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Mechanical Engg. (GATE) 2011

ME-GATE-2011

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Questions

Question 1 Multiple Choice (Single Answer)

A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces P R and Q R at supports P and Q respectively are

  1. 1 kN downward, 1 kN upward
  2. 0.5 kN upward, 0.5 kN downward
  3. 0.5 kN downward, 0.5 kN upward
  4. 1 kN upward, 1 kN upward
Question 2 Multiple Choice (Single Answer)

A column has a rectangular cross-section of 10 mm x 20 mm and a length of 1 m. The slenderness ratio of the column is close to

  1. 200
  2. 346
  3. 477
  4. 1000
Question 3 Multiple Choice (Single Answer)

The crystal structure of austenite is

  1. body centered cubic
  2. face centered cubic
  3. hexagonal closed packed
  4. body centered tetragonal
Question 4 Multiple Choice (Single Answer)

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD (in rad/s) is

  1. 3
  2. $\frac{3}{2}$
  3. 1
  4. $\frac{2}{3}$
Question 5 Multiple Choice (Single Answer)

A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to

  1. 32
  2. 23
  3. 16
  4. 11
Question 6 Multiple Choice (Single Answer)

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist $\theta$at the free end is

  1. $\Big( \frac{32TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
  2. $\Big( \frac{18TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
  3. $\Big( \frac{16TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
  4. $\Big( \frac{2TL}{\pi \theta G} \Big)^{\frac{1}{4}}$
Question 7 Multiple Choice (Single Answer)

The sheer strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100 mm diameter from a 1.5 mm thick sheet is close to

  1. 45 kN
  2. 70 kN
  3. 141 kN
  4. 3500 kN
Question 8 Multiple Choice (Single Answer)

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is

  1. $\frac{bxt^3}{6I}$
  2. $\frac{bxt^3}{12I}$
  3. $\frac{bxt^3}{24I}$
  4. $\frac{xt^3}{12}$
Question 9 Multiple Choice (Single Answer)

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The maximum deflection of the beam is

  1. $\frac{24pI^3}{Ebt^3}$
  2. $\frac{12pI^3}{Ebt^3}$
  3. $\frac{8pI^3}{Ebt^3}$
  4. $\frac{6pI^3}{Ebt^3}$
Question 10 Multiple Choice (Single Answer)

If Log (P) = (1/2) Log (Q) = (1/3) Log (R), which of the following options is TRUE?

  1. P2 = Q3 R2
  2. Q2 = PR
  3. Q2 = R3 P
  4. R = P2 Q2
Question 11 Multiple Choice (Single Answer)

A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

  1. 7.58 litres
  2. 7.84 litres
  3. 7 litres
  4. 7.29 litres
Question 12 Multiple Choice (Single Answer)

The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?

  1. 5
  2. 4
  3. 7
  4. 6
Question 13 Multiple Choice (Single Answer)

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

  1. 4
  2. 5
  3. 6
  4. 7
Question 14 Multiple Choice (Single Answer)

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

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

Which one among the following welding processes uses non-consumable electrode?

  1. Gas metal arc welding
  2. Submerged arc welding
  3. Gas tungsten arc welding
  4. Flux coated arc welding
Question 16 Multiple Choice (Single Answer)

Match the following criteria of material failure, under biaxial stresses $\sigma_1$ and $\sigma_2$ and yield stress $\sigma_y$, with their corresponding graphic representations:
P. Maximum-normal-stress criterion


Q. Maximum-distortion-energy criterion

R. Maximum-shear-stress criterion

  1. P-M, Q-L, R-N
  2. P-N, Q-M, R-L
  3. P-M, Q-N, R-L
  4. P-N, Q-L, R-M
Question 17 Multiple Choice (Single Answer)

A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress (in MPa) is

  1. 100
  2. 250
  3. 500
  4. 1000
Question 18 Multiple Choice (Single Answer)

A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

  1. $\frac{1}{2 \pi} \sqrt{\frac{k}{m}}$
  2. $\frac{1}{2 \pi} \sqrt{\frac{2k}{m}}$
  3. $\frac{1}{2 \pi} \sqrt{\frac{2k}{3m}}$
  4. $\frac{1}{2 \pi} \sqrt{\frac{3k}{2m}}$
Question 19 Multiple Choice (Single Answer)

A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is

  1. - 1
  2. 0
  3. 1
  4. 2
Question 20 Multiple Choice (Single Answer)

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800 kJ/kg and 1800 kJ/kg respectively. Neglecting pump work, the specific steam consumption (in kg/kW-hour) is

  1. 3.60
  2. 0.36
  3. 0.06
  4. 0.01
Question 21 Multiple Choice (Single Answer)

Heat and work are

  1. intensive properties
  2. extensive properties
  3. point functions
  4. path functions
Question 22 Multiple Choice (Single Answer)

The crank radius of a single-cylinder I. C. engine is 60 mm and the diameter of the cylinder is 80 mm. The swept volume of the cylinder (in cm3) is

  1. 48
  2. 96
  3. 302
  4. 603
Question 23 Multiple Choice (Single Answer)

The contents of a well-insulated tank are heated by a resistor of 23 W in which 10 A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system
and the heat transfer tothe system are positive. The rates of heat (Q), work (W) and change in internal energy (DU) during the process (in kW) are

  1. Q = 0, W = −23, $\triangle$U = +23
  2. Q = +23, W = 0, $\triangle$U = +23
  3. Q = −23, W = 0, $\triangle$U = −23
  4. Q = 0, W = +23, $\triangle$U = −23
Question 24 Multiple Choice (Single Answer)

An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300 K and 1500 K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures (in Kelvin) at the end of the compression and expansion processes are respectively

  1. 500 and 900
  2. 900 and 500
  3. 500 and 500
  4. 900 and 900
Question 25 Multiple Choice (Single Answer)

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air:
Specific heat at constant pressure, Cp = 1.005 kJ/kgK;
Specific heat at constant volume, Cv = 0.718 kJ/kgK;
Characteristic gas constant, R = 0.287 kJ/kgK
Enthalpy, h = cp T
Internal energy, u = Cv T

If the pressure at station Q is 50 kPa, the change in entropy (sQ - sP ) in kJ/kgK is

  1. -0.155
  2. 0
  3. 0.160
  4. 0.355
Question 26 Multiple Choice (Single Answer)

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air:
Specific heat at constant pressure, Cp = 1.005 kJ/kgK;
Specific heat at constant volume, Cv = 0.718 kJ/kgK;
Characteristic gas constant, R = 0.287 kJ/kgK
Enthalpy, h = cp T
Internal energy, u = Cv T

If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at station Q is close to

  1. 50
  2. 87
  3. 128
  4. 150
Question 27 Multiple Choice (Single Answer)

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m2 is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The density of air (in kg/m3) at the nozzle exit is

  1. 0.560
  2. 0.600
  3. 0.727
  4. 0.800
Question 28 Multiple Choice (Single Answer)

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m2 is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The mass flow rate of air through the nozzle in kg/s is

  1. 1.30
  2. 1.77
  3. 1.85
  4. 2.06
Question 29 Multiple Choice (Single Answer)

What is $\lim\limits_{\theta \rightarrow0} \frac{sin \theta}{\theta}$ equal to?

  1. $\theta$
  2. sin$\theta$
  3. 0
  4. 1
Question 30 Multiple Choice (Single Answer)

The integral $\int\limits_1^3 \frac{1}{x}$ when evaluated by using Simpson's 1/3 rule on two equal subintervals each of length 1, equals

  1. 1.000
  2. 1.098
  3. 1.111
  4. 1.120
Question 31 Multiple Choice (Single Answer)

A series expansion for the function sin$\theta$ is

  1. 1 - $\frac{\theta^2}{2!} + \frac{\theta^4}{4!}$
  2. $\frac{\theta^3}{3!} + \frac{\theta^5}{5!}$
  3. 1 + $\theta$+ $\frac{\theta^2}{2!} + \frac{\theta^3}{3!}$
  4. $\theta$ + $\frac{\theta^3}{3!} + \frac{\theta^5}{5!}$
Question 32 Multiple Choice (Single Answer)

The product of two complex numbers 1+i and 2-5i is

  1. 7-3i
  2. 3-4i
  3. -3-4i
  4. 7+3i
Question 33 Multiple Choice (Single Answer)

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

  1. $\frac{1}{32}$
  2. $\frac{13}{32}$
  3. $\frac{16}{32}$
  4. $\frac{31}{32}$
Question 34 Multiple Choice (Single Answer)

If f(x) is an even function and a is a positive real number, then $\int\limits_{-a}^a f(x) dx$equals

  1. 0
  2. a
  3. 2a
  4. 2$\int\limits_0^a f(x) dx$
Question 35 Multiple Choice (Single Answer)

Consider the following system of equations:
2x1 + x2 + x3 = 0
x2 - x3 = 0
x1 + x2 = 0
This system has

  1. a unique solution
  2. no solution
  3. infinite number of solutions
  4. five solutions
Question 36 Multiple Choice (Single Answer)

Eigen values of a real symmetric matrix are always

  1. positive
  2. negative
  3. real
  4. complex
Question 37 Multiple Choice (Single Answer)

Consider the differential equation $\frac{dy}{dx} = (1+y^2)x$. The general solution with constant c is

  1. y = tan $\frac{x^2}{2}$+ tan c
  2. y = tan2 $\Big( \frac{x}{2} + c \Big)$
  3. y = tan2 $\Big( \frac{x}{2} \Big)+c$
  4. y = tan $\Big( \frac{x^2}{2} + c \Big)$
Question 38 Multiple Choice (Single Answer)

The coefficient of restitution of a perfectly plastic impact is

  1. 0
  2. 1
  3. 2
  4. $\infty$
Question 39 Multiple Choice (Single Answer)

A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force in N exerted by the rubber band as a function of distance x (in m) is given by Fx = 300 x2. If the stone is displaced by 0.1 m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber band is

  1. 0.01J
  2. 0.1J
  3. 1J
  4. 10J
Question 40 Multiple Choice (Single Answer)

A 1 kg block is resting on a surface with coefficient of friction ى = 0.1. A force of 0.8 N is applied to the block as shown in figure. The friction force is

  1. 0
  2. 0.8 N
  3. 0.98 N
  4. 1.2 N
Question 41 Multiple Choice (Single Answer)

A streamline and an equipotential line in a flow field

  1. are parallel to each other
  2. are perpendicular to each other
  3. intersect at an acute angle
  4. are identical
Question 42 Multiple Choice (Single Answer)

Figure shows the schematic for the measurement of velocity of air (density = 1.2kg/m3) through a constant–area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg/m3) in the two columns of the manometer is 10 mm. Take acceleration due to gravity as 2 9.8 m/s2 . The velocity of air (in m/s) is

  1. 6.4
  2. 9.0
  3. 12.8
  4. 25.6
Question 43 Multiple Choice (Single Answer)

In a condenser of a power plant, the steam condenses at a temperature of 60oC. The cooling water enters at 30oC and leaves at 45oC. The logarithmic mean temperature difference (LMTD) of the condenser is

  1. 16.2oC
  2. 21.6oC
  3. 30oC
  4. 37.5oC
Question 44 Multiple Choice (Single Answer)

A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K. The heat transfer coefficient between the steel ball and the surrounding is 5 W/m2K. The thermal conductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of the steel ball is

  1. large because conduction resistance is far higher than the convective resistance
  2. large because conduction resistance is far less than the convective resistance
  3. small because conduction resistance is far higher than the convective resistance
  4. small because conduction resistance is far less than the convective resistance
Question 45 Multiple Choice (Single Answer)

A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 25 W/m K . It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?

  1. The outer radius of the pipe is equal to the critical radius.
  2. The outer radius of the pipe is less than the critical radius.
  3. Adding the insulation will reduce the heat loss.
  4. Adding the insulation will increase the heat loss.
Question 46 Multiple Choice (Single Answer)

Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is

  1. 10 minutes
  2. 20 minutes
  3. 25 minutes
  4. 50 minutes
Question 47 Multiple Choice (Single Answer)

One unit of product P1 requires 3 kg of resource R1 and 1 kg of resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2. The profits per unit by selling product P1 and P2 are Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource R1 and 100 kg of resource R2.

The unit worth of resource R2 i.e., dual price of resource R2 (in Rs. per kg) is

  1. 0
  2. 1350
  3. 1500
  4. 2000
Question 48 Multiple Choice (Single Answer)

One unit of product P1 requires 3 kg of resource R1 and 1 kg of resource R2. One unit of product P2 requires 2 kg of resource R1 and 2 kg of resource R2 . The profits per unit by selling product P1 and P2 are Rs.2000 and Rs.3000 respectively. The manufacturer has 90 kg of resource R1 and 100 kg of resource R2.

The manufacturer can make a maximum profit of Rs.

  1. 60000
  2. 135000
  3. 150000
  4. 200000
Question 49 Multiple Choice (Single Answer)

Two identical ball bearings P and Q are operating at loads 30 kN and 45 KN respectively. The ratio of the life of bearing P to the life of bearing Q is

  1. 81/16
  2. 27/8
  3. 9/4
  4. 3/2
Question 50 Multiple Choice (Single Answer)

The word kanban is most appropriately associated with

  1. economic order quantity
  2. just-in-time production
  3. capacity planning
  4. product design
Question 51 Multiple Choice (Single Answer)

Green sand mould indicates that

  1. polymeric mould has been cured
  2. mould has been totally dried
  3. mould is green in colour
  4. mould contains moisture
Question 52 Multiple Choice (Single Answer)

The maximum possible draft in cold rolling of sheet increases with the

  1. increase in coefficient of friction
  2. decrease in coefficient of friction
  3. decrease in roll radius
  4. increase in roll velocity
Question 53 Multiple Choice (Single Answer)

A single-point cutting tool with 120 rake angle is used to machine a steel work- piece. The depth of cut, i.e. uncut thickness is 0.81 mm. The chip thickness under orthogonal machining condition is 1.8 mm. The shear angle is approximately

  1. 220
  2. 260
  3. 560
  4. 760
Question 54 Multiple Choice (Single Answer)

Match the following non-traditional machining processes with the corresponding material removal mechanisms:<blockquote |||="" |---|---|="" |="" <b="">Mechanical process| Mechanism of material removal|
| P. Chemical machining| 1. Erosion|
| Q. Electro-chemical machining| 2. Corrosive reaction|
| R. Electro - discharge machining| 3. Ion displacement|
| S. Ultrasonic machining| 4. Fusion and vapourization|

  1. P-2, Q-3, R-4, S-1
  2. P-2, Q-4, R-3, S-1
  3. P-3, Q-2, R-4, S-1
  4. P-2, Q-3, R-1, S-4
Question 55 Multiple Choice (Single Answer)

A hole is dimension $\phi$$9 ^{\begin{matrix} \ +0.015 \ \ +0 \ \end{matrix}}$mm. The corresponding shaft is of dimension $\phi$$9 ^{\begin{matrix} \ +0.010 \ \ +0.001 \ \end{matrix}}$mm. The resulting assembly has

  1. loose running fit
  2. close running fit
  3. transition fit
  4. interference fit
Question 56 Multiple Choice (Single Answer)

A cubic casting of 50 mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is

  1. 48.32 mm
  2. 49.90 mm
  3. 49.94 mm
  4. 49.96 mm
Question 57 Multiple Choice (Single Answer)

If a mass of moist air in an airtight vessel is heated to a higher temperature, then

  1. specific humidity of the air increases
  2. specific humidity of the air decreases
  3. relative humidity of the air increases
  4. relative humidity of the air decreases
Question 58 Multiple Choice (Single Answer)

A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of the liquid as 990 kg/m3. The isentropic specific work done by the pump in kJ/kg is

  1. 0.10
  2. 0.30
  3. 2.50
  4. 2.93
Question 59 Multiple Choice (Single Answer)

The operation in which oil is permeated into the pores of a powder metallurgy product is known as

  1. Mixing
  2. Sintering
  3. Impregnation
  4. Infiltration
Question 60 Multiple Choice (Single Answer)

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are $\frac{1}{2}$ and 2 respectively. The Reynolds number based on the plate length for both the flows is 104. The Prandtl and Nusselt numbers for P are $\frac{1}{8}$ and 35 respectively. The Prandtl and Nusselt numbers for Q are respectively

  1. 8 and 140
  2. 8 and 70
  3. 4 and 70
  4. 4 and 35
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