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GATE 2014 Mechanical Engineering (Set 3)

Complete GATE 2014 Mechanical Engineering exam paper covering thermodynamics, fluid mechanics, heat transfer, manufacturing technology, mechanics of materials, machine design, and engineering mathematics

35 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Find the next term in the sequence: 7G, 11K, 13M, ______

  1. 15Q
  2. 17Q
  3. 15P
  4. 17P
Question 2 Multiple Choice (Single Answer)

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

  1. M < R > P > S
  2. M > S < P < F
  3. Q < M < F = P
  4. P = A < R < M
Question 3 Multiple Choice (Single Answer)

The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are:

(i) Butterflies are birds.
(ii) There are more tigers in this forest than red ants.
(iii) All reptiles in this forest are either snakes or crocodiles.
(iv) Elephants are the largest mammals in this forest.

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

If a function is continuous at a point,

  1. the limit of the function may not exist at the point
  2. the function must be derivable at the point
  3. the limit of the function at the point tends to infinity
  4. the limit must exist at the point and the value of limit should be same as the value of the function at that point
Question 5 Multiple Choice (Single Answer)

Divergence of the vector field x2 zi + xyj – yz2 k at (1, - 1, 1) is

  1. 0
  2. 3
  3. 5
  4. 6
Question 6 Multiple Choice (Single Answer)

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

  1. 0
  2. 45
  3. 90
  4. 135
Question 7 Multiple Choice (Single Answer)

A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

  1. 0.6
  2. 0.1
  3. 0.01
  4. 0
Question 8 Multiple Choice (Single Answer)

Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is

  1. 300 rpm counterclockwise
  2. 300 rpm clockwise
  3. 4800 rpm counterclockwise
  4. 4800 rpm clockwise
Question 9 Multiple Choice (Single Answer)

Which one of following is NOT correct?

  1. Intermediate principal stress is ignored when applying the maximum principal stress theory.
  2. The maximum shear stress theory gives the most accurate results amongst all the failure theories.
  3. As per the maximum strain energy theory, failure occurs when the strain energy per unit volume exceeds a critical value.
  4. As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value.
Question 10 Multiple Choice (Single Answer)

Consider a long cylindrical tube of inner and outer radii, ri and ro, respectively, length, L and thermal conductivity, k. Its inner and outer surfaces are maintained at Ti and To, respectively (Ti > To). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

  1. $\frac{1}{2 \pi KL}1n \Big( \frac{r_i}{r_o} \Big)$
  2. $\frac{1}{2 \pi r_iL}$
  3. $\frac{1}{2 \pi KL}1n \Big( \frac{r_o}{r_i} \Big)$
  4. $\frac{1}{4 \pi KL}1n \Big( \frac{r_o}{r_i} \Big)$
Question 11 Multiple Choice (Single Answer)

Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a $\neq$ 0, b $\neq$ 0 with respective eigenvectors $\begin{bmatrix}
\ x1 \
\ x2 \
\ x3 \
\end{bmatrix}$, $\begin{bmatrix}
\ y1 \
\ y2 \
\ y3 \
\end{bmatrix}$. If a $\neq$ b than x1 y1 + x2 y2 + x3 y3 equals

  1. a
  2. b
  3. ab
  4. 0
Question 12 Multiple Choice (Single Answer)

For a gas turbine power plant, identify the correct pair of statements.
P. Smaller in size compared to steam power plant for same power output
Q. Starts quickly compared to steam power plant
R. Works on the principle of Rankine cycle
S. Good compatibility with solid fuel

  1. P, Q
  2. R, S
  3. Q, R
  4. P, S
Question 13 Multiple Choice (Single Answer)

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

I. The fluid is well-mixed.
II. The fluid is unmixed.
III. ReD < 2300
IV. ReD < 2300

  1. I, III
  2. II, IV
  3. II, III
  4. I, IV
Question 14 Multiple Choice (Single Answer)

The process utilizing mainly thermal energy for removing material is

  1. Ultrasonic Machining
  2. Electrochemical Machining
  3. Abrasive Jet Machining
  4. Laser Beam Machining
Question 15 Multiple Choice (Single Answer)

Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because

  1. extra hardness is imparted to the workpiece due to coolant used
  2. oxide layers on the workpiece surface impart extra hardness to it
  3. extra hardness is imparted to the workpiece due to severe rate of strain
  4. vibration is induced in the machine tool
Question 16 Multiple Choice (Single Answer)

A minimal spanning tree in network flow models involves

  1. all the nodes with cycle/loop allowed
  2. all the nodes with cycle/loop not allowed
  3. shortest path between start and end nodes
  4. all the nodes with directed arcs
Question 17 Multiple Choice (Single Answer)

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

  1. $\oint SQ$ > 0 and $\oint \frac{SQ}{T}$ < 0
  2. $\oint SQ$ < 0 and $\oint \frac{SQ}{T}$ < 0
  3. $\oint SQ$ > 0 and $\oint \frac{SQ}{T}$ > 0
  4. $\oint SQ$ < 0 and $\oint \frac{SQ}{T}$ > 0
Question 18 Multiple Choice (Single Answer)

The hot tearing in a metal casting is due to

  1. high fluidity
  2. high melt temperature
  3. wide range of solidification temperature
  4. low coefficient of thermal expansion
Question 19 Multiple Choice (Single Answer)

Consider a simply supported beam of length, 50h, with a rectangular crosssection of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

  1. 0.02
  2. 0.10
  3. 0.05
  4. 0.01
Question 20 Multiple Choice (Single Answer)

The distance x from the end of the beam as shown in the figure. What would be the value of x so that the displacement at ‘A’ is equal to zero?

  1. 0.5L
  2. 0.25L
  3. 0.33L
  4. 0.66L
Question 21 Multiple Choice (Single Answer)

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

  1. 1 and 1/3
  2. 1/3 and 1
  3. 1 and 4/3
  4. 1/3 and 4/3
Question 22 Multiple Choice (Single Answer)

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

  1. $\frac{9}{16}$ mv2
  2. $\frac{11}{16}$ mv2
  3. $\frac{13}{16}$ mv2
  4. $\frac{15}{16}$ mv2
Question 23 Multiple Choice (Single Answer)

Consider two solutions x(t) = x1(t) and x(t) = x2 (t) of the differential equation $\frac{d^2x(t)}{dt^2}$ + x (t) = 0, t > 0, such that x1 (0) = 1,$\frac{dx_1(t)}{dt} \Big|{t -0} = 0, x_2(0) = 0, \frac{dx_2(t)}{dt}\Big|{t-0}$ = 1

The Wronskian W (t) = $\begin{bmatrix}
\ x_1(t) & x_2(t) \
\ \frac{dx_1(t)}{dt} & \frac{dx_2(t)}{dt} \
\end{bmatrix}$ at t = $\frac{\pi}{2}$ is

  1. 1
  2. – 1
  3. 0
  4. 2$\pi$
Question 24 Multiple Choice (Single Answer)

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by t, lying in the interval 0 to 2p, is associated with the maximum translation of the follower during one full rotation of the cam rotating about the center at (x, y) = (0, 0)?

  1. x(t) = cos t, y(t) = sint
  2. x(t) = cos t, y(t) = 2 sint
  3. x (t) $\frac{1}{2}$ + cos(t) = 1 +, y(t) = 2 sint
  4. x(t) $\frac{1}{2}$ + cos (t) = 1 +, y(t) = sint
Question 25 Multiple Choice (Single Answer)

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

     
Group A 
        </strong>|<strong> </strong>|<strong>Group B</strong>|

|P |Hot tears|1|Improper fusion of two streams of liquid metal|
|Q|Shrinkage|2|Low permeability of the sand mould|
|R|Blow holes|3|Volumetric contraction both in liquid and solid stage|
| | |4|Stresses in different regions of metal|

  1. P - 1, Q - 3, R - 2, S - 4
  2. P - 4, Q - 3, R - 2, S - 1
  3. P - 3, Q - 4, R - 2, S - 1
  4. P - 1, Q - 2, R - 4, S - 3
Question 26 Multiple Choice (Single Answer)

A manufacturer can produce 12000 bearing per day. The manufacturer received an order of 8000 bearings per day from a customer. The cost of holding a bearing in stock is Rs. 0.20 per month. Setup cost per production run is Rs. 500. Assuming 300 working days in a year, the frequency of production run should be

  1. 4.5 days
  2. 4.5 months
  3. 6.8 days
  4. 6.8 months
Question 27 Multiple Choice (Single Answer)

A certain amount of an ideal gas is initially at a pressure p1and temperature T1. FIrst, it undergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is

  1. 0.25
  2. 0.75
  3. 1.0
  4. 1.5
Question 28 Multiple Choice (Single Answer)

A solid sphere of radius r1 = 20 mm is placed concentrically inside a hollow sphere of radius r2 = 30 mm as shown in the figure.

The view factor F21 for radiation heat transfer is

  1. $\frac{2}{3}$
  2. $\frac{4}{9}$
  3. $\frac{8}{27}$
  4. $\frac{9}{4}$
Question 29 Multiple Choice (Single Answer)

Consider the given project network, where numbers along various activities represent the normal time. The free float on activity 4-6 and the project duration, respectively, are

  1. 2, 13
  2. 0, 13
  3. – 2, 13
  4. 2, 12
Question 30 Multiple Choice (Single Answer)

Which pair of following statements is correct for orthogonal cutting using a singlepoint cutting tool?
P. Reduction in friction angle increases cutting force
Q. Reduction in friction angle decreases cutting force
R. Reduction in friction angle increases chip thickness
S. Reduction in friction angle decreases chip thickness

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

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.

  1. P - 1, Q - 2, R - 3, S - 4, T - 5, U - 6
  2. P - 3, Q - 1, R - 4, S - 2, T - 6, U - 5
  3. P - 3, Q - 4, R - 1, S - 5, T - 2, U - 6
  4. P - 4, Q - 1, R - 5, S - 2, T - 3, U - 6
Question 32 Multiple Choice (Single Answer)

A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry and exit. At the exit of the siphon, the velocity of water is

  1. $\sqrt{2g(Z_O - Z_R)}$
  2. $\sqrt{2g(Z_P - Z_R)}$
  3. $\sqrt{2g(Z_O - Z_R)}$
  4. $\sqrt{2gZ_O}$
Question 33 Multiple Choice (Single Answer)

A cylindrical blind riser with diameter d and height h, is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h : d is

  1. 1 : 2
  2. 2 : 1
  3. 1 : 4
  4. 4 : 1
Question 34 Multiple Choice (Single Answer)

An analytic function of a complex variable z = x + iy is expressed as f(z) = u (x, y) + iv (x, y), where i = $\sqrt{-1}$. If u (x, y) = x2 – y2, then expression for v (x, y) in terms of x, y and a general constant c would be

  1. xy + c
  2. $\frac{x^2 + y^2}{2}+c$
  3. 2xy + c
  4. $\frac{x^2 - y^2}{2}+c$
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