GATE Solved Question Papers for Engineering Sciences [XE] by AglaSem.Com

GATE

ENGINEERING SCIENCES (XE)

aglaem

CONTENTS

• Introduction

• Question Paper Pattern

•

Design of Questions

•

Marking Scheme

•

Syllabus

• Previous Year Solved Papers

o

Solved Question Paper 2014

o

Answer Key 2014

o

Solved Question Paper 2013

o

Answer Key 2013

o

Solved Question Paper 2012

o

Answer Key 2012

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.

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.

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.

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).

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-(sub-total 8 marks). Some questions

may be of numerical answer type questions.

Each of the other sections of the XE paper (Sections B through G) contains 22 questions

carrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13

questions carrying 2 marks each (sub-total 26 marks). Some questions may be of

numerical answer type.

XL Paper (Life Sciences)

In XL paper, Chemistry section (Section H) is compulsory. This section contains 15

questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks)

and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be of

numerical answer type.

Each of the other sections of the XL paper (Sections I through M) contains 20 questions

carrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10

questions carrying 2 marks each (sub-total 20 marks). Some questions may be of

numerical answer type.

Note on Negative Marking for Wrong Answers

For a wrong answer chosen for the multiple choice questions, there would be negative

marking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wrong

answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a

wrong answer. However, there is no negative marking for a wrong answer in numerical

answer type questions.

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 Engineering Sciences (XE)

Section A: Engineering Mathematics (Compulsory)

Linear Algebra: Algebra of matrices, inverse, rank, system of linear equations, symmetric,

skew-symmetric and orthogonal matrices. Hermitian, skew-Hermitian and unitary

matrices.eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamilton

Theorem.

Calculus: Functions of single variable, limit, continuity and differentiability, Mean value

theorems, Indeterminate forms and L’Hospital rule, Maxima and minima,Taylor’s series,

Fundamental and mean value-theorems of integral calculus. Evaluation of definite and

improper integrals, Beta and Gamma functions, Functions of two variables, limit,

continuity, partial derivatives, Euler’s theorem for homogeneous functions, total

derivatives, maxima and minima, Lagrange method of multipliers, double and triple

integrals and their applications, sequence and series, tests for convergence, power series,

Fourier Series, Half range sine and cosine series.

Complex variable: Analytic functions, Cauchy-Riemann equations, Application in solving

potential problems, Line integral, Cauchy’s integral theorem and integral formula (without

proof), Taylor’s and Laurent’ series, Residue theorem (without proof) and its applications.

Vector Calculus: Gradient, divergence and curl, vector identities, directional derivatives,

line, surface and volume integrals, Stokes, Gauss and Green’s theorems (without proofs)

applications.

Euler’s equations, power series solutions, Legendre polynomials and Bessel’s functions of

the first kind and their properties.

Partial Differential Equations: Separation of variables method,Laplace equation,

solutions of one dimensional heat and wave equations.

Probability and Statistics: Definitions of probability and simple theorems, conditional

probability, Bayes Theorem, random variables, discrete and continuous distributions,

Binomial, Poisson, and normal distributions, correlation and linear regression.

Numerical Methods: Solution of a system of linear equations by L-U decomposition,

Gauss-Jordan and Gauss-Seidel Methods, Newton’s interpolation formulae, Solution of a

polynomial and a transcendental equation by Newton-Raphson method, numerical

integration by trapezoidal rule, Simpson’s rule and Gaussian quadrature, numerical

solutions of first order differential equation by Euler’s method and 4

th

_{order Runge-Kutta}

method.

Section B: Fluid Mechanics

Fluid Properties: Relation between stress and strain rate for Newtonian fluids.

Hydrostatics: Buoyancy, manometry, forces on submerged bodies.

Eulerian and Lagrangian description of fluid motion, concept of local and convective

accelerations, steady and unsteady flows, control volume analysis for mass, momentum

and energy.

Differential equations of mass and momentum (Euler equation), Bernoulli’s equation and

its applications.

Concept of fluid rotation, vorticity, stream function and potential function.

Potential flow: elementary flow fields and principle of superposition, potential flow past a

circular cylinder.

Dimensional analysis: Concept of geometric, kinematic and dynamic similarity,

relation.

Qualitative ideas of boundary layer and separation, streamlined and bluff bodies, drag and

lift forces.

Basic ideas of flow measurement using venturimeter, pitot-static tube and orifice plate.

Section C: Materials Science

Structure: Atomic structure and bonding in materials. Crystal structure of materials,

crystal systems, unit cells and space lattices, determination of structures of simple crystals

by x-ray diffraction, miller indices of planes and directions, packing geometry in metallic,

ionic and covalent solids. Concept of amorphous, single and polycrystalline structures and

their effect on properties of materials.Crystal growth techniques.Imperfections in

crystalline solids and their role in influencing various properties.

Diffusion: Fick’s laws and application of diffusion in sintering, doping of semiconductors

and surface hardening of metals.

Metals and Alloys: Solid solutions, solubility limit, phase rule, binary phase diagrams,

intermediate phases, intermetallic compounds, iron-iron carbide phase diagram, heat

treatment of steels, cold, hot working of metals, recovery, recrystallization and grain

growth. Microstrcture, properties and applications of ferrous and non-ferrous alloys.

Ceramics: Structure, properties, processing and applications of traditional and advanced

ceramics.

Polymers: Classification, polymerization, structure and properties, additives for polymer

products, processing and applications.

Composites: Properties and applications of various composites.

Advanced Materials and Tools: Smart materials, exhibiting ferroelectric, piezoelectric,

scanning tunneling microscopy, atomic absorption spectroscopy, differential scanning

calorimetry.

Mechanical Properties: stress-strain diagrams of metallic, ceramic and polymeric

materials, modulus of elasticity, yield strength, tensile strength, toughness, elongation,

plastic deformation, viscoelasticity, hardness, impact strength, creep, fatigue, ductile and

brittle fracture.

Thermal Properties: Heat capacity, thermal conductivity, thermal expansion of materials.

Electronic Properties: Concept of energy band diagram for materials – conductors,

semiconductors and insulators, electrical conductivity – effect of temperature on

conductility, intrinsic and extrinsic semiconductors, dielectric properties.

Optical Properties: Reflection, refraction, absorption and transmission of electromagnetic

radiation in solids.

Magnetic Properties: Origin of magnetism in metallic and ceramic materials,

paramagnetism, diamagnetism, antiferro magnetism, ferromagnetism, ferrimagnetism,

magnetic hysterisis.

Environmental Degradation: Corrosion and oxidation of materials, prevention.

Section D: Solid Mechanics

Equivalent force systems; free-body diagrams; equilibrium equations; analysis of

determinate trusses and frames; friction; simple relative motion of particles; force as

function of position, time and speed; force acting on a body in motion; laws of motion; law

of conservation of energy; law of conservation of momentum.

Stresses and strains; principal stresses and strains; Mohr’s circle; generalized Hooke’s Law;

thermal strain; theories of failure.

Axial, shear and bending moment diagrams; axial, shear and bending stresses; deflection

(for symmetric bending); torsion in circular shafts; thin cylinders; energy methods

(Castigliano’s Theorems); Euler buckling.

Section E: Thermodynamics

Basic Concepts: Continuum, macroscopic approach, thermodynamic system (closed and

open or control volume); thermodynamic properties and equilibrium; state of a system,

state diagram, path and process; different modes of work; Zeroth law of thermodynamics;

concept of temperature; heat.

First Law of Thermodynamics: Energy, enthalpy, specific heats, first law applied to

systems and control volumes, steady and unsteady flow analysis.

Second Law of Thermodynamics: Kelvin-Planck and Clausius statements, reversible and

irreversible processes, Carnot theorems, thermodynamic temperature scale, Clausius

inequality and concept of entropy, principle of increase of entropy; availability and

irreversibility.

Properties of Pure Substances: Thermodynamic properties of pure substances in solid,

liquid and vapor phases, P-V-T behaviour of simple compressible substances, phase rule,

thermodynamic property tables and charts, ideal and real gases, equations of state,

compressibility chart.

Thermodynamic Relations: T-ds relations, Maxwell equations, Joule-Thomson

coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities,

Clapeyron equation.

Thermodynamic cycles: Carnot vapor power cycle, Ideal Rankine cycle, Rankine Reheat

cycle, Air standard Otto cycle, Air standard Diesel cycle, Air-standard Brayton cycle,

Vapor-compression refrigeration cycle.

Ideal Gas Mixtures:Dalton’s and Amagat’s laws, calculations of properties, air-water vapor

mixtures and simple thermodynamic processes involving them.

and other newer techniques of polymerization, copolymerization, monomer reactivity

ratios and its significance, kinetics, different copolymers, random, alternating, azeotropic

copolymerization, block and graft copolymers, techniques for copolymerization-bulk,

solution, suspension, emulsion.

Polymer Characterization: Solubility and swelling, concept of average molecular weight,

determination of number average, weight average, viscosity average and Z-average

molecular weights, polymer crystallinity, analysis of polymers using IR, XRD, thermal (DSC,

DMTA, TGA), microscopic (optical and electronic) techniques.

Synthesis and properties: Commodity and general purpose thermoplastics: PE, PP, PS,

PVC, Polyesters, Acrylic, PU polymers. Engineering Plastics: Nylon, PC, PBT, PSU, PPO, ABS,

Fluoropolymers Thermosetting polymers: PF, MF, UF, Epoxy, Unsaturated polyester,

Alkyds. Natural and synthetic rubbers: Recovery of NR hydrocarbon from latex, SBR, Nitrile,

CR, CSM, EPDM, IIR, BR, Silicone, TPE.

Polymer blends and composites: Difference between blends and composites, their

significance, choice of polymers for blending, blend miscibility-miscible and immiscible

blends, thermodynamics, phase morphology, polymer alloys, polymer eutectics,

plastic-plastic, rubber-plastic and rubber-rubber blends, FRP, particulate, long and short fibre

reinforced composites.

Polymer Technology: Polymer compounding-need and significance, different

compounding ingredients for rubber and plastics, crosslinking and vulcanization,

vulcanization kinetics.

Polymer rheology: Flow of Newtonian and non-Newtonian fluids, different flow

equations, dependence of shear modulus on temperature, molecular/segmental

deformations at different zones and transitions. Measurements of rheological parameters

by capillary rotating, parallel plate, cone-plate rheometer. viscoelasticity-creep and stress

relaxations, mechanical models, control of rheological characteristics through

compounding, rubber curing in parallel plate viscometer, ODR and MDR.

molding, reaction injection molding, extrusion, pultrusion, calendaring, rotational

molding, thermoforming, rubber processing in two-roll mill, internal mixer.

Polymer testing: Mechanical-static and dynamic tensile, flexural, compressive, abrasion,

endurance, fatigue, hardness, tear, resilience, impact, toughness. Conductivity-thermal

and electrical, dielectric constant, dissipation factor, power factor, electric resistance,

surface resistivity, volume resistivity, swelling, ageing resistance, environmental stress

cracking resistance.

Section G: Food Technology

Food Chemistry and Nutrition: Carbohydrates: Structure and functional properties of

mono- oligo-polysaccharides including starch, cellulose, pectic substances and dietary

fibre; Proteins: Classification and structure of proteins in food; Lipids: Classification and

structure of lipids, Rancidity of fats, Polymerization and polymorphism; Pigments:

Carotenoids, chlorophylls, anthocyanins, tannins and myoglobin; Food flavours: Terpenes,

esters, ketones and quinones; Enzymes: Specificity, Kinetics and inhibition, Coenzymes,

Enzymatic and non-enzymatic browning; Nutrition: Balanced diet, Essential amino acids

and fatty acids, PER, Water soluble and fat soluble vitamins, Role of minerals in nutrition,

Antinutrients, Nutrition deficiency diseases.

Food Microbiology: Characteristics of microorganisms: Morphology, structure and

detection of bacteria, yeast and mold in food, Spores and vegetative cells; Microbial

growth in food: Intrinsic and extrinsic factors, Growth and death kinetics, serial dilution

method for quantification; Food spoilage: Contributing factors, Spoilage bacteria,

Microbial spoilage of milk and milk products, meat and meat products; Foodborne

disease: Toxins produced by Staphylococcus, Clostridium and Aspergillus; Bacterial

pathogens: Salmonella, Bacillus, Listeria, Escherichia coli, Shigella, Campylobacter;

Fermented food: Buttermilk, yoghurt, cheese, sausage, alcoholic beverage, vinegar,

sauerkraut and soya sauce.

parboiling of paddy, production of bread, biscuits, extruded products and breakfast

cereals, Solvent extraction, refining and hydrogenation of oil; Fruits, vegetables and

plantation products processing: Extraction, clarification concentration and packaging of

fruit juice, Production of jam, jelly, marmalade, squash, candies, and pickles, pectin from

fruit waste, tea, coffee, chocolate and essential oils from spices; Milk and milk products

processing: Pasteurized and sterilized milk, cream, butter, ghee, ice-cream, cheese and

milk powder; Animal products processing: Drying and canning of fish, post mortem

changes, tenderization and freezing of meat, egg powder.

Food Engineering: Mass and energy balance; Momentum transfer: Flow rate and

pressure drop relationships for Newtonian fluids flowing through pipe, Characteristics of

non-Newtonian fluids – generalized viscosity coefficient and Reynolds number, Flow of

compressible fluid, Flow measurement, Pumps and compressors; Heat transfer: Heat

transfer by conduction, convection, radiation, boiling and condensation, Unsteady state

heat transfer in simple geometry, NTU- effectiveness relationship of co-current and

counter current double pipe heat exchanger; Mass transfer: Molecular diffusion and Fick’s

Law, Steady state mass transfer, Convective mass transfer, Permeability of films and

laminates; Mechanical operations: Energy requirement and rate of operations involved in

size reduction of solids, high pressure homogenization, filtration, centrifugation, settling,

sieving, flow through porous bed, agitation of liquid, solid-solid mixing, and single screw

extrusion; Thermal operations: Energy requirement and rate of operations involved in

process time evaluation in batch and continuous sterilization, evaporation of liquid foods,

hot air drying of solids, spray and freeze-drying, freezing and crystallization; Mass transfer

operations: Properties of air-water vapor mixture; Humidification and dehumidification

operations.

GATE

Previous Year Solved Papers

Engineering Sciences - XE

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 paper consists of 8sections: GA (General Aptitude), A (Engineering Mathematics), B (Fluid Mechanics), C (Materials Science), D (Solid Mechanics), E (Thermodynamics), F (Polymer Science & Engineering) and G (Food Technology).

Section GA (General Aptitude) and Section A (Engineering Mathematics) are compulsory. Attempt any 2 sections out of the 6 optional Sections B through G.

There are 10 questions carrying 15 marks in the compulsory General Aptitude (GA) section.

Question numbers 1 to 5 of this section carry 1 mark each, and question numbers 6 to 10 carry 2 marks each.

There are 11 questions carrying 15 marks in Section A(Engineering Mathematics).

Question numbers 1 to 7 of this section carry 1 mark each, and question numbers 8 to 11 carry 2 marks each.

Each of the other sections (Sections B through G) contains 22 questions carrying 35 marks.

In each of these sections, question numbers 1 to 9 carry 1 mark each and question numbers 10 to 22 carry 2 marks each.

4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If this 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 entered by 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 of

⅓

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 is in proper working condition”.

Q. 1 – Q. 5 carry one mark each.

Q.1 A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences.

The word closest in meaning to comprehension is

(A) understanding (B) meaning (C) concentration (D) stability

Q.2 Choose the most appropriate word from the options given below to complete the following sentence.

One of his biggest ______ was his ability to forgive.

(A) vice (B) virtues (C) choices (D) strength

Q.3 Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently.

Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group.

(B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajan’s request to work with him. (D) Rajan had believed that Sajan and he would be working together. Q.4 If y = 5x2 _{+ 3, then the tangent at x = 0, y = 3}

(A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of −1

Q.5 A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

Q. 6 – Q. 10 carry two marks each.

Q.6 Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

(A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK

Q.7 Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct?

Anuj Bhola Chandan Dilip Eswar Faisal

(A) 6 2 5 1 3 4

Q.8 The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

Q.9 One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

(A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25

Q.10 The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)

(i) On average, it rains more in July than in December

(ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall

(A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv)

A : ENGINEERING MATHEMATICS ( COMPULSORY)

Q. 1 – Q. 7 carry one mark each.

Q.1 _{If 1, 0, and -1 are the eigenvalues of a}

_3

₃

_{matrix A, then the trace of A}2 _{+5Ais equal to} ______________.

Q.2 Which of the following is a solution of the differential equation

?

0

),

sin(ln

4

'

''

2

₊

₊

₌

_>

x

x

y

xy

y

x

(A) y=2xsin(lnx) (B) y=−2xsin(lnx) (C) y= −2lnxcos(lnx) (D) y=2lnxcos(lnx)

Q.3 _{At z=0, the complex function}

₍

₎

_|

_|

2

z

z

z

f

=

(A) satisfies the Cauchy-Riemann equations and is differentiable (B) satisfies the Cauchy-Riemann equations but is not differentiable. (C) does not satisfy the Cauchy-Riemann equations but is differentiable. (D) does not satisfy the Cauchy-Riemann equations and is not differentiable.

Q.4 Ten chocolates are distributed randomly among three children standing in a row. The probability that the first child receives exactly three chocolates is

(A) ₉ 11

3

2

5

(B) ₉ 10

3

2

5

(C) ₉ 3 1 (D)

3

1

Q.5 Let the functionf :[0,5]R be defined by

= ) (x f          +   +   + . 5 2 , 3 23 3 2 2 1 , 5 2 1 0 , 5 2 3 2 x x x x x x

Q.6 _{An integrating factor of the differential equation}

₍

₃

2 3

₊

3

₊

2

₎

₊

₍

3 3

₋

₎

₌

₀

dy

xy

e

y

x

dx

y

y

e

y

x

y y is (A)

y

1

(B) 1₂ y (C)

1

₃

y

(D) lny

Q.7 If a cubic polynomial passes through the points (0, 1), (1, 0), (2, 1) and (3, 10), then it also passes through the point

(A) (−2,−11) (B) (−1,−2) (C) (−1,−4) (D) (−2,−23)

Q. 8 – Q. 11 carry two marks each.

Q.8

Let the function f :[0,)R be such that

4

3

8

)

(

₂

+

+

=



x

x

x

f

for x>0and f(0)=1.Then

) 1 (

f lies in the interval

(A) [0, 1] (B) [2, 3] (C) [4, 5] (D) [6, 7]

Q.9 The perimeter of a rectangle having the largest area that can be inscribed in the ellipse

1

32

8

2 2

=

+

y

x

, is ________.

Q.10 If the work done in moving a particle once around a circle 2

_{+ y}

2

₌

4

x

under the force field

j

ax

y

i

ay

x

y

x

F



(

,

)

=

(

2

−

)



+

(

2

+

)



is

16



, then a is equal to _________.

Q.11

Let r _and

s

be real numbers. If





















=

0

3

0

2

0

2

1

s

r

A

and





















−

=

1

1

1

s

b

, then the system of linear equations AX =b _has

(A) no solutions for s2r.

(B) infinitely many solutions for s= r2 2. (C) a unique solution for s= r2 =2.

(D) infinitely many solutions for s= r2 =2.

B : FLUID MECHANICS

Q. 1 – Q. 9 carry one mark each.

Q.1 A dam with a curved shape is shown in the figure. The cross sectional area of the dam (shaded portion) is 100 m2 _{and its centroid is at}

₁₀

x

=

m. The vertical component of the hydrostatic force,

z

F

, is acting at a distance x_p. The value of xpis ____ m.

Q.2 _{For an unsteady incompressible fluid flow, the velocity field is}

(

₃ 2 ₃

)

ˆ ₆ ˆ

V = x + t i − xyt j, where

x

,

y

are in meters and

t

is in seconds. Acceleration in m/s2 _{at the point}

_x

₌

₁₀

_{m and}

_y

₌

₀

_{, as} measured by a stationary observer is

(A) 303 (B) 162 (C) 43 (D) 13

Q.3 For an incompressible flow, the existence of components of acceleration for different types of flow is described in the table below.

Type of Flow Components of Acceleration

P: Steady and uniform 1: Local exists, convective does not exist Q: Steady and non-uniform 2: Both exist

R: Unsteady and uniform 3: Both do not exist

S: Unsteady and non-uniform 4: Local does not exist, convective exists

Which one of the following options connecting the left column with the right column is correct? (A) P – 1; Q – 4; R – 3; S – 2 (B) P – 4; Q – 1; R – 2; S – 3 (C) P – 3; Q – 2; R – 1; S – 4 (D) P – 3; Q – 4; R – 1; S – 2

15 m

40 m

O

G

p

x

x

x

z

z

F

Q.4 _{Velocity in a two-dimensional flow field is specified as:} 2

_;

2

u

=

x y v

= −

y x

. The magnitude of

the rate of angular deformation at a location (x=2 m and

y

=

1

m) is ____ s-1.

Q.5 For a plane irrotational flow, equi-potential lines and streamlines are

(A) parallel to each other. (B) at an angle of 90o _{to each other.} (C) at an angle of 45o _{to each other. (D) at an angle of 60}o _{to each other.}

Q.6 Flow around a Rankine half-body is represented by the superposition of (A) source and vortex flows. (B) source and uniform flows.

(C) vortex and uniform flows. (D) source, vortex and uniform flows.

Q.7 It is required to carry out model studies on a boat having a characteristic length of 3.6 m and travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s2 _{and neglect the} effects due to viscous and surface tension forces. The value of appropriate non-dimensional number is ____.

Q.8 Which one of the following velocity profiles typically represents a fully developed incompressible, turbulent flow in a pipe?

Q.9 Consider an incompressible, laminar flow past a circular cylinder of diameter

d

. The flow is uniform at the far upstream. Which one of the following figures typically represents the wake velocity profile just downstream of the cylinder?

(A) (B)

(C) (D)

d

d

Q. 10 – Q. 22 carry two marks each.

Q.10 A container of square cross-section is partially filled with a liquid of density

ρ

₁. The cylinder is intended to float in another liquid of density

ρ

₂ as shown in the figure. The distance between metacentre and centre of buoyancy is

sub

I

V , where I and

V

sub are area moment of inertia of the

cross-section and submerged volume, respectively. Neglect the weight of the container.

Which one of the following is the correct condition for stability?

(A) 2 1 1 2

1

0

6

b

h

h

b

ρ

ρ

ρ

ρ





−

_

−

_

>





(B) 2 1 1 2

1

0

6

b

h

h

b

ρ

ρ

ρ

ρ





−

_

+

_

>





(C) 2 1 1 2

1

0

6

b

h

h

b

ρ

ρ

ρ

ρ





+

_

−

_

>





(D) 2 1 1 2

1

0

6

b

h

h

b

ρ

ρ

ρ

ρ





+

_

+

_

>





Q.11 In a steady state two-dimensional potential flow field due to a point source, the acceleration of a particle at a distance rfrom the point source is

(A) proportional to 1

r

− . (B) proportional to r.

(C) a constant. (D) proportional to 3

r

− .

Q.12 Velocity in a two-dimensional flow at time

t

and location

( )

x y, is described as:

(

)

2 _{ˆ ˆ}

3 1

V= t i+ x− j. The equation for the path line of a particle passing through the point (1,0) at

0

t

=

is

h

Q.13 The gravity driven flow over a hump of height

h

in a canal is shown in the figure. The height of the free surface from the canal bed at upstream of the hump isH. The free surface height reduces

to

H

₁ above the hump.

Assuming the canal bed to be horizontal, the discharge per unit width is given by (A) � 2�(� − �₁− ℎ) 1 �12− 1 �2 (B) � 2�ℎ 1 (�₁+ℎ)2− 1 �2 (C) � 2�(� − �₁) 1 (�1+ℎ)2− 1 �2 (D) � 2�(� − �₁) 1 �12− 1 �2

Q.14 Steady state incompressible flow through a pipe network is shown in the figure. Inlets marked as (1), (2) and (3) and exit marked as (4), are shown with their respective diameters. The exit flow rate at (4) is 0.1 m3_{/s. A 20% increase in flow rate through (3) results in a 10% increase in flow rate} through (4). The original velocity through inlet (3) is _____ m/s.

H

h

1

H

5 cm

10 cm

(3)

(2)

(1)

(4)

Q.15 A reducing elbow is used to deflect water upward by 30o _{as shown in the figure. The mass flow rate} at the inlet is 14 kg/s. Water is entering at a gauge pressure of 200 kPa and exits to the atmosphere. The cross-sectional area is 113 cm2 _{at the inlet and 7 cm}2 _{at the exit. Density of water and} acceleration due to gravity are 1000 kg/m3 _{and 10 m/s}2_{, respectively. Magnitude of}

x- component

of the water force on the elbow is ____ N.

Q.16 A source with a strength of

k

₁ and a vortex with a strength of

k

₂ are located at the origin. The

resultant velocity at a radial distance

r

from the origin due to the superposition of the source and vortex is expressed as (A)

k

1

k

2

r

+

(B) 2 2 1 2

k

k

r

+

(C) 2 2 1 2 k k r − _(D)

k

1

k

2

r

−

Q.17 Velocity potential for an incompressible fluid flow is given as: ₂

(

2 ₂ 2

)

x y y

φ

= + − . Assume the value of stream function at the origin to be zero. The value of stream function at [

(

x y,

) ( )

≡ 2, 2 ] is ____.

Q.18 The model of a conduit is scaled to 1/100 of the actual size. Seawater is used in the prototype and fresh water is used in the model. Velocity in the prototype is 0.5 m/s. Density and dynamic viscosity of the seawater are 1025 kg/m3 _{and 1.07 × 10}-3 _{kg/m-s, respectively. Density and} dynamic viscosity of fresh water are 1000 kg/m3 _{and 1 × 10}-3 _{kg/m-s, respectively. Assume the} viscous forces to be dominant. The velocity to be maintained in the model to ensure dynamic similarity is____ m/s.

Q.19 A fluid is flowing through a pipe of circular cross-section. Reynolds number of the flow is 1600. The head loss over a 45 m length of the pipe is 0.6 m. The average flow velocity of the fluid is 1 m/s and the acceleration due to gravity is 10 m/s2_{. The diameter of the pipe is ____ m.}

Q.20 Consider a laminar flow over a flat plate of width

w

. At Section 1-1, the velocity profile is uniform as shown in the figure. The

x

-direction velocity profile at Section 2-2 is given by

2 2 , u y y U

δ

δ

  = _{−  }

  where

δ

is the boundary layer thickness.

The volume flow rate through Section 2-2 is given by (A) 1 2U w

δ

(B) 1 3U w

δ

(C)

U w

δ

(D) 2 3U w

δ

Q.21 A cube of weight

W

and side a falls at a constant speed in a medium as shown in the figure. If the

medium is air (mass density =�air) let

U

air be the velocity of the cube. If the medium is water

(mass density =_�water) let

U

waterbe the velocity of the cube.

Neglecting the buoyancy force and assuming drag coefficient to be same for both cases, the ratio of velocities, air water

U

U













is given by (A) air water

ρ

ρ

(B) _waterair

ρ

ρ

(C) water_air

ρ

ρ

(D) 1

δ

1

1

2

2

U

U

( )

u y

x

y

a

W

Q.22 Water is flowing through a venturimeter having a diameter of 0.25 m at the entrance (Station 1) and 0.125 m at the throat (Station 2) as shown in the figure. A mercury manometer measures the piezometric head difference between Stations 1 and 2 as 1.3505 m. The loss of head between these two stations, is 1/7 times the velocity head at the Station 2. Assume the acceleration due to gravity to be 10 m/s2_{. The velocity of water at the throat is ____ m/s.}

END OF THE QUESTION PAPER

• •

1

₂

diameter 0.125 m

diameter 0.25m

Mercury Manometer

C : MATERIALS SCIENCE

Useful constants

Avogadro’s Number : 6.023 x 1023 _mol-1 Boltzmann’s constant, k : 1.38 x 10-23 _J.K-1 Electron Charge, e : 1.6 x 10-19 _C Electron rest mass, mo : 9.1 x 10-31 kg

Universal gas constant, R : 8.314 J.mol-1_.K-1 Speed of light, c : 3 x 108 _m.s-1 Planck’s constant, h : 6.63 x 10-34 _J.s 1 eV = 1.6 x 10-19 _J

Q. 1 – Q. 9 carry one mark each.

Q.1 Neoprene is rendered non-inflammable because (A) it has a highly cross-linked structure (B) it has a highly linear chain structure

(C) of the presence of chlorine atom in the structure (D) of the absence of chlorine atom in the structure Q.2 Nylon-6 is manufactured from

(A) caprolactum

(B) adipic acid and hexamethylene diamine (C) maleic anhydride and hexamethylene diamine (D) sebasic acid and hexamethylene diamine

Q.3 At room temperature, the typical barrier potential for silicon p-n junction in Volt (V) is (A) 0.7x10-23 _{(B) 0.07 (C) 0.70 (D) 7.0}

Q.4 Quantitative measurement of the roughness of a polysilicon wafer can be performed with (A) scanning tunneling microscopy (B) scanning electron microscopy (C) transmission electron microscopy (D) atomic force microscopy Q.5 The temperature of the antiferromagnetic-to-paramagnetic transition is called (A) Curie temperature (B) Curie-Weiss temperature (C) Neel temperature (D) Debye temperature Q.6 At low injection level, a forward biased p-n junction would have

(A) no charge carriers

(B) minority carrier concentration much more than majority carrier concentration (C) minority carrier concentration equal to majority carrier concentration

(D) minority carrier concentration much less than majority carrier concentration

Q.7 Which of the following mechanical properties of a material depend on the mobile dislocation density in it.

(P) Young’s modulus (Q) yield strength (R) ductility (S) fracture toughness (A) P, Q, R (B) Q, R, S (C) P, R, S (D) S, P, Q

Q.8 The equilibrium concentration of vacancies in a pure metal

(A) increases exponentially with temperature (B) decreases exponentially with temperature (C) varies linearly with temperature (D) is independent of temperature

Q.9 The materials belonging to which one of the following crystal classes would be both piezoelectric and ferroelectric

(A) 222 (B) 4mm (C) 1� (D) 2/m

Q. 10 – Q. 22 carry two marks each.

Q.10 Polymerized isotactic polybutadiene has a molecular weight of 3 x 105 _{g/mol. The degree of} polymerization is _______________.

Q.11 A bar of Ti with Young’s modulus of 110 GPa and yield strength of 880 MPa is tested in tension. It is noticed that the alloy does not exhibit any strain hardening and fails at a total strain of 0.108. The mechanical energy that is necessary to break the material in MJ/m3 _{is ____________.}

Q.12 A copper cup weighing 140 g contains 80 g of water at 4 °C. Specific heats of water and copper are 4.18 and 0.385 J/g °C, respectively. If 100 g of water that is at 90 °C is added to the cup, the final temperature of water in °C is ______________.

Q.13 Match the reaction in Column I with its name in Column II.

L – liquid, α, β, γ – different solid solution phases

Column I (P) L �������_{�⎯⎯⎯⎯�} α + β (Q) L + β��������⎯⎯⎯⎯� γ (R) α ��������⎯⎯⎯⎯� β + γ Column II (1) peritectic (2) eutectic (3) monotectic (4) eutectoid (A) P-1, Q-4, R-3 (B) P-2, Q-1, R-4 (C) P-2, Q-3, R-1 (D) P-4, Q-2, R-3

Q.14 The Young’s modulus of a unidirectional SiC fiber reinforced Ti matrix composite is 185 GPa. If the Young’s moduli of Ti and SiC are 110 and 360 GPa respectively, the volume fraction of fibers in the composite is _________.

Q.15 Match the composite in Column I with the most suitable application in Column II. Column I Column II

(P) Glass fibre reinforced plastic (1) Missile cone heads

(Q) SiC particle reinforced Al alloy (2) Commercial automobile chasis (R) Carbon-carbon composite (3) Airplane wheel tyres

(S) Metal fibre reinforced rubber (4) Car piston rings

(5) High performance skate boards (A) P-4, Q-5, R-1, S-2 (B) P-3, Q-5, R-2, S-4

Q.16 Which among the following rules need to be satisfied for obtaining an isomorphous phase diagram in a binary alloy system?

(P) The atomic size difference should be less than 15%.

(Q) Both the end components should have the same crystal structure (R) The valency of the end components should be the same.

(S) The end components should have dissimilar electronegativities

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

Q.17 The energy in eV and the wavelength in µm, respectively, of the photon emitted when an electron in a hydrogen atom falls from n = 4 to n = 2 state is

(A) 3.0, 0.413 (B) 2.55, 0.365 (C) 2.75, 0.451 (D) 2.55, 0.487 Q.18 The weight in kg of gallium (Ga) to be mixed with arsenic (As) for obtaining 1.0 kg of gallium

arsenide (GaAs) is ______________. (MGa = 69.72 g/mol; MAs = 74.92 g/mol) Q.19 Match the material in Column I with the property in Column II

Column I Column II

(P) Pb(Zr,Ti)O3 (1) Shape memory alloy (Q) Ni50Ti50 (2) Piezoelectric ceramic

(R) GaAs (3) High temperature superconductor (S) YBa2Cu3O7 (4) Optoelectronic semiconductor (A) P-1, Q-2, R-3, S-4 (B) P-2, Q-3, R-4, S-1

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

Q.20 Relevant portion of a binary phase diagram of elements A and B is shown below. The mass fraction of liquid phase at 1000 °C for an alloy with 15 wt.% B is ___________.

Q.21 The expected diffraction angle (in degrees) for the first order reflection from the (113) set of planes for face centered cubic Pt (lattice parameter = 0.392 nm) using monochromatic radiation of

Q.22 The diffusion coefficients of Mg in Al at 500 and 550 °C are 1.9x10-13 _{and 5.8x10}-13 _m2_/s respectively. The activation energy for diffusion of Mg in Al in kJ/mol is ___________.

D: SOLID MECHANICS

Q. 1 – Q. 9 carry one mark each.

Q.1 A steel wire of diameter 5 mm is bent around a cylindrical drum of radius 0.5 m. The steel wire has modulus of elasticity of 200 GPa. Find the bending moment in the wire in N-m.

Q.2 A compressed air tank having an inner diameter of 480 mm and a wall thickness of 8 mm is formed by welding two steel hemispheres. If the allowable shear stress in the steel is 40 MPa, find the maximum permissible pressure (in MPa) inside the tank.

Q.4 A point in a body is subjected to a bi-axial state of stress, equal in magnitude but opposite in nature. On a plane inclined at an angle 45° _{with respect to x-axis (passing through the point), the}

(A) shear and normal stresses are zero

(B) normal stress is maximum and shear stress is zero (C) shear stress is maximum and normal stress is zero (D) shear stress is maximum and normal stress is non-zero

Q.3 The Euler’s buckling load of a column fixed at both the ends is P. If one of the ends is made free, the buckling load shall change to

(A) P/16 (B) P/8

(C) P/4 (D) P/2

Q.6 For the pin jointed truss, find the axial force (in kN) in the member 2-5. Q.5 A weightless beam subjected to two point loads is shown in the figure below.

The shear force diagram of the beam is

(A) (B) (C) (D) 10 kN 10 kN 2 m 1 m 1 m 10 kN 10 kN 10 kN 10 kN 5 kN 5 kN 5 kN 10 kN

Q.7 The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross section of inner diameter di, outer diameter do, height l, and Young’s modulus E. The mass of the

tank is m. If mass of the supporting structure is neglected, then the natural frequency of the water tank in transverse direction is

(A)

�

3����� −4 ��4� 64�3_� (B)

�

����_{� −}4 _� � 4_� 8�3_� (C) )

�

384����� −4 ��4� 360�3_� (D)

�

����_{� −}4 _� �4� 64�3_�

Q.8 A mass is attached to a spring and placed horizontally in a frictionless surface. A simple pendulum has been pivoted to the mass. The degree of freedom of this system is

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

X

y

x l

Q.9 Consider the following two statements

Statement 1: A body of weight W falls from a height h and strikes the ground. If the body starts from rest, the velocity with which it strikes the ground is �2�ℎ , where g is the acceleration due to gravity.

Statement 2: If the same body (initially at rest) slides without friction along an inclined plane PQ (angle of inclination α) starting from an elevation h above point Q, then its velocity at point Q is

�2�ℎ

The correct option is

(A) Both statements 1 and 2 are true (B) Statement 1 is true and 2 is false (C) Statement 1 is false and 2 is true (D) Both statements 1 and 2 are false

W h h P Q W α

Q. 10 – Q. 22 carry two marks each.

Q.10 A composite bar of length ‘L’ is made of a centrally placed steel plate (50 mm wide x 10 mm thick) with two copper plates (each 30 mm wide x 5 mm thick) connected rigidly on each side. If the temperature of the composite bar is raised by 50°_{C, find the stress developed in each copper plate in} MPa.

(For Steel: Es = 2x105 MPa and αs= 12x10-6 /°C; For Copper: Ec = 1x105 MPa and αc= 17x10-6 /°C)

Q.11 The vertical deflection at the free end of the cantilever beam as shown in figure is

(A) 1400/EI (B) 1400/3EI (C) 200/EI (D) 100/EI

Q.12 A hollow shaft and a solid shaft have the same length and the same outer radius R. The inner radius of the hollow shaft is 0.6 R. Assuming that both the shafts are made of same material and are subjected to the same torque, find the ratio of shear stress in hollow shaft to that in solid shaft.

Q.13 A beam with overhangs carries one point load acting downwards and the other upward. The clockwise moment Pb is applied at each support. The bending moment at the midpoint of the beam is (A) 0 (B) PL/2 (C) PL (D) PbL L Steel plate 5 mm 5 mm Copper plate Copper plate 10 mm 100 kN EI = flexural rigidity 1 m 2 m L P P b _b Pb Pb

Q.14 A cantilever beam of length L supports a concentrated load P at the free end. The cross section of the beam is rectangular with constant width b and varying depth h. The depth h of this idealized cantilever beam varies in such a way that the maximum normal stress at every cross section remains equal to the allowable bending stress. Considering only the bending stresses, the depth hxof the

fully stressed beam at any distance x from the free end shall vary

(A) with square of x (B) with square root of x (C) linearly with x (D) with cube of x

Q.15 A cantilever beam is subjected to following three different loading conditions: (a) a concentrated load P at its free end,

(b) a couple Mo at its free end and

(c) both loads acting simultaneously

(a)

(b)

(c)

The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when both loads act simultaneously

(A) can be determined by applying the principle of superposition and the strain energy is

� 2_�3

6��

+

��2�

2��

(B) can be determined by applying the principle of superposition and the strain energy is �2�2

6��

+

���3

2��

(C) cannot be determined by applying the principle of superposition and the strain energy is

� 2_�3 6��

+

��2� 2��

+

��� �2 2�� P L P L Mo L Mo L P

Q.16 A tapered rod has diameter d1 at one end which reduces uniformly to a diameter d2 over the length (L). If the modulus of elasticity of the material is E, the change in the length of the rod due to the application of axial force (P) is

(A) 4�� ���1�2 (B) 4�� ����12−�22� (C) �� ���1�2 (D) 2�� ����12−�22�

Q.17 For a point in a body subjected to a plane stress condition (σx= 100 MPa, σy= 50 MPa and

τxy = τyx = 25 MPa), the maximum principal stress in MPa is_____________

Q.18 An isotropic body is subjected to a state of stress given by: σx= 10 MPa and τxy= τyx = −20 MPa.

Assuming G = 0.4E, the volumetric strain is

(A) 5/E (B) 7.5/E (C) 10/E (D) 15/E

Q.19 A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between the block of weight Q and the inclined plane is µ. Consider the following cases:

Case I: weight Q starts moving down the inclined plane Case II: weight P starts falling down

The limiting values of ratio P/Q for Case I and Case II respectively are (A) (sin_{� − � cos �) and (sin � + � cos �)}

(B) (�sin � − cos �) and (�sin � + cos �) (C) (sin� + � cos �) and (sin � − � cos �) (D) (_{�sin � + cos �) and �(sin � − cos �)}

Q.20 To unload an item from a truck a crane boom is raised with a constant angular velocity of 1 rad/s relative to the cab and then the cab is rotated about a vertical axis with constant angular velocity of 0.5 rad/s.

If the length of the boom (OP) is 10 m, the velocity of the tip (P) of the boom in m/s is (A) √2 5 �−2� � − �̂ + 2��� (B) √2 5 �−� � − 2�̂ + ��� (C) 5 √2�−2� � − �̂ + 2��� (D) 5 √2�−� � − 2 �̂ + 2���

Q.21 A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact is (A) 12.54 at 30° (B) 13.84 at 51.78° (C) 13.84 at 30° (D) 15.62 at 51.78° Z X Y Cab Boom 45° O P 30° x y 500 m/s 10 m/s

Q.22 A balloon with ballast (weight) inside it has a gross weight of 500 N. It is falling vertically with a constant acceleration of 2 m/s2_{. If air resistance is negligible, find the weight of ballast (in N) that} must be thrown out in order to give the balloon an upward acceleration of 2 m/s2_{. (Acceleration due} to gravity, g = 9.81 m/s2₎

END OF THE QUESTION PAPER

E : THERMODYNAMICS

Notations used:

P-pressure, V-volume, T-temperature, S-entropy, H-enthalpy, U-internal energy, cp-specific heat at constant pressure, cv-specific heat at constant volume; specific properties are designated by lower case symbols. Subscripts: R-reduced, C-critical, f-saturated liquid, g-saturated vapor,

Properties of air: cp = 1.005 kJ/(kg.K), specific heat ratio γ = 1.4, Gas constant = 0.287 kJ/(kg.K), Molecular weight = 29 gm/mol.

Universal gas constant = 8.314 kJ/(kmol.K). Q. 1 – Q. 9 carry one mark each.

Q.1 Entropy is a

(A) Path function (B) Point function

(C) Property independent function (D) Neither path nor point function

Q.2 A small container has gas at high pressure. It is placed in an evacuated space. If the container is punctured, work done by the gas is

(A) Positive (B) Negative (C) Zero (D) ∞

Q.3 The molecular weight of a mixture is 38.4 gm/mol. The mixture is composed of methane and carbon-dioxide gases. The atomic weights of the elements C, H, and O are 12, 1, and 16 gm/mol, respectively. The mole fraction of methane (Xmethane) is ____________ and that of carbon-dioxide

(X carbon-dioxide) is _______.

(A) Xmethane = 0.2; X carbon-dioxide = 0.8

(B) Xmethane = 0.8; X carbon-dioxide = 0.2

(C) Xmethane = 0.3; X carbon-dioxide = 0.7

(D) Xmethane= 0.7; X carbon-dioxide = 0.3

Q.4 A system undergoes a change from state 1 to state 2. During this process, the change in the internal energy is ∆U. The change in internal energy of the system when executing the cycle 1-2-1 is equal

to

Q.5 Which among the following plots represents a line joining two states with the same dew point temperature on a standard psychrometric chart, with the dry bulb temperature on the X-axis and the humidity ratio on the Y-axis?

(A) (B)

(C) (D)

Q.6 The efficiency of a reversible engine operating between two temperatures is 40 % . The COP of a reversible refrigerator operating between the same temperatures is

(A) 1.5 (B) 2.5 (C) 0.4 (D) 3.5

Q.7 For a superheated vapor that cannot be approximated as an ideal gas, the expression determining a small change in the specific internal energy is

(A)

dv

v

u

dT

c

du

T p

∂

∂

+

=

(B)

dP

P

u

dT

c

du

T p

_∂

∂

+

=

(C)

dv

v

u

dT

c

du

T v

_∂

∂

+

=

(D)

du

=

c

_v

dT

Q.8 The minimum and maximum volumes in an air standard Otto cycle are 100 and 800 cm3_{. Its} thermal efficiency (%) is

(A) 56.47 (B) 94.55 (C) 54.08 (D) 87.50

Q.9 At a saturation temperature Tsat, the difference between the entropy of saturated vapor and entropy

of saturated liquid can be expressed as

(A)

(

hf −hg

)

Tsat (B)

(

hg −hf

)

Tsat

(C)

(

u_g −u_f

)

T_sat (D)

(

u_f −u_g

)

T_sat

Q. 10 – Q. 22 carry two marks each.

Q.10 A gas in a closed system is compressed reversibly from an initial volume of 0.2 m3 _{to 0.1 m}3 _{at a} constant pressure of 3 bar. During this process, there was a heat transfer of 50 kJ from the gas. The change in internal energy of the gas during this process in kJ is