Can you provide me the Mechanical GATE solved question papers

The Mechanical GATE solved question paper is as follows:

1. The partial differential equation

2

2

u u u

u

t x x

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

Answer: (D)

2. The eigen values of 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

Answer: (C)

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

Answer: (D)

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 1 E to 2 E along the length of the rod, the normal stress

developed at the section-SS is

Answer: (A)

5. The 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 the bolt B

and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is

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

Answer: (B)

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 = 1m, the magnitude of the absolute acceleration of the block at location A in

2 m/ s is

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

Answer: (C)

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 w

are related by

(A) w

pD

4L

(B)

2

w 2

pD

4L

(C) w

pD

2L

(D) w

4 pL

D

Answer: (A)

8. The pressure, dry bulb temperature, and relative humidity of air in a room are

1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is

4.25kPa, 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

Answer: (C)

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 0 k k bT ; where 0 k and b are positive

constants and T is temperature.

As x increases, the temperature gradient dT / dx will

(A) Remain constant (B) Be zero (C) Increase (D) Decrease

Answer: (D)

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

Answer: (C)

11. Match the CORRECT pairs.

Processes Characteristics / Application

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

Answer: (A)

12. A metric thread of pitch 2mm and thread angle 60º 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

Answer: (C)

13. Customers arrive at a ticket counter at a rate of 50 per hour and tickets are

issued in the order of their arrival. The average time taken for issuing a ticket is

1min. Assuming that customer arrivals form a Poisson process and service times

are exponentially distributed, the average waiting time in queue in minutes is:

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

Answer: (C)

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

Answer: (D)

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 3 mm / s is

(A) 160 (B) 167.6 (C) 1600 (D) 1675.5

Answer: (D)

16. A cube shaped casting solidifies in 5 minutes. The solidification time in minutes

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

Answer: (B)

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

Answer: (B)

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 the jet speed

(C) Equal to twice the jet speed (D) Independent of the jet speed

Answer: (B)

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 0ºC and 100ºC. Heat is generated uniformly throughout the wall.

Choose the CORRECT statement.

(A) The direction of heat transfer will be from the surface at 100ºC to surface at

0ºC.

(B) The maximum temperature inside the wall must be greater than 100ºC

(C) The temperature distribution is linear within the wall

(D) The temperature distribution is symmetric about the mid-plane of the wall

Answer: (B)

20. A cylinder contains 3 5m of 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

Answer: (A)

21. A long thin walled cylindrical shell, closed at both 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

Answer: (C)

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

Answer: (D)

23. A planar closed kinematic chain is formed with rigid links PQ = 2.0m, QR = 3.0m,

RS = 2.5m and SP = 2.7m 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

Answer: (C)

24. Let X be a nominal variable with mean 1 and variance 4. The probability P X 0 is

(A) 0.5

(B) Greater than zero and less than 0.5

(C) Greater than 0.5 and less than 1

(D) 1.0

Answer: (B)

25. Choose the CORRECT set of functions, which are linearly dependent.

(A) 2 2 sinx, sin x and cos x (B) cosx, sinx and tan x

(C) 2 2 cos2x, sin x and cos x (D) cos2x, sinx and cosx

Answer: (C)

Remaining question with answer is in the attachment given below

**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.

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.

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.

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.