gate solved question papers for mechanical engineering [me] by aglasem.com

SOLVED PAPERS

GATEMECHANICAL ENGINEERING (ME)

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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 (Set-1)o Answer Key 2014 (Set-1)o Solved Question Paper 2014 (Set-2)o Answer Key 2014 (Set-2)o Solved Question Paper 2014 (Set-3)o Answer Key 2014 (Set-3)o Solved Question Paper 2014 (Set-4)o Answer Key 2014 (Set-4)o Solved Question Paper 2013o Answer Key 2013o Solved Question Paper 2012o 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

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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.


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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.


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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)


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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


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


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.


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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 Mechanical Engineering (ME)

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.


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APPLIED MECHANICS AND DESIGN

Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual

work; kinematics and dynamics of particles and of rigid bodies in plane motion, including

impulse and momentum (linear and angular) and energy formulations; impact.

Strength of Materials: Stress and strain, stress-strain relationship and elastic constants,

Mohr’s circle for plane stress and plane strain, thin cylinders; shear force and bending

moment diagrams; bending and shear stresses; deflection of beams; torsion of circular

shafts; Euler’s theory of columns; strain energy methods; thermal stresses.

Theory of Machines: Displacement, velocity and acceleration analysis of plane

mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels.

Vibrations: Free and forced vibration of single degree of freedom systems; effect of

damping; vibration isolation; resonance, critical speeds of shafts.

Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-

N diagram;principles of the design of machine elements such as bolted, riveted and

welded joints, shafts, spur gears, rolling and sliding contact bearings, brakes and clutches.

FLUID MECHANICS AND THERMAL SCIENCES

Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-volume

analysis of mass, momentum and energy; fluid acceleration; differential equations of

continuity and momentum; Bernoulli’s equation; viscous flow of incompressible fluids;

boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes,

bends etc.

Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance

concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in

free and forced convective heat transfer, various correlations for heat transfer in flow over

flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat

transfer, black and grey surfaces, shape factors, network analysis; heat exchanger

performance, LMTD and NTU methods.


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Thermodynamics:Zeroth, First and Second laws of thermodynamics; thermodynamic

system and processes; Carnot cycle.irreversibility and availability; behaviour of ideal and

real gases, properties of pure substances, calculation of work and heat in ideal processes;

analysis of thermodynamic cycles related to energy conversion.

Applications:Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration

and reheat.I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning:

Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air:

psychrometric chart, basic psychrometric processes. Turbomachinery:Pelton-wheel,

Francis and Kaplan turbines — impulse and reaction principles, velocity diagrams.

MANUFACTURING AND INDUSTRIAL ENGINEERING

Engineering Materials: Structure and properties of engineering materials, heat

treatment, stress-strain diagrams for engineering materials.

Metal Casting: Design of patterns, moulds and cores; solidification and cooling; riser and

gating design, design considerations.

Forming: Plastic deformation and yield criteria; fundamentals of hot and cold working

processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet

(shearing, deep drawing, bending) metal forming processes; principles of powder

metallurgy.

Joining: Physics of welding, brazing and soldering; adhesive bonding; design

considerations in welding.

Machining and Machine Tool Operations: Mechanics of machining, single and multi-

point cutting tools, tool geometry and materials, tool life and wear; economics of

machining; principles of non-traditional machining processes; principles of work holding,

principles of design of jigs and fixtures

Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements;

comparators; gauge design; interferometry; form and finish measurement; alignment and

testing methods; tolerance analysis in manufacturing and assembly.


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Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration

tools.

Production Planning and Control: Forecasting models, aggregate production planning,

scheduling, materials requirement planning.

Inventory Control: Deterministic and probabilistic models; safety stock inventory control

systems.

Operations Research: Linear programming, simplex and duplex method, transportation,

assignment, network flow models, simple queuing models, PERT and CPM.


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GATEPrevious Year Solved Papers

Mechanical Engineering - ME

2012 - 14


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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 2014 Solved Paper ME: Mechanical Engineering


SET - 1

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Q. 1 – Q. 5 carry one mark each.

Q.1 Choose the most appropriate phrase from the options given below to complete the following

sentence.

The aircraft take off as soon as its flight plan was filed.

(A) is allowed to (B) will be allowed to

(C) was allowed to (D) has been allowed to

Q.2 Read the statements:

All women are entrepreneurs.

Some women are doctors.

Which of the following conclusions can be logically inferred from the above statements?

(A) All women are doctors (B) All doctors are entrepreneurs

(C) All entrepreneurs are women (D) Some entrepreneurs are doctors

Q.3 Choose the most appropriate word from the options given below to complete the following

sentence.

Many ancient cultures attributed disease to supernatural causes. However, modern science has

largely helped _________ such notions.

(A) impel (B) dispel (C) propel (D) repel

Q.4 The statistics of runs scored in a series by four batsmen are provided in the following table. Who is

the most consistent batsman of these four?

Batsman Average Standard deviation

K 31.2 5.21

L 46.0 6.35

M 54.4 6.22

N 17.9 5.90

(A) K (B) L (C) M (D) N

Q.5 What is the next number in the series?

12 35 81 173 357 ____

Q. 6 – Q. 10 carry two marks each.

Q.6 Find the odd one from the following group:

W,E,K,O I,Q,W,A F,N,T,X N,V,B,D

(A) W,E,K,O (B) I,Q,W,A (C) F,N,T,X (D) N,V,B,D

GATE 2014 General Aptitude - GASET-1


Q.7 For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up

Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people

with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs

15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who

should fill Form T is

(A) a resident male with annual income Rs 9 lakh

(B) a resident female with annual income Rs 9 lakh

(C) a non-resident male with annual income Rs 16 lakh

(D) a non-resident female with annual income Rs 16 lakh

Q.8 A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and

passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

Q.9 The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the

following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is

the trade deficit 1/5th of the exports?

(A) 2005 (B) 2004 (C) 2007 (D) 2006

Q.10 You are given three coins: one has heads on both faces, the second has tails on both faces, and the

third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it

comes up heads. The probability that the other face is tails is

(A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3

END OF THE QUESTION PAPER

0

10

20

30

40

50

60

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90

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110

120

2000 2001 2002 2003 2004 2005 2006 2007

Exports Imports

GATE 2014 General Aptitude - GASET-1



Q.1 Given that the determinant of the matrix is 12, the determinant of the matrix 8 is

(A) 96 (B) 24 (C) 24 (D) 96

Q.2

0

sinLt

1 cosx

x x

x→

−−

is

(A) 0 (B) 1 (C) 3 (D) not defined

Q.3 The argument of the complex number

i

i

−+

1

1, where 1−=i , is

(A) π− (B) 2

π− (C)

2

π (D) π

Q.4 The matrix form of the linear system and 8 is

(A)3 5d

4 8d

x x

y yt

−⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥

⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (B)

3 8d

4 5d

x x

y yt

⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥−⎩ ⎭ ⎣ ⎦ ⎩ ⎭

(C) 4 5d

3 8d

x x

y yt

−⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥

⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (D)

4 8d

3 5d

x x

y yt

⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥−⎩ ⎭ ⎣ ⎦ ⎩ ⎭

Q.5 Which one of the following describes the relationship among the three vectors, kji ˆˆˆ ++ ,

kji ˆˆ3ˆ2 ++ and kji ˆ4ˆ6ˆ5 ++ ?

(A) The vectors are mutually perpendicular (B) The vectors are linearly dependent

(C) The vectors are linearly independent (D) The vectors are unit vectors

Q.6 A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and

coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the

temperature of the rod is increased by ∆T, then

(A) stress developed in the rod is E α ∆T and strain developed in the rod is α ∆T

(B) both stress and strain developed in the rod are zero

(C) stress developed in the rod is zero and strain developed in the rod is α ∆T

(D) stress developed in the rod is E α ∆T and strain developed in the rod is zero

GATE 2014 Mechanical Engineering - MESET-1


Q.7 A m

at t

0.0

Q.8 Cri

(A)

(B)

(C)

(D)

Q.9 A c

vel

(A)

(C)

Q.10 For

I. M

II. A

Ind

(A)

(C)

Q.11 A r

mag

of V

(A)

Q.12 Bio

(A)

(B)

(C)

(D)

metallic rod

the ends, ex

15 mm. The

itical dampin

) largest amo

) smallest am

) largest amo

) smallest am

circular objec

ocity V. The

) zero

) V opposite t

r the given st

Mating spur

A revolute jo

dicate the cor

) Both I and I

) I is false an

rigid link PQ

gnitude and

VP (in m/s) a

) 2.14

ot number sig

) convective

) conductive

) inertia force

) buoyancy fo

of 500 mm l

xperiences an

Poisson’s ra

ng is the

ount of damp

mount of dam

ount of damp

mount of dam

ct of radius r

velocity at t

to the directi

tatements:

gear teeth is

oint is an exa

rrect answer.

II are false

d II is true

Q is 2 m lo

direction of

at this instant

(B)

gnifies the ra

resistance in

resistance in

e to viscous f

force to visco

length and 50

n increase in

atio of the ro

ping for whic

mping for whi

ing for whic

mping for whi

r rolls witho

the point of c

ion of motion

an example

ample of low

ong and orie

f velocity VQ

t is

1.89

atio of

n the fluid to

n the solid to

force in the f

ous force in t

0 mm diame

n its length b

d material is

ch no oscillat

ich no oscilla

h the motion

ich the motio

ut slipping o

contact betw

(

n (

of higher pa

wer pair

(

(

ented at 20o

Q, and the dir

(C)

conductive r

convective r

fluid

the fluid

eter, when su

by 0.5 mm

s _______

tion occurs in

ation occurs

n is simple ha

on is simple

on a horizont

een the objec

(B) V in the

(D) V vertica

air

(B) I is true a

(D) Both I an

to the horiz

rection of ve

1.21

resistance in

resistance in

ubjected to a

and a reduc

n free vibrati

in free vibra

armonic in fr

harmonic in

tal level floor

ct and the flo

direction of

ally upward

and II is false

nd II are true

zontal as sho

elocity VP are

(D)

the solid

the fluid

tensile force

ction in its d

ion

ation

ree vibration

free vibratio

r with the ce

oor is

motion

from the floo

e

own in the

e given. The

0.96

e of 100 kN

diameter by

n

on

nter having

or

figure. The

e magnitude



Q.13 The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference

environment, is called

(A) Entropy (B) Enthalpy (C) Exergy (D) Rothalpy

Q.14 Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.

The free stream velocity is U∞ and the free stream temperature T∞ is lower than the cylinder

surface temperature Ts. The local heat transfer coefficient is minimum at point

(A) 1 (B) 2 (C) 3 (D) 4

Q.15 For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the

condition of stability will be

(A) G is located below B (B) G is located above B

(C) G and B are coincident (D) independent of the locations of G and B

Q.16 In a power plant, water (density = 1000 kg/m3) is pumped from 80 kPa to 3 MPa. The pump has an

isentropic efficiency of 0.85. Assuming that the temperature of the water remains the same, the

specific work (in kJ/kg) supplied to the pump is

(A) 0.34 (B) 2.48 (C) 2.92 (D) 3.43

Q.17 Which one of the following is a CFC refrigerant?

(A) R744 (B) R290 (C) R502 (D) R718

Q.18 The jobs arrive at a facility, for service, in a random manner. The probability distribution of number

of arrivals of jobs in a fixed time interval is

(A) Normal (B) Poisson (C) Erlang (D) Beta

Q.19 In exponential smoothening method, which one of the following is true?

(A) 0 ≤ α ≤ 1 and high value of α is used for stable demand

(B) 0 ≤ α ≤ 1 and high value of α is used for unstable demand

(C) α ≥ 1 and high value of α is used for stable demand

(D) α ≤ 0 and high value of α is used for unstable demand

2

U∞ 1

3

4T∞

Ts



Q.20 For machining a rectangular island represented by coordinates P(0,0), Q(100,0), R(100,50) and

S(0,50) on a casting using CNC milling machine, an end mill with a diameter of 16 mm is used.

The trajectory of the cutter centre to machine the island PQRS is

(A) (−8, −8), (108, −8), (108,58), (−8,58) , (−8, −8)

(B) (8,8), (94,8), (94,44), (8,44), (8,8)

(C) (−8,8), (94,0), (94,44), (8,44), (−8,8)

(D) (0,0), (100,0), (100,50), (50,0), (0,0)

Q.21 Which one of the following instruments is widely used to check and calibrate geometric features of

machine tools during their assembly?

(A) Ultrasonic probe (B) Coordinate Measuring Machine (CMM)

(C) Laser interferometer (D) Vernier calipers

Q.22 The major difficulty during welding of aluminium is due to its

(A) high tendency of oxidation (B) high thermal conductivity

(C) low melting point (D) low density

Q.23 The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal

is 400 N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The

specific cutting pressure (in N/mm2) is

(A) 1000 (B) 2000 (C) 3000 (D) 4000

Q.24 The process of reheating the martensitic steel to reduce its brittleness without any significant loss in

its hardness is

(A) normalising (B) annealing (C) quenching (D) tempering

Q.25 In solid-state welding, the contamination layers between the surfaces to be welded are removed by

(A) alcohol (B) plastic deformation

(C) water jet (D) sand blasting



Q. 26 – Q.

Q.26 The

clo

(A)

Q.27 If y

x =

Q.28 In

stan

(A)

Q.29 Usi

def

Q.30 The

max

Q.31 A b

tied

sur

(A)

e integral ∫ckwise direc

) 0

y = f(x) is the

10, f(15) =

the followin

ndard deviati

) 0.18

ing the trape

finite integral

e state of st

ximum tensi

block R of m

d to the wall

faces is 0.4,

) 0.69

two mark

( d dC

y x x−∫ction. The int

(B)

e solution of

_______

ng table, x i

ion of x is

(B)

ezoidal rule,

l

1

1

dx x

+

−∫ is

tress at a po

ile stress (in M

mass 100 kg i

by a massle

the minimum

(B)

)dy is evalu

tegral is equa

4

π−

f 2

2

d0

d

y

x= w

s a discrete

x

p(x)

0.36

and dividing

_______

oint is given

MPa) at the p

is placed on

ess and inext

m force F (in

0.88

uated along

al to

(C)

with the boun

random var

1

x) 0.3

(C)

g the interval

n by x = −point is ____

a block S of

tensible strin

n kN) needed

(C)

the circle

2

π−

ndary conditi

riable and p

2 3

0.6 0.1

0.54

l of integratio

6 MPa, y =

____

f mass 150 kg

ng PQ. If the

d to move the

0.98

2 2 1

4x y+ =

(D)

ions y = 5 at

p(x) is the p

(D)

on into three

= 4 MPa, an

g as shown i

e coefficient

e block S is

(D)

4 traversed

4

π

t x = 0, and

probability d

0.6

e equal subin

nd xy = −8

in the figure.

of static fric

1.37

in counter

d2

d

y

x= at

ensity. The

ntervals, the

MPa. The

Block R is

ction for all

ks each.

55 carry



Q.32 A pair of spur gears with module 5 mm and a center distance of 450 mm is used for a speed

reduction of 5:1. The number of teeth on pinion is _______

Q.33 Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length

0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is

100 Hz. The flexural rigidity (in N.m2) of the beam is _______

Q.34 An ideal water jet with volume flow rate of 0.05 m3/s strikes a flat plate placed normal to its path

and exerts a force of 1000 N. Considering the density of water as 1000 kg/m3, the diameter (in mm)

of the water jet is _______

Q.35 A block weighing 200 N is in contact with a level plane whose coefficients of static and kinetic

friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton)

P=10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after

10 seconds is _______

Q.36 A slider crank mechanism has slider mass of 10 kg, stroke of 0.2 m and rotates with a uniform

angular velocity of 10 rad/s. The primary inertia forces of the slider are partially balanced by a

revolving mass of 6 kg at the crank, placed at a distance equal to crank radius. Neglect the mass of

connecting rod and crank. When the crank angle (with respect to slider axis) is 30°, the unbalanced

force (in newton) normal to the slider axis is _______

Q.37 An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick

Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______

10 mm 20 mm

40 mm



Q.38 A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends

A and B are supported by springs of spring constant k. The natural frequency of the system is given

by

(A) (B) (C) (D)

Q.39 A hydrodynamic journal bearing is subject to 2000 N load at a rotational speed of 2000 rpm. Both

bearing bore diameter and length are 40 mm. If radial clearance is 20 µm and bearing is lubricated

with an oil having viscosity 0.03 Pa.s, the Sommerfeld number of the bearing is _______

Q.40 A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls.

The temperature of the rod is uniformly raised by 250°C. If the Young’s modulus and coefficient of

thermal expansion are 200 GPa and 1×10−5 /°C, respectively, the magnitude of the longitudinal

stress (in MPa) developed in the rod is _______

Q.41 1.5 kg of water is in saturated liquid state at 2 bar (vf = 0.001061 m3/kg, uf = 504.0 kJ/kg,

hf = 505 kJ/kg). Heat is added in a constant pressure process till the temperature of water reaches

400°C (v = 1.5493 m3/kg, u = 2967.0 kJ/kg, h = 3277.0 kJ/kg). The heat added (in kJ) in the process

is _______

k k

2L/3L/3

AC

B



Q.42 Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of

thickness 30 mm and thermal conductivity 15 W/m.K. At x = 0, a constant heat flux,

q" = 1×105 W/m2 is applied. On the other side of the wall, heat is removed from the wall by

convection with a fluid at 25°C and heat transfer coefficient of 250 W/m2.K. The temperature

(in °C), at x = 0 is _______

Q.43 Water flows through a pipe having an inner radius of 10 mm at the rate of 36 kg/hr at 25°C. The

viscosity of water at 25°C is 0.001 kg/m.s. The Reynolds number of the flow is _______

Q.44 For a fully developed flow of water in a pipe having diameter 10 cm, velocity 0.1 m/s and

kinematic viscosity 10−5 m2/s, the value of Darcy friction factor is _______

Q.45 In a simple concentric shaft-bearing arrangement, the lubricant flows in the 2 mm gap between the

shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure

gradient. The diameter of the shaft is 100 mm and its tangential speed is 10 m/s. The dynamic

viscosity of the lubricant is 0.1 kg/m.s. The frictional resisting force (in newton) per 100 mm length

of the bearing is _______

Q.46 The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is

given by2

⎟⎠

⎞⎜⎝

⎛++=−−

∞ L

yc

L

yba

TT

TT

W

W , where y is measured perpendicular to the plate, L is the plate

length, and a, b and c are arbitrary constants. TW and T∞ are wall and ambient temperatures,

respectively. If the thermal conductivity of the fluid is k and the wall heat flux is "q , the Nusselt

number k

L

TT

qNu

W ∞−=

" is equal to

(A) a (B) b (C) 2c (D) (b+2c)

T1

q" = 1×105 W/m2

T2

T∞ = 25°C

x

x=0



Q.47 In an air-standard Otto cycle, air is supplied at 0.1 MPa and 308 K. The ratio of the specific heats

(γ) and the specific gas constant (R) of air are 1.4 and 288.8 J/kg.K, respectively. If the compression

ratio is 8 and the maximum temperature in the cycle is 2660 K, the heat (in kJ/kg) supplied to the

engine is _______

Q.48 A reversible heat engine receives 2 kJ of heat from a reservoir at 1000 K and a certain amount of

heat from a reservoir at 800 K. It rejects 1 kJ of heat to a reservoir at 400 K. The net work output

(in kJ) of the cycle is

(A) 0.8 (B) 1.0 (C) 1.4 (D) 2.0

Q.49 An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with

reheat being done at 4 MPa. The temperature of steam at the inlets of both turbines is 500°C and

the enthalpy of steam is 3185 kJ/kg at the exit of the high pressure turbine and 2247 kJ/kg at the

exit of low pressure turbine. The enthalpy of water at the exit from the pump is 191 kJ/kg. Use the

following table for relevant data.

Superheated steam temperature

(°C)

Pressure

(MPa)

ν (m3/kg)

h

(kJ/kg)

s

(kJ/kg.K)

500 4 0.08644 3446 7.0922

500 8 0.04177 3399 6.7266

Disregarding the pump work, the cycle efficiency (in percentage) is _______

Q.50 Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows

Poisson distribution. The average service time of a job on the facility is 40 minutes. The service

time follows exponential distribution. Idle time (in hours) at the facility per shift will be

(A)5

7 (B)

14

3 (C)

7

5 (D)

10

3

Q.51 A metal rod of initial length L0 is subjected to a drawing process. The length of the rod at any

instant is given by the expression, )1()( 2

0 tLtL += , where t is the time in minutes. The true strain

rate (in min−1) at the end of one minute is _______

Q.52 During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness

of the chip produced is 0.5 mm. The feed given to the zero degree rake angle tool is 0.2 mm/rev.

The shear strain produced during the operation is _______



Q.53 For the given assembly: 25 H7/g8, match Group A with Group B

Group A Group B

P. H I. Shaft Type

Q. IT8 II. Hole Type

R. IT7 III. Hole Tolerance Grade

S. g IV. Shaft Tolerance Grade

(A) P-I, Q-III, R-IV, S-II (B) P-I, Q-IV, R-III, S-II

(C) P-II, Q-III, R-IV, S-I (D) P-II, Q-IV, R-III, S-I

Q.54 If the Taylor’s tool life exponent n is 0.2, and the tool changing time is 1.5 min, then the tool life

(in min) for maximum production rate is _______

Q.55 An aluminium alloy (density 2600 kg/m3) casting is to be produced. A cylindrical hole of 100 mm

diameter and 100 mm length is made in the casting using sand core (density 1600 kg/m3). The net

buoyancy force (in newton) acting on the core is _______




GATE 2014 - Answer Keys(SET – 1)

General Aptitude – GA

Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 C 5 725 to 725 9 D2 D 6 D 10 B3 B 7 B4 A 8 560 to 560


Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 A 20 A 39 0.75 to 0.852 A 21 C 40 499 to 5013 C 22 A 41 4155 to 41604 A 23 B 42 620 to 6305 B 24 A 43 635 to 6386 C 25 B 44 0.06 to 0.077 0.29 to 0.31 26 C 45 15 to 168 B 27 34 to 36 46 B9 A 28 D 47 1400 to 142010 D 29 1.10 to 1.12 48 C11 D 30 8.4 to 8.5 49 40 to 4212 B 31 D 50 B13 C 32 29 to 31 51 0.9 to 1.114 B 33 0.064 to

0.06752 2.8 to 3.0

15 A 34 56 to 57 53 D16 D 35 4.8 to 5.0 54 5.9 to 6.117 C 36 29 to 31 55 7 to 818 B 37 1.2 to 1.319 B 38 D


________________________________________























type.



before the choice.
















GATE 2014 Solved Paper

ME: Mechanical Engineering


SET - 2

_______________________________________


Q.1 Choose the most appropriate word from the options given below to complete the following

sentence.

Communication and interpersonal skills are important in their own ways.

(A) each (B) both (C) all (D) either

Q.2 Which of the options given below best completes the following sentence?

She will feel much better if she ________________.

(A) will get some rest (B) gets some rest

(C) will be getting some rest (D) is getting some rest

Q.3 Choose the most appropriate pair of words from the options given below to complete the following

sentence.

She could not _____ the thought of _________ the election to her bitter rival.

(A) bear, loosing (B) bare, loosing (C) bear, losing (D) bare, losing

Q.4 A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of

throws show the following frequencies of occurrence: 1 → 0.167; 2 → 0.167; 3 → 0.152; 4 → 0.166; 5 → 0.168; 6 → 0.180. We call this die

(A) irregular (B) biased (C) Gaussian (D) insufficient

Q.5 Fill in the missing number in the series.

2 3 6 15 157.5 630


Q.6 Find the odd one in the following group

Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X

(A) Q,W,Z,B (B) B,H,K,M (C) W,C,G,J (D) M,S,V,X

Q.7 Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder

there are two lights. If one of the lights is red, the other light on that step will always be blue. If one

of the lights on a step is green, the other light on that step will always be yellow. Which of the

following statements is not necessarily correct?

(A) The number of red lights is equal to the number of blue lights

(B) The number of green lights is equal to the number of yellow lights

(C) The sum of the red and green lights is equal to the sum of the yellow and blue lights

(D) The sum of the red and blue lights is equal to the sum of the green and yellow lights

Q.8 The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is

87. What is the sum of the smallest odd number and second largest even number?

General Aptitude - GAGATE 2014 SET-2


Q.9 The total exports and revenues from the exports of a country are given in the two charts shown

below. The pie chart for exports shows the quantity of each item exported 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 500 thousand

tonnes and the total revenues are 250 crore rupees. Which item among the following has generated

the maximum revenue per kg?

(A) Item 2 (B) Item 3 (C) Item 6 (D) Item 5

Q.10 It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to

simultaneously pump water into the half-full tank while draining it. What is the rate at which water

has to be pumped in so that it gets fully filled in 10 minutes?

(A) 4 times the draining rate (B) 3 times the draining rate

(C) 2.5 times the draining rate (D) 2 times the draining rate


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

General Aptitude - GAGATE 2014 SET-2


Q.1 One of the eigenvectors of the matrix

−−

69

25is

(A)

−

1

1 (B)

−

9

2 (C)

−1

2 (D)

1

1

Q.2

2

0

1Lt

sin(4 )

x

x

e

x→

−

is equal to

(A) 0 (B) 0.5 (C) 1 (D) 2

Q.3 Curl of vector kzyjzyxizxF ˆ2ˆ2ˆ 32222 +−=

is

(A) kzyjzxixyyz ˆ2ˆ2ˆ)24( 2223 −++ (B) kzyjzxixyyz ˆ2ˆ2ˆ)24( 2223 −−+

(C) kzyjzyxizx ˆ6ˆ4ˆ2 222 +− (D) kzyjzyxizx ˆ6ˆ4ˆ2 222 ++

Q.4 A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a

random manner from the box. The probability of both the parts being good is

(A)7

20 (B)

42

125 (C)

25

29 (D)

5

9

Q.5 The best approximation of the minimum value attained by e− sin(100) for ≥ 0 is _______

Q.6 A steel cube, with all faces free to deform, has Young’s modulus, E, Poisson’s ratio, ν, and

coefficient of thermal expansion, α. The pressure (hydrostatic stress) developed within the cube,

when it is subjected to a uniform increase in temperature, ΔT, is given by

(A) 0 (B)( )1 2

T Eαν

∆−

(C) ( )1 2

T Eαν

∆−

− (D)

( )( )3 1 2

T Eαν

∆−


GATE 2014 SET-2 Mechanical Engineering - ME


A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is

_______

Q.8 A 4-bar mechanism with all revolute pairs has link lengths lf = 20 mm, lin = 40 mm, lco = 50 mm

and lout = 60 mm. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler

and output link respectively. Which one of the following statements is true about the input and

output links?

(A) Both links can execute full circular motion

(B) Both links cannot execute full circular motion

(C) Only the output link cannot execute full circular motion

(D) Only the input link cannot execute full circular motion

Q.9 In vibration isolation, which one of the following statements is NOT correct regarding

Transmissibility (T)?

(A) T is nearly unity at small excitation frequencies

(B) T can be always reduced by using higher damping at any excitation frequency

(C) T is unity at the frequency ratio of 2

(D) T is infinity at resonance for undamped systems

Q.10 In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a

cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is _______

10 kN

1 m

0.5 m

A

B

C

Q.7



A thin plate of uniform thickness is subject to pressure as shown in the figure below

Under the assumption of plane stress, which one of the following is correct?

(A) Normal stress is zero in the z-direction

(B) Normal stress is tensile in the z-direction

(C) Normal stress is compressive in the z-direction

(D) Normal stress varies in the z-direction

Q.12 For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2,

the average heat transfer coefficient

(A) remains same (B) decreases by a factor of 2

(C) rises by a factor of 2 (D) rises by a factor of 4

Q.13 The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio and

γ (= cp/cv) is given by

(A) 1

11

prγ −− (B)

11

prγ− (C)

1/

11

prγ− (D) ( )1 /

11

prγ γ−

−

Q.14 For an incompressible flow field, , which one of the following conditions must be satisfied?

(A) ∇ ∙ = 0 (B) ∇× = 0 (C) ∙ ∇ = 0 (D) + ∙ ∇ = 0

Q.15 A pure substance at 8 MPa and 400 °C is having a specific internal energy of 2864 kJ/kg and a

specific volume of 0.03432 m3/kg. Its specific enthalpy (in kJ/kg) is _______

Q.16 In a heat exchanger, it is observed that ∆T1 = ∆T2, where ∆T1 is the temperature difference between

the two single phase fluid streams at one end and ∆T2 is the temperature difference at the other end.

This heat exchanger is

(A) a condenser (B) an evaporator

(C) a counter flow heat exchanger (D) a parallel flow heat exchanger

Q.17 The difference in pressure (in N/m2) across an air bubble of diameter 0.001 m immersed in water

(surface tension = 0.072 N/m) is _______

x

y y z

Q.11



If there are m sources and n destinations in a transportation matrix, the total number of basic

variables in a basic feasible solution is

(A) m + n (B) m + n + 1 (C) m + n − 1 (D) m

Q.19 A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the

variable cost for each of the processes are listed below. The most economical process for producing

a batch of 100 pieces is

Process Fixed cost (in Rs.) Variable cost per piece (in Rs.)

I 20 3

II 50 1

III 40 2

IV 10 4

(A) I (B) II (C) III (D) IV

Q.20 The flatness of a machine bed can be measured using

(A) Vernier calipers (B) Auto collimator

(C) Height gauge (D) Tool maker’s microscope

Q.21 A robot arm PQ with end coordinates P(0,0) and Q(2,5) rotates counter clockwise about P in the

XY plane by 90°. The new coordinate pair of the end point Q is

(A) (−2,5) (B) (−5,2) (C) (−5, −2) (D) (2, −5)

Q.22 Match the Machine Tools (Group A) with the probable Operations (Group B):

Group A Group B

P: Centre Lathe 1: Slotting

Q: Milling 2: Counter-boring

R: Grinding 3: Knurling

S: Drilling 4: Dressing

(A) P-1, Q-2, R-4, S-3 (B) P-2, Q-1, R-4, S-3

(C) P-3, Q-1, R-4, S-2 (D) P-3, Q-4, R-2, S-1

Q.23 The following four unconventional machining processes are available in a shop floor. The most

appropriate one to drill a hole of square cross section of 6 mm × 6 mm and 25 mm deep is

(A) Abrasive Jet Machining (B) Plasma Arc Machining

(C) Laser Beam Machining (D) Electro Discharge Machining

Q.24 The relationship between true strain () and engineering strain () in a uniaxial tension test is

given as

(A) ( )ln 1E Tε ε= + (B) ( )ln 1E Tε ε= −

(C) ( )ln 1T Eε ε= + (D) ( )ln 1T Eε ε= −

Q.18




Q.26 An analytic function of a complex variable = + is expressed as () = (,) + (,),

where = √−1 . If (,) = 2 , then (,) must be

(A) 2 + 2 + constant (B) 2 − 2 + constant

(C) − 2 + 2 + constant (D) − 2 − 2 + constant

Q.27 The general solution of the differential equation

dcos( )

d

yx y

x= + , with c as a constant, is

(A) cxyxy +=++ )(sin (B) tan2

x yy c

+ = +

(C) cos2

x yx c

+ = +

(D) tan2

x yx c

+ = +

Q.28 Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured

red, blue or green such that each colour appears only two times on the dice. If the dice is thrown

thrice, the probability of obtaining red colour on top face of the dice at least twice is _______

Q.29 The value of

4

2.5

ln( )dx x∫ calculated using the Trapezoidal rule with five subintervals is _______

Q.25 With respect to metal working, match Group A with Group B:

Group A Group B

P: Defect in extrusion I: alligatoring

Q: Defect in rolling II: scab

R: Product of skew rolling III: fish tail

S: Product of rolling through cluster mill IV: seamless tube

V: thin sheet with tight tolerance

VI: semi-finished balls of ball bearing

(A) P-II, Q-III, R-VI, S-V (B) P-III, Q-I, R-VI, S-V

(C) P-III, Q-I, R-IV, S-VI (D) P-I, Q-II, R-V, S-VI



The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam

shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then

the value of the slope at the free end is

(A)

21

2

PL

EI (B)

2PL

EI (C)

23

2

PL

EI (D)

25

2

PL

EI

Q.31 A cantilever beam of length, L, with uniform cross-section and flexural rigidity, EI, is loaded

uniformly by a vertical load, w per unit length. The maximum vertical deflection of the beam is

given by

(A)

4

8

wL

EI (B)

4

16

wL

EI (C)

4

4

wL

EI (D)

4

24

wL

EI

Q.32 For the three bolt system shown in the figure, the bolt material has shear yield strength of 200 MPa.

For a factor of safety of 2, the minimum metric specification required for the bolt is

(A) M8 (B) M10 (C) M12 (D) M16

Q.33 Consider a flywheel whose mass M is distributed almost equally between a heavy, ring-like rim of

radius R and a concentric disk-like feature of radius R/2. Other parts of the flywheel, such as

spokes, etc, have negligible mass. The best approximation for α, if the moment of inertia of the flywheel about its axis of rotation is expressed as αMR2

, is _______

P

L

PL/2

Q.30



What is the natural frequency of the spring mass system shown below? The contact between the

block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring

constants are denoted by k1 and k2 as shown below.

(A) 1 2

2

k k

m

+ (B) 1 2

4

k k

m

+ (C) 1 2k k

m

− (D) 1 2k k

m

+

Q.35 A disc clutch with a single friction surface has coefficient of friction equal to 0.3. The maximum

pressure which can be imposed on the friction material is 1.5 MPa. The outer diameter of the clutch

plate is 200 mm and its internal diameter is 100 mm. Assuming uniform wear theory for the clutch

plate, the maximum torque (in N.m) that can be transmitted is _______

Q.36 A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction

between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s2) of the

truck such that the crate does not slide down is _______

Q.37 Maximum fluctuation of kinetic energy in an engine has been calculated to be 2600 J. Assuming

that the engine runs at an average speed of 200 rpm, the polar mass moment of inertia (in kg.m2) of

a flywheel to keep the speed fluctuation within ±0.5% of the average speed is _______

Q.38 Consider the two states of stress as shown in configurations I and II in the figure below. From the

standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?

(A) I yields after II (B) II yields after I

(C) Both yield simultaneously (D) Nothing can be said about their relative yielding

Q.34



A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of

12 rad/s2. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant

acceleration (in m/s2) of the end P is _______

Q.40 A spur pinion of pitch diameter 50 mm rotates at 200 rad/s and transmits 3 kW power. The pressure

angle of the tooth of the pinion is 20°. Assuming that only one pair of the teeth is in contact, the

total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______

Q.41 A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements.

The balloon is filled with helium (RHe = 2.08 kJ/kg.K) at ambient conditions of 15°C and 100 kPa.

Assuming no disturbances due to wind, the maximum allowable weight (in newton) of balloon

material and rope required to avoid the fall of the balloon (Rair = 0.289 kJ/kg.K) is _______

Q.42 A hemispherical furnace of 1 m radius has the inner surface (emissivity, 1=ε ) of its roof

maintained at 800 K, while its floor ( 5.0=ε ) is kept at 600 K. Stefan-Boltzmann constant is

5.668 × 10−8

W/m2.K

4. The net radiative heat transfer (in kW) from the roof to the floor is _______

Q.43 Water flows through a 10 mm diameter and 250 m long smooth pipe at an average velocity of

0.1 m/s. The density and the viscosity of water are 997 kg/m3 and 855×10

−6 N.s/m

2, respectively.

Assuming fully-developed flow, the pressure drop (in Pa) in the pipe is _______

GATE -2014

Q.39



A material P of thickness 1 mm is sandwiched between two steel slabs, as shown in the figure

below. A heat flux 10 kW/m2 is supplied to one of the steel slabs as shown. The boundary

temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is 10

W/m.K. Considering one-dimensional steady state heat conduction for the configuration, the

thermal conductivity (k, in W/m.K) of material P is _______

Q.45 Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a

distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness

(in mm), at a distance of 0.75 m, is _______

Q.46 In an ideal Brayton cycle, atmospheric air (ratio of specific heats, cp/cv = 1.4, specific heat at

constant pressure = 1.005 kJ/kg.K) at 1 bar and 300 K is compressed to 8 bar. The maximum

temperature in the cycle is limited to 1280 K. If the heat is supplied at the rate of 80 MW, the mass

flow rate (in kg/s) of air required in the cycle is _______

Q.47 Steam at a velocity of 10 m/s enters the impulse turbine stage with symmetrical blading having

blade angle 30°. The enthalpy drop in the stage is 100 kJ. The nozzle angle is 20°. The maximum

blade efficiency (in percent) is _______

Q.48 In a concentric counter flow heat exchanger, water flows through the inner tube at 25°C and leaves

at 42°C. The engine oil enters at 100°C and flows in the annular flow passage. The exit temperature

of the engine oil is 50°C. Mass flow rate of water and the engine oil are 1.5 kg/s and 1 kg/s,

respectively. The specific heat of water and oil are 4178 J/kg.K and 2130 J/kg.K, respectively. The

effectiveness of this heat exchanger is _______

Q.44



Q.49 A heat pump with refrigerant R22 is used for space heating between temperature limits of −20°C

and 25°C. The heat required is 200 MJ/h. Assume specific heat of vapour at the time of discharge

as 0.98 kJ/kg.K. Other relevant properties are given below. The enthalpy (in kJ/kg) of the

refrigerant at isentropic compressor discharge is _______

Saturation

temperature

Pressure Specific enthalpy Specific entropy

Tsat (°C) P (MN/m2) hf (kJ/kg) hg (kJ/kg) sf (kJ/kg.K) sg (kJ/kg.K)

−20 0.2448 177.21 397.53 0.9139 1.7841

25 1.048 230.07 413.02 1.1047 1.7183

Q.50 A project has four activities P, Q, R and S as shown below.

Activity Normal duration (days) Predecessor Cost slope (Rs./day)

P 3 - 500

Q 7 P 100

R 4 P 400

S 5 R 200

The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs. 200/- per day.

If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of

the project is _______

Q.51 Consider the following data with reference to elementary deterministic economic order quantity

model

Annual demand of an item 100000

Unit price of the item (in Rs.) 10

Inventory carrying cost per unit per year (in Rs.) 1.5

Unit order cost (in Rs.) 30

The total number of economic orders per year to meet the annual demand is _______

Q.52 For the CNC part programming, match Group A with Group B:

Group A Group B

P: circular interpolation, counter clock wise I: G02

Q: dwell II: G03

R: circular interpolation, clock wise III: G04

S: point to point countering IV: G00

(A) P-II, Q-III, R-I, S-IV (B) P-I, Q-III, R-II, S-IV

(C) P-I, Q-IV, R-II, S-III (D) P-II, Q-I, R-III, S-IV

Q.53 A mild steel plate has to be rolled in one pass such that the final plate thickness is 2/3rd

of the initial

thickness, with the entrance speed of 10 m/min and roll diameter of 500 mm. If the plate widens by

2% during rolling, the exit velocity (in m/min) is _______



Q.54 A hole of 20 mm diameter is to be drilled in a steel block of 40 mm thickness. The drilling is

performed at rotational speed of 400 rpm and feed rate of 0.1 mm/rev. The required approach and

over run of the drill together is equal to the radius of drill. The drilling time (in minute) is

(A) 1.00 (B) 1.25 (C) 1.50 (D) 1.75

Q.55 A rectangular hole of size 100 mm × 50 mm is to be made on a 5 mm thick sheet of steel having

ultimate tensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is

made by punching process. Neglecting the effect of clearance, the punching force (in kN) is

(A) 300 (B) 450 (C) 600 (D) 750






Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 B 5 45 to 45 9 D2 B 6 C 10 A3 C 7 D4 B 8 163 to 163


Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 D 20 B 39 39 to 412 B 21 B 40 638 to 6393 A 22 C 41 5300 to 53304 A 23 D 42 24.0 to 25.25 -1.00 to -0.94 24 C 43 6800 to 69006 A 25 B 44 0.09 to 0.117 18 to 22 26 C 45 13.5 to 14.28 A 27 D 46 105 to 1129 B 28 0.25 to 0.27 47 85.1 to 89.910 99 to 101 29 1.74 to 1.76 48 0.65 to 0.6711 A 30 B 49 430 to 44012

C31

A50 12490 to

1251013 D 32 B 51 49 to 5114 A 33 0.55 to 0.57 52 A15 3135 to 3140 34 D 53 14.6 to 14.816 C 35 529 to 532 54 B17 287 to 289 36 1.0 to 1.3 55 B18 C 37 590 to 59519 B 38 C


________________________________________























type.



before the choice.


















SET - 3

_________________________________________


Q.1 “India is a country of rich heritage and cultural diversity.”

Which one of the following facts best supports the claim made in the above sentence?

(A) India is a union of 28 states and 7 union territories.

(B) India has a population of over 1.1 billion.

(C) India is home to 22 official languages and thousands of dialects.

(D) The Indian cricket team draws players from over ten states.

Q.2 The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian Rupee

has ____________.

(A) depressed (B) depreciated (C) appreciated (D) stabilized

Q.3 'Advice' is ________________.

(A) a verb (B) a noun (C) an adjective (D) both a verb and a noun

Q.4 The next term in the series 81, 54, 36, 24, … is ________

Q.5 In which of the following options will the expression P < M be definitely true?

(A) M < R > P > S (B) M > S < P < F (C) Q < M < F = P (D) P = A < R < M


Q.6 Find the next term in the sequence: 7G, 11K, 13M, ___

(A) 15Q (B) 17Q (C) 15P (D) 17P

GATE 2014 SET-3 General Aptitude - GA


Q.7 The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The

correct conclusions from this information are:

(i) Butterflies are birds

(ii) There are more tigers in this forest than red ants

(iii) All reptiles in this forest are either snakes or crocodiles

(iv) Elephants are the largest mammals in this forest

(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)

(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only

Q.8 A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to

row downstream, then find the stream velocity in km per hour.



Q.9 A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of

raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing

cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw

material expenses increased by 30% and all other expenses increased by 20%. If the company

registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air purifier sold?

Q.10 A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is

rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The

probability that the current batch is accepted is





Q.1 Consider a 3×3 real symmetric matrix S such that two of its eigenvalues are , with

respective eigenvectors , . If then equals

(A) a (B) b (C) ab (D) 0

Q.2 If a function is continuous at a point,

(A) the limit of the function may not exist at the point

(B) the function must be derivable at the point

(C) the limit of the function at the point tends to infinity

(D) the limit must exist at the point and the value of limit should be same as the value of the

function at that point

Q.3 Divergence of the vector field kzyjyxizx ˆˆˆ 22 −+ at (1, −1, 1) is

(A) 0 (B) 3 (C) 5 (D) 6

Q.4 A group consists of equal number of men and women. Of this group 20% of the men and 50% of

the women are unemployed. If a person is selected at random from this group, the probability of the

selected person being employed is _______

Q.5 The definite integral d is evaluated using Trapezoidal rule with a step size of 1. The correct

answer is _______

Q.6 A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The

maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance

strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of

safety for the shaft is _______

Q.7 Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear

stresses developed in the two shafts are and . If R1/ R2=2, then / is _______

Q.8 Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At

resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

(A) 0 (B) 45 (C) 90 (D) 135



Q.9 A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a

stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same

velocity. The coefficient of restitution is

(A) 0.6 (B) 0.1 (C) 0.01 (D) 0

Q.10 Which one of following is NOT correct?

(A) Intermediate principal stress is ignored when applying the maximum principal stress theory

(B) The maximum shear stress theory gives the most accurate results amongst all the failure

theories

(C) As per the maximum strain energy theory, failure occurs when the strain energy per unit

volume exceeds a critical value

(D) As per the maximum distortion energy theory, failure occurs when the distortion energy per

unit volume exceeds a critical value

Q.11 Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and

Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears

2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is

(A) 300 rpm counterclockwise (B) 300 rpm clockwise

(C) 4800 rpm counterclockwise (D) 4800 rpm clockwise

Q.12 Consider a long cylindrical tube of inner and outer radii, ir and

or , respectively, length, L and

thermal conductivity, k. Its inner and outer surfaces are maintained at iT and oT , respectively

(iT >

oT ). Assuming one-dimensional steady state heat conduction in the radial direction, the

thermal resistance in the wall of the tube is

(A) ⎟⎟⎠

⎞⎜⎜⎝

⎛

o

i

r

r

kLln

2

1

π (B)

kr

L

iπ2

(C) ⎟⎟⎠

⎞⎜⎜⎝

⎛

i

o

r

r

kLln

2

1

π (D) ⎟⎟

⎠

⎞⎜⎜⎝

⎛

i

o

r

r

kLln

4

1

π

3



Q.13 Which one of the following pairs of equations describes an irreversible heat engine?

(A) 0 and 0Q

QT

δδ > <∫ ∫ (B) 0 and 0Q

QT

δδ < <∫ ∫

(C) 0 and 0Q

QT

δδ > >∫ ∫ (D) 0 and 0Q

QT

δδ < >∫ ∫

Q.14 Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct

pair of statements.

I. The fluid is well-mixed

II. The fluid is unmixed

III. ReD < 2300

IV. ReD > 2300

(A) I, III (B) II, IV (C) II, III (D) I, IV

Q.15

For a gas turbine power plant, identify the correct pair of statements.

P. Smaller in size compared to steam power plant for same power output

Q. Starts quickly compared to steam power plant

R. Works on the principle of Rankine cycle

S. Good compatibility with solid fuel

(A) P, Q (B) R, S (C) Q, R (D) P, S

Q.16 A source at a temperature of 500 K provides 1000 kJ of heat. The temperature of environment is

27°C. The maximum useful work (in kJ) that can be obtained from the heat source is _______

Q.17 A sample of moist air at a total pressure of 85 kPa has a dry bulb temperature of 30°C (saturation

vapour pressure of water = 4.24 kPa). If the air sample has a relative humidity of 65%, the absolute

humidity (in gram) of water vapour per kg of dry air is _______

Q.18 The process utilizing mainly thermal energy for removing material is

(A) Ultrasonic Machining (B) Electrochemical Machining

(C) Abrasive Jet Machining (D) Laser Beam Machining

Q.19 The actual sales of a product in different months of a particular year are given below:

September October November December January February

180 280 250 190 240 ?

The forecast of the sales, using the 4-month moving average method, for the month of February

is _______



Q.20 A straight turning operation is carried out using a single point cutting tool on an AISI 1020 steel

rod. The feed is 0.2 mm/rev and the depth of cut is 0.5 mm. The tool has a side cutting edge angle

of 60°. The uncut chip thickness (in mm) is _______

Q.21 A minimal spanning tree in network flow models involves

(A) all the nodes with cycle/loop allowed (B) all the nodes with cycle/loop not allowed

(C) shortest path between start and end nodes (D) all the nodes with directed arcs

Q.22 Match the casting defects (Group A) with the probable causes (Group B):

Group A Group B

P: Hot tears 1: Improper fusion of two streams of liquid metal

Q: Shrinkage 2: Low permeability of the sand mould

R: Blow holes 3: Volumetric contraction both in liquid and solid stage

S: Cold Shut 4: Differential cooling rate

(A) P-1, Q-3, R-2, S-4 (B) P-4, Q-3, R-2, S-1

(C) P-3, Q-4, R-2, S-1 (D) P-1, Q-2, R-4, S-3

Q.23 Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work

interaction, because

(A) extra hardness is imparted to the workpiece due to coolant used

(B) oxide layers on the workpiece surface impart extra hardness to it

(C) extra hardness is imparted to the workpiece due to severe rate of strain

(D) vibration is induced in the machine tool



Q.24 The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option

referring to both figure and table.

Point on the graph Description of the point

P 1. Upper Yield Point

Q 2. Ultimate Tensile Strength

R 3. Proportionality Limit

S 4. Elastic Limit

T 5. Lower Yield Point

U 6. Failure

(A) P-1, Q-2, R-3, S-4, T-5, U-6

(B) P-3, Q-1, R-4, S-2, T-6, U-5

(C) P-3, Q-4, R-1, S-5, T-2, U-6

(D) P-4, Q-1, R-5, S-2, T-3, U-6

Q.25 The hot tearing in a metal casting is due to

(A) high fluidity (B) high melt temperature

(C) wide range of solidification temperature (D) low coefficient of thermal expansion




Q.26 An analytic function of a complex variable yixz += is expressed as ),(),()( yxviyxuzf += ,

where 1−=i . If 22),( yxyxu −= , then expression for ),( yxv in terms of x, y and a general

constant c would be

(A) cyx + (B) cyx

++2

22

(C) cyx +2 (D) cyx

+−2

)( 2

Q.27 Consider two solutions and of the differential equation

, , such that , , , .

The Wronskian at / is

(A) 1 (B) −1 (C) 0 (D) π/2

Q.28 A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and

1/6, respectively. The mean value and the variance of the number of defective pieces produced by

the machine in a day, respectively, are

(A) 1 and 1/3 (B) 1/3 and 1

(C) 1 and 4/3 (D) 1/3 and 4/3

Q.29 The real root of the equation 01cos25 =−− xx (up to two decimal accuracy) is _______

Q.30 A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The

coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure

are in mm. The braking torque (in N.m) for the brake shoe is _______

1000 N

800



Q.31 A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The

coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the

plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane

is _______

Q.32 Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and

width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum

shear stress to the maximum bending stress in the beam is

(A) 0.02 (B) 0.10 (C) 0.05 (D) 0.01

Q.33 The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg,

stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______

Q.34 An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface

without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

(A) 2

16

9mv (B)

2

16

11mv (C)

2

16

13mv (D)

2

16

15mv

Q.35 A force P is applied at a distance x from the end of the beam as shown in the figure. What would be

the value of x so that the displacement at ‘A’ is equal to zero?

(A) 0.5L (B) 0.25L (C) 0.33L (D) 0.66L

M

45°



Q.36 Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the

following pitch curves, parameterized by t, lying in the interval 0 to 2π, is associated with the

maximum translation of the follower during one full rotation of the cam rotating about the center

at (x, y) = (0, 0) ?

(A) ( ) ( )cos , sinx t t y t t= =

(B) ( ) ( )cos , 2sinx t t y t t= =

(C) ( ) ( )1cos , 2sin

2x t t y t t= + =

(D) ( ) ( )1cos , sin

2x t t y t t= + =

Q.37 A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving

at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is

applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop

in 10 s, the braking torque (in N.m) on each wheel is _______

Q.38 A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in

figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the

given configuration, the speed (in m/s) of the slider is _______

Q.39 Consider an objective function , and the constraints

, , , .

The maximum value of the objective function is _______

60 240

90°



Q.40 A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a

harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is

40 mm. The damping coefficient (c, in N.s/m) of the dashpot is _______

Q.41 A certain amount of an ideal gas is initially at a pressure p1 and temperature T1. First, it undergoes a

constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process

2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is

(A) 0.25 (B) 0.75 (C) 1.0 (D) 1.5

Q.42 An amount of 100 kW of heat is transferred through a wall in steady state. One side of the wall is

maintained at 127°C and the other side at 27°C. The entropy generated (in W/K) due to the heat

transfer through the wall is _______

Q.43 A siphon is used to drain water from a large tank as shown in the figure below. Assume that the

level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry

and exit. At the exit of the siphon, the velocity of water is

(A) Z Z (B) Z Z (C) Z Z (D) Z

m

kc

F=10 cos(25t)

Datum R

ZQ ZP

ZR

Q

P



Q.44 Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal

thickness (l). The conductivity of one section is k and that of the other is 2k. The left face of the

wall is at 600 K and the right face is at 300 K.

The interface temperature Ti (in K) of the composite wall is _______

Q.45 A fluid of dynamic viscosity 2 × 10−5 kg/m.s and density 1 kg/m3 flows with an average velocity of

1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow,

the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______

Q.46 At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of

absolute velocity is 100 m/s and the angle between them is 25°. The relative velocity and the axial

component of velocity remain the same between the inlet and outlet of the blades. The blade inlet

and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in J/kg)

is _______

Q.47 A solid sphere of radius r1 = 20 mm is placed concentrically inside a hollow sphere of radius

r2 = 30 mm as shown in the figure.

The view factor F21 for radiation heat transfer is

(A) (B) (C) (D)

Heat flow

l

k

2k

600 K Ti 300 K

l

78 m/s

58.6 m/s78 m/s

100 m/s

25 m/s

25°

r1

r2

12



Q.48 A d

wat

Ass

LM

Q.49 A d

Ass

Q.50 Con

tim

(A)

Q.51 A m

bea

Set

pro

(A)

Q.52 A c

clo

soli

(A)

double-pipe

ter at 19 lite

sume constan

MTD (in °C) i

diesel engin

suming ratio

nsider the gi

me. The free f

) 2, 13

manufacturer

arings per da

tup cost per

oduction run

) 4.5 days

cylindrical b

sed type san

idification in

) 1:2

1

2

3

4

3

2

2

counter-flow

er/s is heated

nt properties

is _______

ne has a com

of specific h

iven project

float on activ

(B)

r can produc

ay from a cu

production r

should be

(B)

lind riser wi

nd mold as s

n the riser is t

(B)

2

3

4

2

5

4

w heat excha

d from 10°C

s of water; d

mpression ra

heats (γ) as 1

network, wh

vity 4-6 and t

0, 13

ce 12000 bea

ustomer. The

run is Rs. 50

4.5 months

ith diameter

shown in the

the least whe

2:1

5

6

3

anger transfe

to 38°C. Sh

density is 100

atio of 17 a

1.4, the air-st

here number

the project du

(C)

arings per da

e cost of hol

00. Assuming

(C)

d and height

e figure. If th

en the ratio h

(C)

75

ers heat betw

hell side wat

00 kg/m3 an

and cut-off

tandard effici

rs along vari

uration, resp

−2, 13

ay. The manu

lding a beari

g 300 worki

6.8 days

t h, is placed

he riser is o

h:d is

1:4

ween two wa

ter at 25 lite

nd specific he

takes place

iency (in per

ious activitie

pectively, are

(D)

ufacturer rec

ing in stock

ng days in a

(D)

d on the top

f constant v

(D)

ater streams.

er/s is enterin

eat is 4186 J

at 10% of

rcent) is ____

es represent

e

2, 12

ceived an ord

is Rs. 0.20

a year, the fr

6.8 months

of the mold

volume, then

4:1

. Tube side

ng at 46°C.

J/kg.K. The

the stroke.

____

the normal

der of 8000

per month.

requency of

cavity of a

the rate of



Q.53 The diameter of a recessed ring was measured by using two spherical balls of diameter d2=60 mm

and d1=40 mm as shown in the figure.

The distance H2=35.55 mm and H1=20.55 mm. The diameter (D, in mm) of the ring gauge

is _______

Q.54 Which pair of following statements is correct for orthogonal cutting using a single-point cutting

tool?

P. Reduction in friction angle increases cutting force

Q. Reduction in friction angle decreases cutting force

R. Reduction in friction angle increases chip thickness

S. Reduction in friction angle decreases chip thickness

(A) P and R (B) P and S (C) Q and R (D) Q and S

Q.55 For spot welding of two steel sheets (base metal) each of 3 mm thickness, welding current of

10000 A is applied for 0.2 s. The heat dissipated to the base metal is 1000 J. Assuming that the heat

required for melting 1 mm3 volume of steel is 20 J and interfacial contact resistance between sheets

is 0.0002 Ω, the volume (in mm3) of weld nugget is _______






Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1

C5

D9 20000 to

200002 B 6 B 10 0.80 to 0.823 B 7 D4 16 to 16 8 4 to 4


Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 D 20 0.08 to 0.12 39 17 to 192 D 21 B 40 9 to 113 C 22 B 41 B4 0.64 to 0.66 23 C 42 80 to 855 1.1 to 1.2 24 C 43 B6 1.9 to 2.1 25 C 44 399 to 4017 7.9 to 8.1 26 C 45 1.7 to 2.08 C 27 A 46 3250 to 33009 D 28 A 47 B10 B 29 0.53 to 0.56 48 10.8 to 11.211 A 30 63 to 65 49 58 to 6212 C 31 56 to 59 50 A13 A 32 D 51 C14 D 33 1.24 to 1.26 52 A15 A 34 C 53 92 to 9416 399 to 401 35 C 54 D17 19 to 22 36 C 55 140 to 16018 D 37 9 to 1119 239 to 241 38 0.54 to 0.68


_________________________________________























type.



before the choice.


















SET - 4

________________________________________


Q.1 Which of the following options is the closest in meaning to the word underlined in the sentence

below?

In a democracy, everybody has the freedom to disagree with the government.

(A) dissent (B) descent (C) decent (D) decadent

Q.2 After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.

(A) retract (B) get back to him (C) move in reverse (D) retreat

Q.3 While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest

in meaning to the word ‘vindicated’?

(A) punished (B) substantiated (C) appreciated (D) chastened

Q.4 Let (,) = = . If x is doubled and y is halved, the new value of f is

(A) 2− (B) 2− (C) 2( −) (D) 2( − )

Q.5 In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the

sum of the last 5 numbers in the sequence?


Q.6 Find the next term in the sequence: 13M, 17Q, 19S, ___

(A) 21W (B) 21V (C) 23W (D) 23V

Q.7 If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the

following indicates ‘ace the exam’?

(A) MCHTX (B) MXHTC (C) XMHCT (D) XMHTC

Q.8 Industrial consumption of power doubled from 2000-2001 to 2010-2011. Find the annual rate of

increase in percent assuming it to be uniform over the years.

(A) 5.6 (B) 7.2 (C) 10.0 (D) 12.2



Q.9

Q.10 A five digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is

the sum of all such possible five digit numbers?

(A) 6666660 (B) 6666600 (C) 6666666 (D) 6666606


A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of

raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing

cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw

material expenses increased by 30% and all other expenses increased by 20%. What is the

percentage increase in total cost for the company in 2013?



Q.2 The value of the integral

2 2

2

0

( 1) sin( 1)d

( 1) cos( 1)

x xx

x x

− −− + −∫

is

(A) 3 (B) 0 (C) −1 (D) −2

Q.3 The solution of the initial value problem dd = −2 ; (0) = 2 is

(A) 1 + e−2 (B) 2 e−2

(C) 1 + e2 (D) 2 e2

Q.4 A nationalized bank has found that the daily balance available in its savings accounts follows a

normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of

savings account holders, who maintain an average daily balance more than Rs. 500 is _______

Q.5 Laplace transform of cos( ) is 2+ 2

. The Laplace transform of e−2 cos(4) is

(A) −2

(−2)2+ 16 (B)

+2

(−2)2+ 16

(C) −2

(+2)2+ 16 (D)

+2

(+2)2+ 16

Q.6 In a statically determinate plane truss, the number of joints (j) and the number of members (m) are

related by

(A) j = 2m – 3 (B) m = 2j + 1 (C) m = 2j – 3 (D) m = 2j − 1

Q.7 If the Poisson's ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young's

modulus is _______

Q.8 Which one of the following is used to convert a rotational motion into a translational motion?

(A) Bevel gears (B) Double helical gears

(C) Worm gears (D) Rack and pinion gears

Q.1 Which one of the following equations is a correct identity for arbitrary 3×3 real matrices P, Q and R?

(A) ( + ) = +

(B) ( − )2 = 2 − 2 + 2

(C) det ( + ) = det + det

(D) ( + )2 = 2 + + + 2




Q.9 The number of independent elastic constants required to define the stress-strain relationship for an

isotropic elastic solid is _______

Q.10 A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of

4 Hz. The maximum acceleration (m/s2) of the mass is _______

Q.11 Ball bearings are rated by a manufacturer for a life of 106 revolutions. The catalogue rating of a

particular bearing is 16 kN. If the design load is 2 kN, the life of the bearing will be × 106

revolutions, where is equal to _______

Q.12 As the temperature increases, the thermal conductivity of a gas

(A) increases (B) decreases

(C) remains constant (D) increases up to a certain temperature and then decreases

Q.13 A reversed Carnot cycle refrigerator maintains a temperature of −5° C. The ambient air temperature

is 35°C. The heat gained by the refrigerator at a continuous rate is 2.5 kJ/s. The power (in watt)

required to pump this heat out continuously is _______

Q.14 A flow field which has only convective acceleration is

(A) a steady uniform flow (B) an unsteady uniform flow

(C) a steady non-uniform flow (D) an unsteady non-uniform flow

Q.15 Match Group A with Group B:

Group A Group B

P: Biot number 1: Ratio of buoyancy to viscous force

Q: Grashof number 2: Ratio of inertia force to viscous force

R: Prandtl number 3: Ratio of momentum to thermal diffusivities

S: Reynolds number 4: Ratio of internal thermal resistance to

boundary layer thermal resistance

(A) P-4, Q-1, R-3, S-2 (B) P-4, Q-3, R-1, S-2

(C) P-3, Q-2, R-1, S-4 (D) P-2, Q-1, R-3, S-4

Q.16 Kaplan water turbine is commonly used when the flow through its runner is

(A) axial and the head available is more than 100 m

(B) axial and the head available is less than 10 m

(C) radial and the head available is more than 100 m

(D) mixed and the head available is about 50 m



Q.17 Moist air at 35°C and 100% relative humidity is entering a psychrometric device and leaving at

25°C and 100% relative humidity. The name of the device is

(A) Humidifier (B) Dehumidifier (C) Sensible heater (D) Sensible cooler

Q.18 The total number of decision variables in the objective function of an assignment problem of size

n × n (n jobs and n machines) is

(A) 2 (B) 2 (C) 2 − 1 (D)

Q.19 Demand during lead time with associated probabilities is shown below:

Demand 50 70 75 80 85

Probability 0.15 0.14 0.21 0.20 0.30

Expected demand during lead time is _______

Q.20

Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes

(A) microstructural changes but does not melt

(B) neither melting nor microstructural changes

(C) both melting and microstructural changes after solidification

(D) melting and retains the original microstructure after solidification

Q.21 Two separate slab milling operations, 1 and 2, are performed with identical milling cutters. The

depth of cut in operation 2 is twice that in operation 1. The other cutting parameters are identical.

The ratio of maximum uncut chip thicknesses in operations 1 and 2 is _______

Q.22 The principle of material removal in Electrochemical machining is

(A) Fick's law (B) Faraday's laws

(C) Kirchhoff'’s laws (D) Ohm’s law

Q.23 Better surface finish is obtained with a large rake angle because

(A) the area of shear plane decreases resulting in the decrease in shear force and cutting force

(B) the tool becomes thinner and the cutting force is reduced

(C) less heat is accumulated in the cutting zone

(D) the friction between the chip and the tool is less



Match the heat treatment processes (Group A) and their associated effects on properties (Group B)

of medium carbon steel

Group A Group B

P: Tempering I: Strengthening and grain refinement

Q: Quenching II: Inducing toughness

R: Annealing III: Hardening

S: Normalizing IV: Softening

(A) P-III, Q-IV, R-II, S-I (B) P-II, Q-III, R-IV, S-I

(C) P-III, Q-II, R-IV, S-I (D) P-II, Q-III, R-I, S-IV

Q.25 In a rolling process, the maximum possible draft, defined as the difference between the initial and

the final thickness of the metal sheet, mainly depends on which pair of the following parameters?

P: Strain

Q: Strength of the work material

R: Roll diameter

S: Roll velocity

T: Coefficient of friction between roll and work

(A) Q, S (B) R, T (C) S, T (D) P, R


Q.26 If z is a complex variable, the value of

3

5

di

z

z∫ is

(A) − 0.511−1.57i (B) − 0.511+1.57i

(C) 0.511− 1.57i (D) 0.511+1.57i

Q.27 The value of the integral

2

0 0

e d d

x

x yy x

+∫ ∫

is

(A) 1

(e 1)2

− (B) 2 21

(e 1)2

− (C) 21

(e e)2

− (D)

21 1

e2 e

−

Q.28 The number of accidents occurring in a plant in a month follows Poisson distribution with mean

as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly

selected month is

(A) 0.029 (B) 0.034 (C) 0.039 (D) 0.044

Q.24



Consider an ordinary differential equation

d4 4

d

xt

t= + . If x = x0 at t = 0, the increment in x

calculated using Runge-Kutta fourth order multi-step method with a step size of ∆t = 0.2 is

(A) 0.22 (B) 0.44 (C) 0.66 (D) 0.88

Q.30 A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is

100 MPa. The yield and ultimate strengths of the shaft material in tension are 300 MPa and

450 MPa, respectively. The factor of safety using maximum distortion energy (von-Mises) theory

is _______

Q.31 A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa.

The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall

thickness (in mm) for safe design must be _______

Q.32 For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The

force (in kN) in the member QS is

(A) 11.25 tension (B) 11.25 compression (C) 13.5 tension (D) 13.5 compression

Q.33 It is desired to avoid interference in a pair of spur gears having a 20° pressure angle. With increase

in pinion to gear speed ratio, the minimum number of teeth on the pinion

(A) increases (B) decreases

(C) first increases and then decreases (D) remains unchanged

Q.29



1 m from its end as shown in the figure. The magnitude of the angular acceleration (in rad/s2) of the

rod at the position shown is _______

Q.35 A bolt of major diameter 12 mm is required to clamp two steel plates. Cross sectional area of the

threaded portion of the bolt is 84.3 mm2. The length of the threaded portion in grip is 30 mm, while

the length of the unthreaded portion in grip is 8 mm. Young's modulus of material is 200 GPa. The

effective stiffness (in MN/m) of the bolt in the clamped zone is _______

Q.36 A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity

EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is

(A)

31

3

PL

EI (B)

32

3

PL

EI (C)

3PL

EI (D)

34

3

PL

EI

Q.37 A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands

on a rough level floor as shown in the figure. A force P is applied at mid-height on the wardrobe so

as to tip it about point Q without slipping. What are the minimum values of the force (in newton)

and the static coefficient of friction µ between the floor and the wardrobe, respectively?

(A) 490.5 and 0.5 (B) 981 and 0.5

(C) 1000.5 and 0.15 (D) 1000.5 and 0.25

L

L

P

A

Y

Y

P

4 m

Q

2m

Q.34 A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis



Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the

figures. The moment of inertia (in kg.m2) of the flywheel is _______

Q.39 A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping

ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is _______

Q.40 A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless

contact at the floor (B) and the wall (A), the magnitude of the force P (in newton) required to

maintain equilibrium of the ladder is _______

Q.41 A closed system contains 10 kg of saturated liquid ammonia at 10°C. Heat addition required to

convert the entire liquid into saturated vapour at a constant pressure is 16.2 MJ. If the entropy of the

saturated liquid is 0.88 kJ/kg.K, the entropy (in kJ/kg.K) of saturated vapour is _______

Q.42 A plane wall has a thermal conductivity of 1.15 W/m.K. If the inner surface is at 1100°C and the

outer surface is at 350°C, then the design thickness (in meter) of the wall to maintain a steady heat

flux of 2500 W/m2 should be _______

θ 2π 3π /2 π

π/2 0

Torque

3000

N-m

-1500

N-m

θ 2π 3π /2 π π/2 0

20 rad/s

10 rad/s

Angular speed

2.5 m

2.5 m

4 m

3 m

W P

B

A

Q.38



Consider the following statements regarding streamline(s):

(i) It is a continuous line such that the tangent at any point on it shows the velocity vector

at that point

(ii) There is no flow across streamlines

(iii) d d dx y z

u v w= = is the differential equation of a streamline, where u, v and w are

velocities in directions x, y and z, respectively

(iv) In an unsteady flow, the path of a particle is a streamline

Which one of the following combinations of the statements is true?

(A) (i), (ii), (iv) (B) (ii), (iii), (iv)

(C) (i), (iii), (iv) (D) (i), (ii), (iii)

Q.44 Consider a velocity field ˆˆK( ),V y i x k= +

where K is a constant. The vorticity, ΩZ , is

(A) − K (B) K (C) − K /2 (D) K /2

Q.45 Water flows through a tube of diameter 25 mm at an average velocity of 1.0 m/s. The properties of

water are = 1000 kg/m3, = 7.25 × 10−4 N.s/m2, = 0.625 W/m.K, Pr = 4.85. Using = 0.023 0.8 0.4 , the convective heat transfer coefficient (in W/m

2.K) is _______

Q.46 Two identical metal blocks L and M (specific heat = 0.4 kJ/kg.K), each having a mass of 5 kg, are

initially at 313 K. A reversible refrigerator extracts heat from block L and rejects heat to block M

until the temperature of block L reaches 293 K. The final temperature (in K) of block M is _______

Q.47 Steam with specific enthalpy (h) 3214 kJ/kg enters an adiabatic turbine operating at steady state

with a flow rate 10 kg/s. As it expands, at a point where h is 2920 kJ/kg, 1.5 kg/s is extracted for

heating purposes. The remaining 8.5 kg/s further expands to the turbine exit, where h = 2374 kJ/kg.

Neglecting changes in kinetic and potential energies, the net power output (in kW) of the turbine

is _______

Q.48 Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is

inserted between the plates without touching any of them to reduce heat exchange between the

plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat

exchange between the plates with and without the shield is

(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/8

Q.49 In a compression ignition engine, the inlet air pressure is 1 bar and the pressure at the end of

isentropic compression is 32.42 bar. The expansion ratio is 8. Assuming ratio of specific heats (γ) as 1.4, the air standard efficiency (in percent) is _______

Q.43



The precedence relations and duration (in days) of activities of a project network are given in the

table. The total float (in days) of activities e and f , respectively, are

Activity Predecessors Duration (days)

a - 2

b - 4

c a 2

d b 3

e c 2

f c 4

g d, e 5

(A) 0 and 4 (B) 1 and 4 (C) 2 and 3 (D) 3 and 1

Q.51 At a work station, 5 jobs arrive every minute. The mean time spent on each job in the work station

is 1/8 minute. The mean steady state number of jobs in the system is _______

Q.52 A GO-No GO plug gauge is to be designed for measuring a hole of nominal diameter 25 mm with a

hole tolerance of ± 0.015 mm. Considering 10% of work tolerance to be the gauge tolerance and no

wear condition, the dimension (in mm) of the GO plug gauge as per the unilateral tolerance

system is

(A) 24.985

+0.003−0.003

(B) 25.015

+0.000−0.006

(C) 24.985

+0.03−0.03

(D) 24.985

+0.003−0.000

Q.53 A cylindrical riser of 6 cm diameter and 6 cm height has to be designed for a sand casting mould

for producing a steel rectangular plate casting of 7 cm × 10 cm × 2 cm dimensions having the total

solidification time of 1.36 minute. The total solidification time (in minute) of the riser is _______

Q.54 A cast iron block of 200 mm length is being shaped in a shaping machine with a depth of cut of

4 mm, feed of 0.25 mm/stroke and the tool principal cutting edge angle of 30°. Number of cutting

strokes per minute is 60. Using specific energy for cutting as 1.49 J/mm3, the average power

consumption (in watt) is _______

Q.55 A butt weld joint is developed on steel plates having yield and ultimate tensile strength of 500 MPa

and 700 MPa, respectively. The thickness of the plates is 8 mm and width is 20 mm. Improper

selection of welding parameters caused an undercut of 3 mm depth along the weld. The maximum

transverse tensile load (in kN) carrying capacity of the developed weld joint is _______


Q.50





Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 A 5 495 to 495 9 22 to 222 B 6 C 10 B3 B 7 B4 A 8 B


Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 D 20 A 39 2.0 to 2.42 B 21 0.70 to 0.72 40 399 to 4013 B 22 B 41 6.4 to 6.74 49 to 51 23 A 42 0.33 to 0.355 D 24 B 43 D6 C 25 B 44 A7 0.35 to 0.36 26 B 45 4600 to 46258 D 27 B 46 333 to 3359 1.9 to 2.1 28 B 47 7580 to 758210 6.3 to 6.4 29 D 48 A11 500 to 540 30 1.7 to 1.8 49 59 to 6112 A 31 9.8 to 10.6 50 B13 370 to 375 32 A 51 1.62 to 1.7014 C 33 A 52 D15 A 34 1.9 to 2.1 53 2.5 to 4.516 B 35 460 to 470 54 295 to 30517 B 36 D 55 68 to 7218 A 37 A19 74 to 75 38 30 to 32


__________________________________________

ME : MECHANICAL ENGINEERING Duration: Three Hours Maximum Marks: 100


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 ME,

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 ME



______________________________________

Q.1 to Q.25 carry one mark each.

Q.1 The partial differential equation 2

2

x

u

x

uu

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.2 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.3 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

Q.4 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 1E to 2E along the

length of the rod, the normal stress developed at the section-SS is

(A) A

P (B)

( )

( )21

21

EEA

EEP

+

− (C)

1

2

AE

PE (D)

2

1

AE

PE

Q.5 Two threaded bolts A and B of same material and length are subjected to identical tensile load. If

the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

(A) 16 (B) 24 (C) 36 (D) 48

S

P P

S

L

L/2

E1 E2

GATE 2013 Mechanical Engineering - ME


Q.6 A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and

a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the

rod, as shown in the figure below. If OA = 1 m, the magnitude of the absolute acceleration of the

block at location A in m/s2 is

(A) 3 (B) 4 (C) 5 (D) 6

Q.7 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 wτ are related by

(A) L

Dpw

4

∆=τ (B)

2

2

4L

Dpw

∆=τ (C)

L

Dpw

2

∆=τ (D)

D

pLw

∆=

4τ

Q.8 The pressure, dry bulb temperature and relative humidity of air in a room are 1 bar, 30°C and 70%,

respectively. If the saturated steam pressure at 30°C is 4.25 kPa, the specific humidity of the room

air in kg water vapour/kg dry air is

(A) 0.0083 (B) 0.0101 (C) 0.0191 (D) 0.0232

Q.9 Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall;

with boundary conditions as shown in the figure below. The conductivity of the wall is given by

bTkk += 0 ; where k0 and b are positive constants, and T is temperature.

As x increases, the temperature gradient ( dxdT ) will

(A) remain constant (B) be zero (C) increase (D) decrease

Q.10 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

B

A

O

1T

2T

x

12where TT >



Q.11 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.12 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.13 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.14 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) 1.0 Q.15 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 mm3/s is

(A) 160 (B) 167.6 (C) 1600 (D) 1675.5 Q.16 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.17 For a ductile material, toughness is a measure of

(A) resistance to scratching (B) ability to absorb energy up to fracture

(C) ability to absorb energy till elastic limit (D) resistance to indentation

Q.18 In order to have maximum power from a Pelton turbine, the bucket speed must be

(A) equal to the jet speed. (B) equal to half of the jet speed.

(C) equal to twice the jet speed. (D) independent of the jet speed. Q.19 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.



Q.20 A cylinder contains 5 m3 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.21 A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure.

The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0

Q.22 If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long

slender rotating shaft, the first critical speed of the shaft in rpm is

(A) 200 (B) 450 (C) 600 (D) 900

Q.23 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.24 Let X be a normal random variable with mean 1 and variance 4. The probability PX < 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.25 Choose the CORRECT set of functions, which are linearly dependent.

(A) xsin , 2sin x and 2cos x (B) cos x , xsin and xtan

(C) cos 2x , 2sin x and 2cos x (D) cos 2x , xsin and xcos



Q.26 to Q.55 carry two marks each.

Q.26 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.

dAS

).(4

1∫∫ nF

where S is the sphere, 1222 =++ zyx and n is the outward unit normal vector to the sphere. The

value of the surface integral is

(A) π (B) 2π (C) 3π /4 (D) 4π

Q.27 The function ( )tf satisfies the differential equation 02

2

=+ fdt

fd and the auxiliary

conditions, 4)0( ,0)0( ==dt

dff . The Laplace transform of )(tf is given by

(A) 1

2

+s (B)

1

4

+s (C)

1

42 +s

(D) 1

24 +s

Q.28 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.29 Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream

diameter is 20 mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s2.

Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting

curvature and surface tension effects, the diameter in mm of the stream 0.5 m below the tap is

approximately

(A) 10 (B) 15 (C) 20 (D) 25

Q.30 A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is

suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat

transfer coefficient h = 20 W/m2K. The thermo-physical properties of steel are: density

ρ = 7800 kg/m3, conductivity k = 40 W/mK and specific heat c = 600 J/kgK. The time required in

seconds to cool the steel ball in air from 1030°C to 430°C is

(A) 519 (B) 931 (C) 1195 (D) 2144



Q.31 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-m2 is

(A) 25 (B) 50 (C) 100 (D) 125

Q.32 A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20,

respectively. Gears Q and R are mounted on the same shaft as shown in the figure below. The

diameter of the gear Q is twice that of the gear R. If the module of the gear R is 2 mm, the center

distance in mm between gears P and S is

(A) 40 (B) 80 (C) 120 (D) 160

Q.33 A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external

force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

(A) zero (B) 4W (C) 2W (D) W

Q.34 Two cutting tools are being compared for a machining operation. The tool life equations are:

Carbide tool: 30006.1 =VT

HSS tool: 2006.0 =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.35 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)

+ + +

P

Q

R

S



Q.36 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.37 Cylindrical pins of 020.0010.025

++ mm diameter are electroplated in a shop. Thickness of the plating is

0.230±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.38 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

Q.39 A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is

subjected to an impulse force of magnitude 5 kN for 10−4 seconds. The amplitude in mm of the

resulting free vibration is

(A) 0.5 (B) 1.0 (C) 5.0 (D) 10.0

Q.40 A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength

of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg

principle, the area of cross-section in mm2 of the bar for a factor of safety of 2 is

(A) 400 (B) 600 (C) 750 (D) 1000

Q.41 A simply supported beam of length L is subjected to a varying distributed load

sin (3π x/L) Nm−1, where the distance x is measured from the left support. The magnitude of the

vertical reaction force in N at the left support is

(A) zero (B) π3L (C) πL (D) πL2

Q.42 Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of

400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is

5.67 × 10−8W/m

2K

4, the net radiation heat exchange rate in kW/m2 between the two plates is

(A) 0.66 (B) 0.79 (C) 0.99 (D) 3.96



Q.43 A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is

shown in the figure below. Density of water is 1000 kg/m3. The minimum mass of the gate in kg per

unit width (perpendicular to the plane of paper), required to keep it closed is

(A) 5000 (B) 6600 (C) 7546 (D) 9623

Q.44 The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s,

respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK

and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the

surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is

(A) 170 (B) 187 (C) 191 (D) 213

Q.45 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.46 The solution to the differential equation 2

20

d u duk

dx dx− = where k is a constant, subjected to the

boundary conditions u(0) = 0 and u(L) = U, is

(A) L

xUu = (B)

−

−=

kL

kx

e

eUu

1

1

(C)

−

−=

−

−

kL

kx

e

eUu

1

1 (D)

+

+=

kL

kx

e

eUu

1

1

Q.47 The value of the definite integral 1

ex∫ ( ) dxxln 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



Common Data Questions

Common Data for Questions 48 and 49:

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical

and material details.

width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the

rivet dr = 10 mm, diameter of the rivet hole dh = 11 mm, allowable tensile stress of the plate σp = 200 MPa,

allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the rivet σc = 150 MPa.

Q.48 If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is

(A) 7.50 (B) 15.00 (C) 22.50 (D) 30.00 Q.49 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


Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The

pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux Wq ′′ in W/m2:

Q.50 If Wq ′′ = 2500x, where x is in m and in the direction of flow (x = 0 at the inlet), the bulk mean

temperature of the water leaving the pipe in °C is

(A) 42 (B) 62 (C) 74 (D) 104

Q.51 If Wq ′′ = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/m2K, the

temperature in °C at the inner surface of the pipe at the outlet is

(A) 71 (B) 76 (C) 79 (D) 81

P

t

t

w w P



Linked Answer Questions

Statement for Linked Answer Questions 52 and 53:

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.52 The orthogonal rake angle of the cutting tool in degree is

(A) zero (B) 3.58 (C) 5 (D) 7.16

Q.53 The normal force acting at the chip-tool interface in N is

(A) 1000 (B) 1500 (C) 2000 (D) 2500


In a simple Brayton cycle, the pressure ratio is 8 and temperatures at the entrance of compressor and

turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies

equal to 0.8. For the gas, assume a constant value of cp (specific heat at constant pressure) equal to 1 kJ/kgK

and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

Q.54 The power required by the compressor in kW/kg of gas flow rate is

(A) 194.7 (B) 243.4 (C) 304.3 (D) 378.5

Q.55 The thermal efficiency of the cycle in percentage (%) is

(A) 24.8 (B) 38.6 (C) 44.8 (D) 53.1




Q.56 to Q.60 carry one mark each.

Q.56 Complete the sentence:

Universalism is to particularism as diffuseness is to _______________.

(A) specificity (B) neutrality (C) generality (D) adaptation

Q.57 Were you a bird, you ___________________ in the sky.

(A) would fly (B) shall fly (C) should fly (D) shall have flown

Q.58 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.59 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.60 What will be the maximum sum of 44, 42, 40, ...... ?

(A) 502 (B) 504 (C) 506 (D) 500

Q. 61 to Q. 65 carry two marks each.

Q.61 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

Q.62 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.63 Find the sum of the expression

8180

1...............

43

1

32

1

21

1

+++

++

++

+

(A) 7 (B) 8 (C) 9 (D) 10

Q.64 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.65 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 of the following assertions is best supported by the above information?

(A) Failure is the pillar of success.

(B) Honesty is the best policy.

(C) Life begins and ends with adventures.

(D) No adversity justifies giving up hope.




GATE 2013 - Answer KeysMechanical Engineering - ME

Q. No Key / Range Q. No Key / Range Q. No Key / Range1 D 23 C 45 D2 C 24 B 46 B3 D 25 C 47 C4 A 26 A 48 C5 B 27 C 49 C6 C 28 A 50 B7 A 29 B 51 D8 C 30 D 52 A9 D 31 A 53 B10 C 32 B 54 C11 A 33 B 55 A12 C 34 B 56 A13 C 35 B 57 A14 D 36 B 58 B15 D 37 D 59 C16 Marks to All 38 C 60 C17 B 39 C 61 D18 B 40 D 62 C19 B 41 B 63 B20 A 42 A 64 B21 C 43 D 65 D22 A 44 B


__________________________________________

Duration: Three Hours Maximum Marks: 100


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 the Question Booklet Code printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, exchange the booklet immediately with a new sealed Question Booklet.

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 ME

ME : MECHANICAL ENGINEERING




Q.1 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.2 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.3 In an interchangeable assembly, shafts of size 010.0040.0

000.25

mm mate with holes of size

020.0030.0

000.25

mm. The maximum interference (in microns) in the assembly is

(A) 40 (B) 30 (C) 20 (D) 10

Q.4 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.5 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 m3/s. The head loss (in m) due to friction is (assume

g = 9.81 m/s2)

(A) 116.18 (B) 0.116 (C) 18.22 (D) 232.36

Q.6 For an opaque surface, the absorptivity , transmissivity and reflectivity are related by

the equation:

(A) (B) 0 (C) 1 (D) 0

Q.7 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 hf = 225.94 kJ/kg and hg = 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.8 The following are the data for two crossed helical gears used for speed reduction:

Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30º

Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5º

If the input speed is 1440 rpm, the output speed in rpm is

(A) 1200 (B) 900 (C) 875 (D) 720

Q.9 A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and

angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is

(A) zero (B) r (C) 2 2 2( ) ( )r r (D)

2r

Q.10 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.11 The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

(A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2

Q.12 Consider the function ( )f x x in the interval 1 1x . 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.13 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.14 20

1 coslimx

x

x

is

(A) 1/4 (B) 1/2 (C) 1 (D) 2

Q.15 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.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



Q.17 The velocity triangles at the inlet and exit of the rotor of a turbomachine are shown. V denotes the

absolute velocity of the fluid, W denotes the relative velocity of the fluid and U denotes the blade

velocity. Subscripts 1 and 2 refer to inlet and outlet respectively. If V2 = W1 and V1 = W2, then the

degree of reaction is

(A) 0 (B) 1 (C) 0.5 (D) 0.25

Q.18 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.19 An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an

initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change S

of the gas is

(A) 2

1

lnP

mRP

(B) 1

2

lnP

mRP

(C) 2

1 1

lnP Q

mRP T

(D) zero

Q.20 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

V2

U

W2

W1

V1

Note: All dimensions are in mm.



Q.21 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

Q.22 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)

2ML

EI (C)

22ML

EI (D)

24ML

EI

Q.23 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.24 At x = 0, the function 3( ) 1f x x has

(A) a maximum value (B) a minimum value

(C) a singularity (D) a point of inflection

Q.25 For the spherical surface 2 2 2 1x y z , the unit outward normal vector at the point

(1 1

, ,02 2

) is given by

(A) 1 1ˆ ˆ2 2

i j (B) 1 1ˆ ˆ2 2

i j

(C) k (D) 1 1 1 ˆˆ ˆ3 3 3

i j k



Q. 26 - Q. 55 carry two marks each.

Q.26 The homogeneous state of stress for a metal part undergoing plastic deformation is

10 5 0

5 20 0

0 0 10

T

,

where the stress component values are in MPa. Using von Mises yield criterion, the value of

estimated shear yield stress, in MPa is

(A) 9.50 (B) 16.07 (C) 28.52 (D) 49.41

Q.27 Details pertaining to an orthogonal metal cutting process are given below.

Chip thickness ratio 0.4

Undeformed thickness 0.6 mm

Rake angle +10°

Cutting speed 2.5 m/s

Mean thickness of primary shear zone 25 microns

The shear strain rate in s–1

during the process is

(A) 0.1781×105 (B) 0.7754×10

5 (C) 1.0104×10

5 (D) 4.397×10

5

Q.28 In a single pass drilling operation, a through hole of 15 mm diameter is to be drilled in a steel plate

of 50 mm thickness. Drill spindle speed is 500 rpm, feed is 0.2 mm/rev and drill point angle is

118°. Assuming 2 mm clearance at approach and exit, the total drill time (in seconds) is

(A) 35.1 (B) 32.4 (C) 31.2 (D) 30.1

Q.29 Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure.

If D1 and D2 are the diameters of the inner and outer tubes respectively, then the view factor F22 is

given by

(A) 2

1

1D

D

(B) zero (C) 1

2

D

D

(D) 1

2

1D

D

1

2



Q.30 An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer

thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid

alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm

will be

(A) 4 (B) 2 (C) 0.5 (D) 0.25

Q.31 A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature of

air in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at

25°C is 3.17 kPa, the relative humidity of the air in the room is

(A) 67% (B) 55% (C) 83% (D) 71%

Q.32 A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the

fillets are of 10 mm size and the weld length is 30 mm. If the allowable shear stress of the weld is

94 MPa, considering the minimum throat area of the weld, the maximum allowable transverse load

in kN is

(A) 14.44 (B) 17.92 (C) 19.93 (D) 22.16

Q.33 A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The

rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude

of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the

system is

(A) k

m (B)

2k

m (C)

2

k

m (D)

4k

m

Q.34 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

Q.35 The inverse Laplace transform of the function 1

( )( 1)

F ss s

is given by

(A) ( ) sinf t t (B) ( ) sintf t e t

(C) ( ) tf t e

(D) ( ) 1 tf t e

F

F



Q.36 For the matrix A = 5 3

1 3

, ONE of the normalized eigen vectors is given as

(A)

1

2

3

2

(B)

1

2

1

2

(C)

3

10

1

10

(D)

1

5

2

5

Q.37 Calculate the punch size in mm, for a circular blanking operation for which details are given below.

Size of the blank 25 mm

Thickness of the sheet 2 mm

Radial clearance between punch and die 0.06 mm

Die allowance 0.05 mm

(A) 24.83

(B) 24.89 (C) 25.01 (D) 25.17 Q.38 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.39 In a DC arc welding operation, the voltage-arc length characteristic was obtained as

20 5arcV l where the arc length l was varied between 5 mm and 7 mm. Here Varc 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.40 A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming

that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

(A) 1 1 2 23

3 3 3 3

2 1h h

ghh h

(B) 1 2 32g h h h

(C) 1 1 2 2 3 3

1 2 3

2h h h

g

(D) 1 2 3 2 3 1 3 1 2

1 1 2 2 3 3

2h h h h h h

gh h h

1

h3

h2

h1

3

2



Q.41 Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of

0.5 kg/s. Air (Cp = 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.42 A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by

ΔT. If the thermal coefficient of the material is α, Young’s modulus is E and the Poisson’s ratio is , the thermal stress developed in the cube due to heating is

(A) ( )

(1 2 )

T E

(B)

2 ( )

(1 2 )

T E

(C)

3 ( )

(1 2 )

T E

(D)

( )

3(1 2 )

T E

Q.43 A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear

stress of the material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design

diameter in mm is

(A) 8 (B) 16 (C) 24 (D) 32 Q.44 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.45 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.46 Consider the differential equation

22

24 0

d y dyx x y

dx dx with the boundary conditions of

0 0y and 1 1y . The complete solution of the differential equation is

(A) 2

x (B) sin2

x

(C) sin2

x xe

(D) sin2

x xe

Q.47

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.



Common Data Questions


Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a

horizontal force F as shown in figure. All the joints are hinged.

Q.48 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

Q.49 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


A refrigerator operates between 120 kPa and 800 kPa in an ideal vapor compression cycle with R-134a as

the refrigerant. The refrigerant enters the compressor as saturated vapor and leaves the condenser as

saturated liquid. The mass flow rate of the refrigerant is 0.2 kg/s. Properties for R-134a are as follows:

Saturated R-134a

P (kPa) T (ºC) hf (kJ/kg) hg (kJ/kg) sf (kJ/kg.K) sg (kJ/kg.K)

120 –22.32 22.5 237 0.093 0.95

800 31.31 95.5 267.3 0.354 0.918

Superheated R-134a

P (kPa) T (ºC) h (kJ/kg) s (kJ/kg.K)

800 40 276.45 0.95

Q.50 The rate at which heat is extracted, in kJ/s from the refrigerated space is

(A) 28.3 (B) 42.9 (C) 34.4 (D) 14.6

Q.51 The power required for the compressor in kW is

(A) 5.94 (B) 1.83 (C) 7.9 (D) 39.5



Linked Answer Questions


Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa

with a velocity of 180 m/s. The inlet area is 80 cm2. The specific heat of air Cp is 1008 J/kg.K.

Q.52 The exit temperature of the air is

(A) 516 K (B) 532 K (C) 484 K (D) 468 K

Q.53 The exit area of the nozzle in cm2 is

(A) 90.1 (B) 56.3 (C) 4.4 (D) 12.9


For a particular project, eight activities are to be carried out. Their relationships with other activities and

expected durations are mentioned in the table below.

Activity Predecessors Duration (days)

a - 3

b a 4

c a 5

d a 4

e b 2

f d 9

g c, e 6

h f, g 2

Q.54 The critical path for the project is

(A) a – b – e – g – h (B) a – c – g – h

(C) a – d – f – h (D) a – b – c – f – h

Q.55 If the duration of activity f alone is changed from 9 to 10 days, then the

(A) critical path remains the same and the total duration to complete the project changes to 19 days.

(B) critical path and the total duration to complete the project remain the same.

(C) critical path changes but the total duration to complete the project remains the same.

(D) critical path changes and the total duration to complete the project changes to 17 days.





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 The cost function for a product in a firm is given by 5q2, 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.58 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.59 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.60 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. 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 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.63 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 – 0.1x2 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

Q.64 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

Q.65 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




GATE 2012 - Answer KeysMechanical Engineering - ME

Q. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 D 23 C 45 D2 A 24 D 46 A3 C 25 A 47 C4 C 26 B 48 A5 A 27 C 49 B6 C 28 A 50 A7 B 29 D 51 C8 B 30 C 52 C9 D 31 D 53 D10 D 32 C 54 C11 A 33 D 55 A12 C 34 B 56 Marks to All13 A 35 D 57 A14 B 36 B 58 B15 B 37 A 59 A16 D 38 C 60 D17 C 39 C 61 A18 A 40 A 62 D19 B 41 C 63 B20 B 42 A 64 B21 B 43 B 65 C22 A 44 B


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