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GATE 2012 Mechanical Engineering (Core Subjects)

GATE 2012 Mechanical Engineering question paper covering thermodynamics, fluid mechanics, mechanics of materials, manufacturing processes, machine design, heat transfer, and industrial engineering topics

58 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

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 300
Gear I : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.50
If the input speed is 1440 rpm, the output speed in rpm is

  1. 1200
  2. 900
  3. 875
  4. 720
Question 2 Multiple Choice (Single Answer)

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

  1. 0
  2. 1
  3. 1.08
  4. 2.02
Question 3 Multiple Choice (Single Answer)

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

  1. 0
  2. 2.07%
  3. 20.7%
  4. 41.42%
Question 4 Multiple Choice (Single Answer)

The homogenous state of stress for a metal part undergoing plastic deformation is

T = $\begin{pmatrix}
\ 10 & 5 & 0 \
\ 5 & 20 & 0 \
\ 0 & 0 & -10 \
\end{pmatrix}$

where the stress component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield stress, in MPa is

  1. 9.50
  2. 16.07
  3. 28.52
  4. 49.41
Question 5 Multiple Choice (Single Answer)

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. The milling time for the slot (in seconds) is

  1. 120
  2. 170
  3. 180
  4. 240
Question 6 Multiple Choice (Single Answer)

A room contains 35 kg of dry air and 0.5 kg of water vapour. The total pressure and temperature of air in the room are 100 kPa and 250C respectively. Given that the saturation pressure for water at 250C is 3.17 kPa, the relative humidity of the air in the room is

  1. 67%
  2. 55%
  3. 83%
  4. 71%
Question 7 Multiple Choice (Single Answer)

A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity $\omega$ and angular acceleration $\alpha$. The magnitude of the acceleration of the point of contact on the disc is

  1. 0
  2. r$\alpha$
  3. $\sqrt{(r \alpha)^2 + (r \omega^2)^2}$
  4. r$\omega$2
Question 8 Multiple Choice (Single Answer)

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

  1. $\sqrt{\frac{k}{m}}$
  2. $\sqrt{\frac{2k}{m}}$
  3. $\sqrt{\frac{k}{2m}}$
  4. $\sqrt{\frac{4k}{m}}$
Question 9 Multiple Choice (Single Answer)

The state of stress at a point under plane stress condition is
$\sigma_{xx}$= 40 MPa, $\sigma_{yy}$= 100 MPa and $\tau_{xy}$= 40 MPa
The radius of the Mohr's circle representing the given state (in MPa) is

  1. 40
  2. 50
  3. 60
  4. 100
Question 10 Multiple Choice (Single Answer)

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 l and the Young's modulus is E. The magnitude of the maximum deflection is

  1. $\frac{ML^2}{2EI}$
  2. $\frac{ML^2}{EI}$
  3. $\frac{2ML^2}{EI}$
  4. $\frac{4ML^2}{Ei}$
Question 11 Multiple Choice (Single Answer)

In a DC arc welding operation, the voltage arc length characteristics was obtained as Varc = 20 + 5l 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 characteristics, the open circuit voltage and the short circuit current for the welding operation are

  1. 45 V, 450 A
  2. 75 V, 750 A
  3. 95 V, 950 A
  4. 150 V, 1500 A
Question 12 Multiple Choice (Single Answer)

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 metres. The maximum possible height of the arch is

  1. 8 metres
  2. 10 metres
  3. 12 metres
  4. 14 metres
Question 13 Multiple Choice (Single Answer)

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

  1. 0.288
  2. 0.334
  3. 0.667
  4. 0.720
Question 14 Multiple Choice (Single Answer)

Which of the following assertions are CORRECT?P : Adding 7 to each entry in a lists adds 7 to the mean of the list
Q : Adding 7 to each entry in a lists adds 7 to the standard deviation of the listR : 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

  1. P,Q
  2. Q,R
  3. P,R
  4. R,S
Question 15 Multiple Choice (Single Answer)

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

  1. 1
  2. 2
  3. 4
  4. 8
Question 16 Multiple Choice (Single Answer)

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\triangle$T. If the thermal coefficient of the material is a, young's module is E and the Poisson's ratio is u, the thermal stress developed in the cube due to heating is

  1. $\frac{\alpha (\triangle T)E}{(1 - 2u)}$
  2. $\frac{2\alpha (\triangle T)E}{(1 - 2u)}$
  3. $\frac{3\alpha (\triangle T)E}{(1 - 2u)}$
  4. $\frac{\alpha (\triangle T)E}{3(1 - 2u)}$
Question 17 Multiple Choice (Single Answer)

A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as fly wheel. If it rotates at 600 rpm, the kinetic energy of the flywheel (in Joules) is

  1. 395
  2. 790
  3. 1580
  4. 3160
Question 18 Multiple Choice (Single Answer)

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

  1. 0.05
  2. 0.1
  3. 5.0
  4. 10.0
Question 19 Multiple Choice (Single Answer)

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 friction) 0.9. The enthalpies of the saturated liquid and vapour at 15 kPa are hf = 225.94 kj/kg and hg = 2598.3 kj/kg respectively. The mass flow rate of stream is 10 kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine (in MW) is

  1. 6.5
  2. 8.9
  3. 9.1
  4. 27.0
Question 20 Multiple Choice (Single Answer)

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

The exit temperature of the air is

  1. 516 k
  2. 532 k
  3. 484 k
  4. 468 k
Question 21 Multiple Choice (Single Answer)

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 $\triangle$S of the gas is

  1. mR ln $\Big(\frac{P_2}{P_1}\Big)$
  2. mR ln $\Big(\frac{P_1}{P_2}\Big)$
  3. mR ln $\Big(\frac{P_2}{P_1}\Big)$ - $\Big(\frac{Q}{T_1}\Big)$
  4. 0
Question 22 Multiple Choice (Single Answer)

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

The exit area of the nozzle in cm2 is

  1. 90.1
  2. 56.3
  3. 4.4
  4. 12.9
Question 23 Multiple Choice (Single Answer)

The area enclosed between the straight line y = x and the parabola y = x2 in the x - y plane is

  1. 1/6 Units
  2. 1/4 Units
  3. 1/3 Units
  4. ½ Units
Question 24 Multiple Choice (Single Answer)

The inverse Laplace transform of the function F (s) = $\frac{1}{s(s+1)}$is given by

  1. f (t) = sin t
  2. f (t) = e- t sin t
  3. f (t) = e- t
  4. f (t) = 1 - e - t
Question 25 Multiple Choice (Single Answer)

Consider the function f (x) = |x| in the interval - 1 $\leq$ x$\leq$ 1. At the point x = 0, f (x) is

  1. continuous and differentiable
  2. non continuous and differentiable
  3. continuous and non differentiable
  4. neither continuous nor differentiable
Question 26 Multiple Choice (Single Answer)

At x = 0, the function f (x) = x3 + 1 has

  1. a maximum value
  2. a minimum value
  3. a singularity
  4. a point of inflection
Question 27 Multiple Choice (Single Answer)

x + 2y + z = 4
2x + y + 2z = 5
x - y + z = 1

The system of algebraic equations given above has

  1. a unique solution of x = 1, y = 1 and z = 1
  2. only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0)
  3. infinite number of solutions
  4. no feasible solution
Question 28 Multiple Choice (Single Answer)

For the spherical surface x2 + y2 + z2 = 1, the unit outward vector at the point $\Big(\frac{1}{\sqrt{2}} , \frac{1}{\sqrt{2}}, 0\Big)$ is given by

  1. $\frac{1}{\sqrt{2}}i + \frac{1}{\sqrt{2}}j$
  2. $\frac{1}{\sqrt{2}}i + \frac{1}{\sqrt{2}}j$
  3. $\hat{k}$
  4. $\frac{1}{\sqrt{3}}\hat{i} + \frac{1}{\sqrt{3}}\hat{j} + \frac{1}{\sqrt{3}}\hat{k}$
Question 29 Multiple Choice (Single Answer)

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

  1. 1/20
  2. 1/12
  3. 3/10
  4. 1/2
Question 30 Multiple Choice (Single Answer)

$\lim\limits_{x \rightarrow 0}\Big( \frac{1 - cos x}{x^2}\Big)$is

  1. 1/4
  2. 1/2
  3. 1
  4. 2
Question 31 Multiple Choice (Single Answer)

Consider the differential equation x2 - 4y = 0 with the boundary conditions of y(0) = 0 and y (1) = 1. The complete solution of the differential equation is

  1. x2
  2. B sin $(\frac{\pi x}{2})$
  3. ex sin $(\frac{\pi x}{2})$
  4. e- x sin $(\frac{\pi x}{2})$
Question 32 Multiple Choice (Single Answer)

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.

If F = 1 kN, the magnitude of the vertical reaction force developed at the point B (in kN) is

  1. 0.63
  2. 0.32
  3. 1.26
  4. 1.46
Question 33 Multiple Choice (Single Answer)

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.

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

  1. 8.17
  2. 11.15
  3. 14.14
  4. 22.30
Question 34 Multiple Choice (Single Answer)

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).

  1. 116.18
  2. 0.116
  3. 18.22
  4. 232.36
Question 35 Multiple Choice (Single Answer)

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

  1. 4
  2. 2
  3. 0.5
  4. 0.25
Question 36 Multiple Choice (Single Answer)

The velocity triangles at the inlet and exit of the rotor of a turbo machine are shown. V denotes the absolute velocity of the fluid. W denotes the relative of the fluid and U denotes the blade velocity. Subscripts 1 and 2 refers to inlet and outlet respectively. If V2 = W1 and V1 = W2, then the degree of reaction is

  1. 0
  2. 1
  3. 0.5
  4. 0.25
Question 37 Multiple Choice (Single Answer)

A large tank with a nozzle attached contains three immiscible, in viscid fluids as shown. Assuming that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

  1. $\sqrt{2gh_3 \Big( 1+ \frac{\rho_1h_1}{\rho_3h_3}+\frac{\rho_2h_2}{\rho_3h_3}\Big)}$
  2. $\sqrt{2g(h_1 + h_2 + h_3)}$
  3. $\sqrt{2gh_3 \Big(\frac{\rho_1h_1 + \rho_2h_2 + \rho_3h_3}{\rho_1 + \rho_2 + \rho_3}\Big)}$
  4. $\sqrt{2g \Big(\frac{\rho_1h_2h_3 + \rho_2h_3h_1+\rho_3h_1h_2}{\rho_1h_1 + \rho_2h_2 + \rho_3h_3}\Big)}$
Question 38 Multiple Choice (Single Answer)

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, the view factor F22 is given by

  1. $\Big(\frac{D_2}{D_1}\Big)$- 1
  2. 0
  3. $\Big(\frac{D_1}{D_2}\Big)$
  4. 1 -$\Big(\frac{D_1}{D_2}\Big)$
Question 39 Multiple Choice (Single Answer)

Water (Cp = 4.18 kJ/kg.K) at 800 C enters a counter flow heat exchanger with a mass flow rate of 0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 300 C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in oC) is

  1. 40
  2. 20
  3. 10
  4. 5
Question 40 Multiple Choice (Single Answer)

Which one of the following configurations has the highest fin effectiveness?

  1. Thin, closely spaced fins
  2. Thin, widely spaced fins
  3. Thick, widely spaced fins
  4. Thick, closely spaced fins
Question 41 Multiple Choice (Single Answer)

Which of the following is NOT a decision taken during the aggregate production planning stage?

  1. scheduling of machines
  2. amount of labour to be committed
  3. rate at which production should happen
  4. inventory to be carried forward
Question 42 Multiple Choice (Single Answer)

For a particular project eight activities are to be carried out. Their relationships with other activities and excepted durations are mentioned in the table below:

<blockquote ||||="" |---|---|---|="" |="" <b="">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|

The critical path for the project is

  1. a - b - e - g - h
  2. a - c - g - h
  3. a - d - f - h
  4. a - b - c - f - h
Question 43 Multiple Choice (Single Answer)

For a particular project eight activities are to be carried out. Their relationships with other activities and excepted durations are mentioned in the table below:

<blockquote ||||="" |---|---|---|="" |="" <b="">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|

If the duration of activity f alone is changed from 9 to 10 days, then the

  1. critical path remains the same and the total duration to complete the project changes to 19 days
  2. critical path and the total duration to complete the project remain the same
  3. critical path changes but the total duration to complete the project remains the same
  4. critical path changes and the total duration to complete the project changes to 17 days
Question 44 Multiple Choice (Single Answer)

A filled 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 allowance shear stress of the weld is 94 MPa, considering the minimum throat area of the weld, the maximum allowable transverse load (in kN) is

  1. 14.44
  2. 17.92
  3. 19.93
  4. 22.16
Question 45 Multiple Choice (Single Answer)

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 1800. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied (in Nm) is

  1. 100.6
  2. 54.4
  3. 22.1
  4. 15.7
Question 46 Multiple Choice (Single Answer)

In abrasive jet machining as the distance between the nozzle tip and the work surface increases, the material removal rate

  1. increases continuously
  2. decreases continuously
  3. decreases becomes stable and then increases
  4. increases becomes stable and then decreases
Question 47 Multiple Choice (Single Answer)

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 1180. Assuming 2 mm clearance at approach and exit, the total drill time (in seconds) is

  1. 35.1
  2. 32.4
  3. 31.2
  4. 30.1
Question 48 Multiple Choice (Single Answer)

Details pertaining to an orthogonal metal cutting process is as below:
Chip thickness ratio 0.4
Undeformed thickness 0.6 mm
Rake angle + 100
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

  1. 0.1781 x 105
  2. 0.7754 x 105
  3. 1.0104 x 105
  4. 4.397 x 105
Question 49 Multiple Choice (Single Answer)

Match the following metal forming processes with their associated stresses in the work piece.

 
Metal forming process 
|        <b> Type of stress</b>
|

| 1. Coining
| P. Tensile
|
| 2. Wire Drawing
| Q. Shear
|
| 3. Blanking
| R. Tensile & Compressive
|
| 4. Deep Drawing
| S. Compressive
|

  1. 1 - S, 2 - P, 3 - Q, 4 - R
  2. 1 - S, 2 - P, 3 - R, 4 - Q
  3. 1 - P, 2 - Q, 3 - S, 4 - R
  4. 1 - P, 2 - R, 3 - Q, 4 - S
Question 50 Multiple Choice (Single Answer)

In an interchangeable assembly, shafts of size 25 mm having range [0.04 to - 0.010] are mated with holes of size 25 mm having range [0.030 to - 0.020]. The maximum interference (in microns) in the assembly is

  1. 40
  2. 30
  3. 20
  4. 10
Question 51 Multiple Choice (Single Answer)

During normalizing process of steel the specimen is heated

  1. between the upper and lower critical temperature and cooled in still air
  2. above the upper critical temperature and cooled in furnace
  3. above the upper critical temperature and cooled in still air
  4. between the upper and lower critical temperature and cooled in furnace
Question 52 Multiple Choice (Single Answer)

Calculate the punch size (in mm), for a circular blanking operation for which details are given below:
<blockquote |||="" |---|---|="" |="" size="" of="" the="" blank|="" 25="" mm|="" thickness="" sheet|="" 2="" radial="" clearance="" between="" punch="" and="" die|="" 0.06="" die="" allowance|="" 0.05="" <="" blockquote="">

  1. 24.83
  2. 24.89
  3. 25.01
  4. 25.17
Question 53 Multiple Choice (Single Answer)

In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and the thickness 8 mm undergoes 10% reduction of thickness. The angle of bite (in radians) is

  1. 0.006
  2. 0.031
  3. 0.062
  4. 0.600
Question 54 Multiple Choice (Single Answer)

A refrigerator operates between 120 kPa in an ideal vapour compression cycle withy R - 134a as the refrigerant enters the compressor as saturated vapour 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)
120
800
---
Superheated R - 134a
---
P (kPa)
800

The rate at which heat is extracted (in kJ/s) from the refrigerated space is

  1. 28.3
  2. 42.9
  3. 34.3
  4. 14.6
Question 55 Multiple Choice (Single Answer)

A refrigerator operates between 120 kPa in an ideal vapour compression cycle with y R - 134a as the refrigerant enters the compressor as saturated vapour and leaves the condenser as saturated liquid. The mass flow rate of the refrigerant is 0.5 kg/s. Properties for R - 134a are as follows:
Saturated R - 134a
---
P (kPa)
120
800
---
Superheated R - 134a
---
P (kPa)
800

The power required for the compressor (in kW) is

  1. 5.94
  2. 1.83
  3. 7.9
  4. 39.5
Question 56 Multiple Choice (Single Answer)

A solid circular shaft needs to be designed to transmit a torque of 50 Nm. 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

  1. 8
  2. 16
  3. 24
  4. 32
Question 57 Multiple Choice (Single Answer)

For the matrix A = $\begin{bmatrix}
\ 5 & 3 \
\ 1 & 3 \
\end{bmatrix}$, ONE of the normalized eigen vectors is given as

  1. $\begin{pmatrix} \ \frac{1}{2} \\ \ \frac{\sqrt{3}}{2} \\ \end{pmatrix}$
  2. $\begin{pmatrix} \ \frac{1}{\sqrt{2}} \\ \ \frac{-1}{\sqrt{2}} \\ \end{pmatrix}$
  3. $\begin{pmatrix} \ \frac{3}{\sqrt{10}} \\ \ \frac{-1}{\sqrt{10}} \\ \end{pmatrix}$
  4. $\begin{pmatrix} \ \frac{1}{\sqrt{5}} \\ \ \frac{2}{\sqrt{5}} \\ \end{pmatrix}$
Question 58 Multiple Choice (Single Answer)

For an opaque surface, the absorptivity $(\alpha)$, transmissivity $(\tau)$ and reflectivity $(\rho)$are related by the equation

  1. $(\alpha)$+$(\rho)$=$(\tau)$
  2. ${\alpha}$+$(\rho)$+$(\tau)$ = 0
  3. $(\alpha)$+$(\rho)$= 1
  4. $(\alpha)$+$(\rho)$= 0

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