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Mechanical Engg. Set 1 (GATE) 2014

2014 (Set - 4)

39 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

While receiving the award, the scientist said, “I feel vindicated”. Which of the following is closest in meaning to the word 'vindicated'?

  1. Punished
  2. Substantiated
  3. Appreciated
  4. Chastened
Question 2 Multiple Choice (Single Answer)

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.

  1. Dissent
  2. Descent
  3. Decent
  4. Decadent
Question 3 Multiple Choice (Single Answer)

After the discussion, Tom said to me, 'Please revert!'. He expects me to ______.

  1. Retract
  2. Get back to him
  3. Move in reverse
  4. Retreat
Question 4 Multiple Choice (Single Answer)

Let f (x, y) = xn ym = P. If x is doubled and y is halved, the new value of f is

  1. 2n-m P
  2. 2m-n P
  3. 2 (n - m) P
  4. 2 (m - n) P
Question 5 Multiple Choice (Single Answer)

Find the next term in the sequence: 13M, 17Q, 19S, _____

  1. 21 W
  2. 21 V
  3. 23 W
  4. 23 V
Question 6 Multiple Choice (Single Answer)

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.

  1. 5.6
  2. 7.2
  3. 10.0
  4. 12.2
Question 7 Multiple Choice (Single Answer)

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?

  1. 6666660
  2. 6666600
  3. 6666666
  4. 6666606
Question 8 Multiple Choice (Single Answer)

If 'KCLFTSB' stands for 'best of luck' and 'SHSWDG' stands for 'good wishes', which of the following indicates 'ace the exam'?

  1. MCHTX
  2. MXHTC
  3. XMHCT
  4. XMHTC
Question 9 Multiple Choice (Single Answer)

In a statically determinate plane truss, the number of joints (j) and the number of members (m)are related by

  1. j = 2m – 3
  2. m = 2j + 1
  3. m = 2j – 3
  4. m = 2j – 1
Question 10 Multiple Choice (Single Answer)

The solution of the initial value problem $\frac{dy}{dx}$ = – 2xy ; y (0) = 2 is

  1. 1 + $e^{-x^2}$
  2. 2$e^{-x^2}$
  3. 1$e^{x^2}$
  4. 2$e^{x^2}$
Question 11 Multiple Choice (Single Answer)

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

  1. Bevel gears
  2. Double helical gears
  3. Worm gears
  4. Rack and pinion gears
Question 12 Multiple Choice (Single Answer)

Laplace transform of cos ($\omega t$) is $\frac{s}{s^2 + \omega^2}$. The Laplace transform of e–2t cos(4t) is

  1. $\frac{s-2}{(s-2)^2 + 16}$
  2. $\frac{s+2}{(s-2)^2 + 16}$
  3. $\frac{s-2}{(s+2)^2 + 16}$
  4. $\frac{s+2}{(s+2)^2 + 16}$
Question 13 Multiple Choice (Single Answer)

The value of the integral $\int\limits_0^2$$\frac{(x-1)^2 sin (x-1)}{(x-1)^2 + cos(x-1)}dx$ is

  1. 3
  2. 0
  3. – 1
  4. – 2
Question 14 Multiple Choice (Single Answer)

A flow field which has only convective acceleration is

  1. a steady uniform flow
  2. an unsteady uniform flow
  3. a steady non-uniform flow
  4. an unsteady non-uniform flow
Question 15 Multiple Choice (Single Answer)

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

  1. axial and the head available is more than 100 m
  2. axial and the head available is less than 10 m
  3. radial and the head available is more than 100 m
  4. mixed and the head available is about 50 m
Question 16 Multiple Choice (Single Answer)

As the temperature increases, the thermal conductivity of a gas

  1. Increases
  2. Decreases
  3. Remains constant
  4. Increases up to a certain temperature and then decreases
Question 17 Multiple Choice (Single Answer)

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

  1. microstructural changes but does not melt
  2. neither melting nor microstructural changes
  3. both melting and microstructural changes after solidification
  4. melting and retains the original microstructure after solidification
Question 18 Multiple Choice (Single Answer)

The total number of decision variables in the objective function of an assignment problem of size n x n (n jobs and n machines) is

  1. n2
  2. 2n
  3. 2n – 1
  4. n
Question 19 Multiple Choice (Single Answer)

The principle of material removal in Electrochemical machining is

  1. Fick’s law
  2. Faraday’s laws
  3. Kirchhoff’s laws
  4. Ohm’s law
Question 20 Multiple Choice (Single Answer)

Moist air at 35oC and 100% relative humidity is entering a psychrometric device and leaving at 25oC and 100% relative humidity. The name of the device is

  1. Humidifier
  2. Dehumidifier
  3. Sensible heater
  4. Sensible cooler
Question 21 Multiple Choice (Single Answer)

Better surface finish is obtained with a large rake angle because

  1. the area of shear plane decreases resulting in the decrease in shear force and cutting force
  2. the tool becomes thinner and the cutting force is reduced
  3. less heat is accumulated in the cutting zone
  4. the friction between the chip and the tool is less
Question 22 Multiple Choice (Single Answer)

Which one of the following equation is a correct identity for arbitrary 3 x 3 real matrices P, Q and R?

  1. P(Q + R) = PQ + RP
  2. (P – Q)2 = P2 – 2PQ + Q2
  3. det (P + Q) = det P + det Q
  4. (P + Q)2 = P2 + PQ + QP + Q2
Question 23 Multiple Choice (Single Answer)

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

  1. Q, S
  2. R, T
  3. S, T
  4. P, R
Question 24 Multiple Choice (Single Answer)

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

  1. 0.029
  2. 0.034
  3. 0.039
  4. 0.044
Question 25 Multiple Choice (Single Answer)

If z is a complex variable, the value of $\int\limits_6^{3i}$$\frac{dz}{z}$ is

  1. – 0.511 – 1.57i
  2. – 0.511 + 1.57i
  3. 0.511 – 1.57i
  4. 0.511 + 1.57i
Question 26 Multiple Choice (Single Answer)

Consider an ordinary differential equation $\frac{dx}{dt}$ 4t + 4 =. if x = x0 at t = 0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of $\triangle$t = 0.2 is

  1. 0.22
  2. 0.44
  3. 0.66
  4. 0.88
Question 27 Multiple Choice (Single Answer)

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

  1. 11.25 tension
  2. 11.25 compression
  3. 13.5 tension
  4. 13.5 compression
Question 28 Multiple Choice (Single Answer)

It is desired to avoid interference in a pair of spur gears having a 200 pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth on the pinion

  1. Increases
  2. Decreases
  3. First increases and then decreases
  4. Remain unchanged
Question 29 Multiple Choice (Single Answer)

The value of the integral $\int\limits_0^2 \int\limits_0^x$ ex+y dydx is

  1. $\frac{1}{2}$ (e – 1)
  2. $\frac{1}{2}$ (e2 – 1)2
  3. $\frac{1}{2}$ (e2 – e)
  4. $\frac{1}{2}$ $\bigg(e - \frac{1}{e}\bigg)^2$
Question 30 Multiple Choice (Single Answer)

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
  1. P - 4, Q - 1, R - 3, S - 2
  2. P - 4, Q - 3, R - 1, S - 2
  3. P - 3, Q - 2, R - 1, S - 4
  4. P - 2, Q - 1, R - 3, S - 4
Question 31 Multiple Choice (Single Answer)

Consider a velocity field V = K (yj + xk), where K is a constant. The vorticity, $\Omega_z$, is

  1. – K
  2. K
  3. – K/2
  4. K/2
Question 32 Multiple Choice (Single Answer)

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

  1. $\frac{1}{3}$ $\frac{PL^3}{EI}$
  2. $\frac{2}{3}$ $\frac{PL^3}{EI}$
  3. $\frac{PL^3}{EI}$
  4. $\frac{4}{3}$ $\frac{PL^3}{EI}$
Question 33 Multiple Choice (Single Answer)

A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the 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 $\mu$ between the floor and the wardrobe, respectively?

  1. 490.5 and 0.5
  2. 981 and 0.5
  3. 1000.5 and 0.15
  4. 1000.5 and 0.25
Question 34 Multiple Choice (Single Answer)

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
  1. P - III, Q - IV, R - II, S - I
  2. P - II, Q - III, R - IV, S - I
  3. P - III, Q - II, R - IV, S - I
  4. P - II, Q - III, R - I, S - IV
Question 35 Multiple Choice (Single Answer)

Consider the following statements regarding streamline(s):

(i) It is a continuous lines such that the tangent at any point on it shows the velocity vector at the point.
(ii) There is no flow across streamlines.
(iii) $\frac{dx}{u}$ = $\frac{dv}{v}$ = $\frac{dz}{w}$ is the differential equation of a streamline, where u, v and w 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?

  1. (i), (ii), (iv)
  2. (ii), (iii), (iv)
  3. (i), (iii), (iv)
  4. (i), (ii), (iii)
Question 36 Multiple Choice (Single Answer)

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

  1. 1/2
  2. 1/3
  3. 1/4
  4. 1/8
Question 37 Multiple Choice (Single Answer)

A GO-No GO plug gauge is to be designed for measuring a hole of nominal diameter 25 mm with a hole tolerance of $\pm$ 0.015 mm. Considering 10% of work tolerence 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

  1. $24.985^{\begin{matrix} \ +0.003 \\ \ -0.003 \\ \end{matrix}}$
  2. $25.015^{\begin{matrix} \ +0.003 \\ \ -0.003 \\ \end{matrix}}$
  3. $24.985^{\begin{matrix} \ +0.003 \\ \ -0.003 \\ \end{matrix}}$
  4. $24.985^{\begin{matrix} \ +0.003 \\ \ -0.003 \\ \end{matrix}}$
Question 38 Multiple Choice (Single Answer)

The precedence relations and duration (in days) of activities of a project network are given in the table. The total flot (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
  1. 0 and 4
  2. 1 and 4
  3. 2 and 3
  4. 3 and 1
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