of product. Operation Precedence Processing time (in min) P none 1 Q P 2 R P 4 S Q, R 3 The above operations are to be assigned to workstations, such that one or more operations are performed in each workstation. Only one unit of product will be processed in each workstation at a time. The minimum number of workstations that will achieve the production target, without violating the precedence constraints, is (A) 1 (B) 2 (C) 3 (D) 4 Production - PI GATE 2013 GATE Previous Year Solved Papers by Common Data Questions Common Data for Questions 48 and 49: A disc of 200 mm outer and 80 mm inner diameter is faced at a feed of 0.1 mm/rev with a depth of cut of 1 mm. The facing operation is undertaken at a constant cutting speed of 90 m/min in a CNC lathe. The main (tangential) cutting force is 200 N. Q.48 Neglecting the contribution of the feed force towards cutting power, the specific cutting energy in J/mm 3 is (A) 0.2 (B) 2 (C) 200 (D) 2000 Q.49 Assuming approach and over-travel of the cutting tool to be zero, the machining time in min is (A) 2.93 (B) 5.86 (C) 6.66 (D) 13.33 Common Data for Questions 50 and 51: The demand for soap at a retailer is 40 kg per day. The retailer buys soap from a company in bulk at the cost of Rs. 50 per kg. The retailer incurs a cost of Rs. 200 to place an order to the company, and a holding cost of Rs. 0.1 per kg per day to store the soap. The lead time between the placing and receiving of orders is 3 days. The retailer’s current ordering policy is to order 200 kg every 5 days. Q.50 To avoid stock out situations, the retailer needs to place orders when the inventory level (in kg) drops to (A) 40 (B) 60 (C) 80 (D) 120 Q.51 If the retailer uses an optimum order policy to minimize the total cost, the saving in Rs. in the total cost as compared to the current policy will be (A) 10 (B) 20 (C) 40 (D) 50 Production - PI GATE 2013 GATE Previous Year Solved Papers by Linked Answer Questions Statement for Linked Answer Questions 52 and 53: A project consists of seven activities, whose durations are independent normal random variables, as shown in the table below. Activities are identified by their beginning node i and ending node j. Activity (node i – node j) Mean duration (in days) Standard deviation (in days) 1 − 2 6 1 1 − 3 9 2 2 − 3 2 0.5 2 − 4 8 0.5 3 − 4 7 1 3 − 5 8 1 4 − 5 4 1 Q.52 The critical path of the project, based on the mean activity duration, is (A) 1−2−3−4−5 (B) 1−2−3−5 (C) 1−3−5 (D) 1−3−4−5 Q.53 Let Φ denote the cumulative distribution function of the standard normal random variable. The probability that all activities on the critical path, based on the mean activity duration, are completed in 22 days is (A) Φ −1 (0.333) (B) Φ −1 (0.816) (C) Φ −1 (1.664) (D) Φ −1 (2.235) Statement for Linked Answer Questions 54 and 55: In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N. Q.54 The orthogonal rake angle of the cutting tool in degree is (A) zero (B) 3.58 (C) 5 (D) 7.16 Q.55 The normal force acting at the chip-tool interface in N is (A) 1000 (B) 1500 (C) 2000 (D) 2500 Production - PI GATE 2013 GATE Previous Year Solved Papers by General Aptitude (GA) Questions Q.56 to Q.60 carry one mark each. Q.56 Were you a bird, you ___________________ in the sky. (A) would fly (B) shall fly (C) should fly (D) shall have flown Q.57 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. Q.58 Complete the sentence: Universalism is to particularism as diffuseness is to _______________. (A) specificity (B) neutrality (C) generality (D) adaptation Q.59 What will be the maximum sum of 44, 42, 40, ...... ? (A) 502 (B) 504 (C) 506 (D) 500 Q.60 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 Q.61 to Q.65 carry two marks each. Q.61 A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is (A) 36 (B) 30 (C) 24 (D) 18 Q.62 The current erection cost of a structure is Rs. 13,200. 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, then the new cost of erection in Rs. is (A) 16,500 (B) 15,180 (C) 11,000 (D) 10,120 Q.63 Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. 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 Production - PI GATE 2013 GATE Previous Year Solved Papers by Q.64 After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history. Which one of the following assertions is best supported by the above information? Q.65 Find the sum of the expression 81 80 1 ..... .......... 4 3 1 3 2 1 2 1 1 + + + + + + + + (A) 7 (B) 8 (C) 9 (D) 10 END OF THE QUESTION PAPER (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. Production - PI GATE 2013 GATE Previous Year Solved Papers by GATE 2013 - Answer Keys Production & Industrial Engineering – PI Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range 1 C 23 C 45 A 2 B 24 D 46 D 3 C 25 D 47 C 4 C 26 B 48 B 5 C 27 C 49 A 6 A 28 D 50 D 7 C 29 C 51 A 8 B 30 D 52 D 9 A 31 C 53 B 10 C 32 A 54 A 11 B 33 B 55 B 12 C 34 D 56 A 13 C 35 B 57 C 14 D 36 C 58 A 15 D 37 A 59 C 16 A 38 C 60 B 17 A 39 A 61 C 18 B 40 C 62 B 19 Marks to All 41 B 63 D 20 D 42 B 64 D 21 B 43 A 65 B 22 D 44 B GATE Previous Year Solved Papers by ___________________________________________________________ Duration: Three Hours Maximum Marks: 100 Read the following instructions carefully. 1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. 3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble corresponding to your test paper code and the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 16 pages including blank pages for rough work. After you are permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the question paper for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ball point pen. Name Registration Number PI GATE Previous Year Solved Papers by GATE 2012 Solved Paper Product ion & Indust rial Engineering - PI Q. 1 – Q. 25 carry one mark each. Q.1 2 0 1 cos lim x x x ÷ ÷ | | | \ ¹ is (A) 1/4 (B) 1/2 (C) 1 (D) 2 Q.2 For the spherical surface 2 2 2 1 x y z + + = , the unit outward normal vector at the point ( 1 1 , , 0 2 2 ) is given by (A) 1 1 ˆ ˆ 2 2 i j + (B) 1 1 ˆ ˆ 2 2 i j ÷ (C) ˆ k (D) 1 1 1 ˆ ˆ ˆ 3 3 3 i j k + + Q.3 Consider the function ( ) f x x = in the interval 1 1 x ÷ s s . At the point x = 0, f(x) is (A) continuous and differentiable. (B) non-continuous and differentiable. (C) continuous and non-differentiable. (D) neither continuous nor differentiable. Q.4 At x = 0, the function 3 ( ) 1 f x x = + has (A) a maximum value (B) a minimum value (C) a singularity (D) a point of inflection Q.5 The area enclosed between the straight line y = x and the parabola y = x 2 in the x-y plane is (A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2 Q.6 For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is (A) 1 (B) 2 (C) 4 (D) 8 Q.7 A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is (A) 0 (B) 1 (C) 1.08 (D) 2.02 Q.8 A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of the maximum deflection is (A) 2 2 ML EI (B) 2 ML EI (C) 2 2ML EI (D) 2 4ML EI Q.9 A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is (A) 395 (B) 790 (C) 1580 (D) 3160 Production - PI GATE 2012 GATE Previous Year Solved Papers by Q.10 In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is (A) 0.05 (B) 0.1 (C) 5.0 (D) 10.0 Q.11 Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid and vapor at 15 kPa are h f = 225.94 kJ/kg and h g = 2598.3 kJ/kg respectively. The mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is (A) 6.5 (B) 8.9 (C) 9.1 (D) 27.0 Q.12 An ideal gas of mass m and temperature T 1 undergoes a reversible isothermal process from an initial pressure P 1 to final pressure P 2 . The heat loss during the process is Q. The entropy change AS of the gas is (A) 2 1 ln P mR P | | | \ ¹ (B) 1 2 ln P mR P | | | \ ¹ (C) 2 1 1 ln P Q mR P T | | ÷ | \ ¹ (D) zero Q.13 For an opaque surface, the absorptivity( ) o , transmissivity ( ) t and reflectivity ( ) µ are related by the equation: (A) o µ t + = (B) 0 µ o t + + = (C) 1 o µ + = (D) 0 o µ + = Q.14 Which one of the following configurations has the highest fin effectiveness? (A) Thin, closely spaced fins (B) Thin, widely spaced fins (C) Thick, widely spaced fins (D) Thick, closely spaced fins Q.15 Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m 3 /s. The head loss (in m) due to friction is (assume g = 9.81 m/s 2 ) (A) 116.18 (B) 0.116 (C) 18.22 (D) 232.36 Q.16 A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is (A) 0 (B) 2.07 (C) 20.7 (D) 41.4 Note: All dimensions are in mm. Q.17 In an interchangeable assembly, shafts of size 010 . 0 040 . 0 000 . 25 ÷ + mm mate with holes of size 020 . 0 030 . 0 000 . 25 + + mm. The maximum interference (in microns) in the assembly is (A) 40 (B) 30 (C) 20 (D) 10 Q.18 A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is (A) 120 (B) 170 (C) 180 (D) 240 Q.19 Match the following metal forming processes with their associated stresses in the workpiece. Metal forming process Type of stress 1. Coining P. Tensile 2. Wire Drawing Q. Shear 3. Blanking R. Tensile and compressive 4. Deep Drawing S. Compressive (A) 1-S, 2-P, 3-Q, 4-R (B) 1-S, 2-P, 3-R, 4-Q (C) 1-P, 2-Q, 3-S, 4-R (D) 1-P, 2-R, 3-Q, 4-S Q.20 During normalizing process of steel, the specimen is heated (A) between the upper and lower critical temperature and cooled in still air. (B) above the upper critical temperature and cooled in furnace. (C) above the upper critical temperature and cooled in still air. (D) between the upper and lower critical temperature and cooled in furnace. Q.21 In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate (A) increases continuously. (B) decreases continuously. (C) decreases, becomes stable and then increases. (D) increases, becomes stable and then decreases. Q.22 Which one of the following is NOT a decision taken during the aggregate production planning stage? (A) Scheduling of machines (B) Amount of labour to be committed (C) Rate at which production should happen (D) Inventory to be carried forward Q.23 Which one of the following is NOT associated with the process of new product development? (A) QFD (B) FEMA (C) KANBAN (D) DFMA Production - PI GATE 2012 GATE Previous Year Solved Papers by Q.24 A process needs to be standardized for method and time. Which one of the following represents the sequence of work study experiments? (A) Time study followed by method study (B) Only time study (C) Time study and method study simultaneously (D) Method study followed by time study Q.25 Reduction in the variability of manufactured product characteristics will definitely result in observations close to (A) the upper control limit in X chart. (B) the lower control limit in X chart. (C) the lower control limit in R chart. (D) the center line in R chart. Production - PI GATE 2012 GATE Previous Year Solved Papers by Q. 26 - Q. 55 carry two marks each. Q.26 2 4 2 2 5 1 x y z x y z x y z + + = + + = ÷ + = The system of algebraic equations given above has (A) a unique solution of x = 1, y = 1 and z = 1. (B) only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0). (C) infinite number of solutions. (D) no feasible solution. Q.27 For the matrix A = 5 3 1 3 ( ( ¸ ¸ , ONE of the normalized eigen vectors is given as (A) 1 2 3 2 | | | | | | \ ¹ (B) 1 2 1 2 | | | | ÷ | | \ ¹ (C) 3 10 1 10 | | | | ÷ | | \ ¹ (D) 1 5 2 5 | | | | | | \ ¹ Q.28 Consider the differential equation 2 2 2 4 0 d y dy x x y dx dx + ÷ = with the boundary conditions of ( ) 0 0 y = and ( ) 1 1 y = . The complete solution of the differential equation is (A) 2 x (B) sin 2 x t | | | \ ¹ (C) sin 2 x x e t | | | \ ¹ (D) sin 2 x x e t ÷ | | | \ ¹ Q.29 The inverse Laplace transform of the function 1 ( ) ( 1) F s s s = + is given by (A) ( ) sin f t t = (B) t e t f t sin ) ( ÷ = (C) ( ) t f t e ÷ = (D) ( ) 1 t f t e ÷ = ÷ Q.30 A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is (A) 1/20 (B) 1/12 (C) 3/10 (D) 1/2 Q.31 The state of stress at a point under plane stress condition is xx = 40 MPa, yy = 100 MPa and xy = 40 MPa. The radius of the Mohr’s circle representing the given state of stress in MPa is (A) 40 (B) 50 (C) 60 (D) 100 Production - PI GATE 2012 GATE Previous Year Solved Papers by Q.32 A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in N.m is (A) 100.6 (B) 54.4 (C) 22.1 (D) 15.7 Q.33 Water (C p = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air (C p = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in °C) is (A) 40 (B) 20 (C) 10 (D) 5 Q.34 Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If D 1 and D 2 are the diameters of the inner and outer tubes respectively, then the view factor F 22 is given by (A) 2 1 1 D D | | ÷ | \ ¹ (B) zero (C) 1 2 D D | | | \ ¹ (D) 1 2 1 D D | | ÷ | \ ¹ Q.35 A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in h 1 , h 2 and h 3 are negligible, the instantaneous discharge velocity is (A) 1 1 2 2 3 3 3 3 3 2 1 h h gh h h µ µ µ µ | | + + | \ ¹ (B) ( ) 1 2 3 2g h h h + + (C) 1 1 2 2 3 3 1 2 3 2 h h h g µ µ µ µ µ µ | | + + | + + \ ¹ (D) 1 2 3 2 3 1 3 1 2 1 1 2 2 3 3 2 h h h h h h g h h h µ µ µ µ µ µ | | + + | + + \ ¹ µ 2 µ 1 h 3 h 2 h 1 µ 3 Q.36 In a DC arc welding operation, the voltage-arc length characteristic was obtained as 20 5 arc V l = + where the arc length l was varied between 5 mm and 7 mm. Here V arc denotes the arc voltage in Volts. The arc current was varied from 400 A to 500 A. Assuming linear power source characteristic, the open circuit voltage and the short circuit current for the welding operation are (A) 45 V, 450 A (B) 75 V, 750 A (C) 95 V, 950 A (D) 150 V, 1500 A Q.37 In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is (A) 0.006 (B) 0.031 (C) 0.062 (D) 0.600 Q.38 A mould having dimensions 100 mm × 90 mm × 20 mm is filled with molten metal through a gate as shown in the figure. For height h and cross-sectional area A, the mould filling time is t 1 . The height is now quadrupled and the cross-sectional area is halved. The corresponding filling time is t 2 . The ratio t 2 /t 1 is (A) 1 2 (B) 1 (C) 2 (D) 2 Q.39 A thin square plate ABCD with side of unit length is kept in the X-Y plane as shown in the figure. The plate is first rotated by 30° in the anti clockwise direction about the Z-axis with A fixed at the origin. The plate is then rotated by 90° in the anti clockwise direction about the X-axis with A fixed at the origin. The final co-ordinates of C are (A) (1.366, 0.366, 0.0) (B) (0.0, 1.366, 0.366) (C) (1.366, 0.0, 0.366) (D) (0.366, 0.0, 1.366) Q.40 A sine bar has a length of 250 mm. Each roller has a diameter of 20 mm. During taper angle measurement of a component, the height from the surface plate to the centre of a roller is 100 mm. The calculated taper angle (in degrees) is (A) 21.1 (B) 22.8 (C) 23.6 (D) 68.9 D X Y A Z B C Production - PI GATE 2012 GATE Previous Year Solved Papers by Q.41 Match the following plastic products with their most appropriate materials. Products Materials 1. Gears P. Polymethylmethacrylate (PMMA) 2. Helmets Q. Polyamides (PA) 3. Lenses R. Polyethylene (PE) 4. Food packaging S. Acrylonitrile-butadiene-styrene (ABS) (A) 1-Q, 2-R, 3-S, 4-P (B) 1-S, 2-P, 3-Q, 4-R (C) 1-P, 2-Q, 3-R, 4-S (D) 1-Q, 2-S, 3-P, 4-R Q.42 In a shaping process, the number of double strokes per minute is 30 and the quick return ratio is 0.6. If the length of the stroke is 250 mm, the average cutting velocity in m/min is (A) 3.0 (B) 4.5 (C) 7.5 (D) 12.0 Q.43 For a linear programming problem, the set of constraints x+y ≤ 2, 3x+5y ≥ 15, x ≥ 0 and y ≥ 0 leads to (A) an infeasible solution. (B) a unique optimal solution. (C) multiple but finite optimal solutions. (D) infinite optimal solutions. Q.44 A milk vendor incurs an overstocking cost of Rs. 2 per litre and a shortage cost of Rs. 0.5 per litre. The demand is uniformly distributed between 1 litre and 6 litres. Using the Newsvendor Model, the maximum quantity of milk in litre(s) the vendor should order is (A) 2 (B) 6 (C) 1 (D) 3 Q.45 The specification limits for the weight of a product are 13.1 kg and 15 kg. If the process has a variance of weight 0.05 kg 2 , then the process capability index is (A) 6.3 (B) 1.9 (C) 1.4 (D) 8.6 Q.46 On an average, there are 30 customers in a queue. If the arrival rate of customers into the system is 16 customers per hour and on average 32 customers leave the system per hour, then the average number of customers in the system is (A) 16.5 (B) 30.5 (C) 32.0 (D) 46.0 Q.47 Data for four jobs that need to be processed on a single machine are given below. Job P Q R S Processing time (days) 12 9 21 10 Due date (days) 20 40 30 19 All the four jobs are available at time zero. If the jobs are scheduled using the Earliest Due Date (EDD) algorithm, then the job with maximum tardiness is (A) P (B) Q (C) R (D) S Production - PI GATE 2012 GATE Previous Year Solved Papers by Common Data Questions Common Data for Questions 48 and 49: Two steel truss members, AC and BC, each having cross sectional area of 100 mm 2 , are subjected to a horizontal force F as shown in figure. All the joints are hinged. Q.48 The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is (A) 8.17 (B) 11.15 (C) 14.14 (D) 22.30 Q.49 If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is (A) 0.63 (B) 0.32 (C) 1.26 (D) 1.46 Common Data for Questions 50 and 51: Data for a plain milling operation are given below. Length of workpiece 200 mm Cutter diameter 100 mm No. of teeth 4 Cutter speed 100 rpm Feed 200 mm/min Depth of cut 2 mm Total clearance (entry and exit) 5 mm Q.50 Mean undeformed chip thickness (in microns) is (A) 142 (B) 100 (C) 71 (D) 50 Q.51 Machining time for a single pass (in seconds) is (A) 60 (B) 66 (C) 126 (D) 150 Linked Answer Questions Statement for Linked Answer Questions 52 and 53: In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of 50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible. Machining is carried out under the following conditions: Resistance 40 Ω Capacitance 20 μF Supply voltage 220 V Discharge voltage 110 V Q.52 The time for one cycle, in milliseconds, is (A) 0.55 (B) 0.32 (C) 0.89 (D) 0.24 Q.53 Average power input (in kW) is (A) 0.373 (B) 0.137 (C) 0.218 (D) 0.500 Statement for Linked Answer Questions 54 and 55: In a particular year, an organization earns cash revenues of Rs. 2,00,000. Total material and labour expenses are Rs. 1,09,000. The depreciation claimed on the equipment is Rs. 25,000. The tax rate is 20%. Q.54 The profit after tax (PAT) is (A) Rs. 92,800 (B) Rs. 66,200 (C) Rs. 72,800 (D) Rs. 52,800 Q.55 The net cash flow is (A) Rs. 97,800 (B) Rs. 77,800 (C) Rs. 66,000 (D) Rs. 72,800 Production - PI GATE 2012 GATE Previous Year Solved Papers by General Aptitude (GA) Questions Q. 56 – Q. 60 carry one mark each. Q.56 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. (A) that (B) which (C) who (D) whom Q.57 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. (A) attempts (B) setbacks (C) meetings (D) delegations Q.58 Choose the grammatically INCORRECT sentence: (A) They gave us the money back less the service charges of Three Hundred rupees. (B) This country’s expenditure is not less than that of Bangladesh. (C) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum. (D) This country’s expenditure on educational reforms is very less. Q.59 The cost function for a product in a firm is given by 5q 2 , where q is the amount of production. The firm can sell the product at a market price of 50 per unit. 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 Q.60 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 Q. 61 - Q. 65 carry two marks each. Q.61 Given the sequence of terms, AD CG FK JP, the next term is (A) OV (B) OW (C) PV (D) PW Q.62 A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x – 0.1x 2 where y is the height of the arch in meters. The maximum possible height of the arch is (A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters Production - PI GATE 2012 GATE Previous Year Solved Papers by Q.63 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 S: Doubling each entry in a list leaves the standard deviation of the list unchanged (A) P, Q (B) Q, R (C) P, R (D) R, S Q.64 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed. 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 Q.65 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is (A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720 END OF THE QUESTION PAPER Production - PI GATE 2012 GATE Previous Year Solved Papers by GATE 2012 - Answer Keys Production & Industrial Engineering-PI Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range 1 B 23 Marks to All 45 C 2 A 24 D 46 B 3 C 25 C 47 C 4 D 26 C 48 B 5 A 27 B 49 A 6 C 28 A 50 C 7 D 29 D 51 B 8 A 30 D 52 A 9 B 31 B 53 C 10 B 32 B 54 D 11 B 33 C 55 B 12 B 34 D 56 Marks to All 13 C 35 A 57 B 14 A 36 C 58 D 15 A 37 C 59 A 16 D 38 D 60 A 17 C 39 B 61 A 18 B 40 A 62 B 19 A 41 D 63 C 20 C 42 D 64 D 21 D 43 A 65 B 22 A 44 A GATE Previous Year Solved Papers by __________________________________________________________