GATE Mechanical Engineering Mock Test Papers

Question

The parabolic arc $y = \sqrt{x},\ 1\le x \le 2$ is revolved around the x-axis. The volume of the solid of revolution is

Possible Answers

Selected	Possible Answer
	$\cfrac{\pi}{4}$
	$\cfrac{\pi}{2}$
	$\cfrac{3 \pi}{4}$
	$\cfrac{3 \pi}{2}$

Question

The Blasius equation, $\cfrac{d^3f}{d \eta}\ +$ $\cfrac{f}{2}\ \cfrac{d^2f}{d \eta^2}$ = 0 is a

Possible Answers

Selected	Possible Answer
	Second order nonlinear ordinary differential equation
	Third order nonlinear ordinary differential equation
	Third order linear ordinary differential equation
	Mixed order nonlinear ordinary differential equation

Question

The value of the integral $\overset{\infty}{\underset{- \infty}{\int}}$ $\cfrac{dx}{1 + X^2}$ is

Possible Answers

Selected	Possible Answer
	$- \pi$
	$- \cfrac{\pi}{2}$
	$\cfrac{\pi}{2}$
	$\pi$

Question

The modulus of the complex number $\Bigg( \cfrac{3 + 4i}{1 - 2i} \Bigg)$ is

Possible Answers

Selected	Possible Answer

	$\sqrt{5}$
	$\cfrac{1}{\sqrt{5}}$
	$\cfrac{1}{5}$

Question

The function y = 2 – 3x

Possible Answers

Selected	Possible Answer
	is continuous $\forall x \in$ R and differentiable $\forall x \in$ R
	is continuous $\forall x \in$ R and differentiable $\forall x \in$ R except at x=3/2
	is continuous $\forall x \in$ R and differentiable $\forall x \in$ R except at x=2/3
	is continuous $\forall x \in$ R except at x=3 and differentiable $\forall x \in$ R

Question

Mobility of a statically indeterminate structure is

Possible Answers

Selected	Possible Answer
	$\le - 1$


	$\ge - 2$

Question

There are two points P and Q on a planar rigid body. The relative velocity between the two points

Possible Answers

Selected	Possible Answer
	should always be along PQ
	Can be oriented along any direction
	should always be perpendicular to PQ
	should be along QP when the body undergoes pure translation

Question

The state of plane-stress at a point is given by $\alpha_x$ = – 200MPa, $\alpha_y$ = 100MPa and $\tau_{xy}$ = 100MPa. The maximum shear stress in MPa is

Possible Answers

Selected	Possible Answer
	111.8
	150.1
	180.3
	223.6

Question

Which of the following statements is INCORRECT?

Possible Answers

Selected	Possible Answer
	Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.
	Inversions of a mechanism are created by fixing different links one at a time.
	Geneva mechanism is an intermittent motion device
	Gruebler’s criterion assumes mobility of a planar mechanism to be one.

Question

The natural frequency of a spring-mass system on earth is $\omega_n$ . The natural frequency of this system on the moon $(g_{moon} = g_{earth} / 6)$ is

Possible Answers

Selected	Possible Answer
	$\omega_n$
	$0.408 \omega_n$
	$0.204 \omega_n$
	$0.167 \omega_n$

Question

Tooth interference in an external involute spur gear pair can be reduced by

Possible Answers

Selected	Possible Answer
	decreasing center distance between gear pair
	decreasing module
	decreasing pressure angle
	increasing number of gear teeth

Question

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Possible Answers

Selected	Possible Answer
	Metacentre should be below centre of gravity
	Metacentre should be above centre of gravity
	Metacentre and centre of gravity must lie on the same horizontal line
	Metacentre and centre of gravity must lie on the same vertical line

Question

The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is $6ms^{-1}$ . The mean velocity $(in\ ms^{-1})$ of the flow is

Possible Answers

Selected	Possible Answer
	2
	3
	4
	5

Question

A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is

Possible Answers

Selected	Possible Answer
	k
	n
	n – k
	n + k

Question

A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259m^3 (25.9litres) . The engine has an output of 950kW at 2200rpm. The mean effective pressure in MPa is closest to

Possible Answers

Selected	Possible Answer
	2
	1
	0.2
	0.1

Question

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

Possible Answers

Selected	Possible Answer
	equal to entropy change of the reservoir
	equal to entropy change of water
	equal to zero
	always positive

Question

A hydraulic turbine develops 1000kW power for a head of 40m. If the head is reduced to 20m, the power developed (in kW) is

Possible Answers

Selected	Possible Answer
	177
	354
	500
	707

Question

The material property which depends only on the basic crystal structure is

Possible Answers

Selected	Possible Answer
	fatigue strength
	work hardening
	fracture strength
	elastic constant

Question

In a gating system, the ratio 1:2:4 represents

Possible Answers

Selected	Possible Answer
	sprue base area: runner area: ingate area
	pouring basin area: ingate area: runner area
	sprue base area: ingate area: casting area
	runner area: ingate area: casting area

Question

A shaft has a dimension, $\Phi 35^{\overset{-0.009}{-0.025}}$ . The respective values of fundamental deviation and tolerance are

Possible Answers

Selected	Possible Answer
	-0.025, $\pm$ 0.008
	-0.025,0.016
	-0.009, $\pm$ 0.008
	-0.009,0.016

Question

In a CNC program block, N002 G02 G91 X40 Z40…, G02 AND G91 refer to

Possible Answers

Selected	Possible Answer
	circular interpolation in counterclockwise direction and incremental dimension
	circular interpolation in counterclockwise direction and absolute dimension
	circular interpolation in clockwise direction and incremental dimension
	circular interpolation in clockwise direction and absolute dimension

Question

The demand and forecast for February are 12000 and 10275, respectively. Using single exponential smoothening method (smoothening coefficient = 0.25), forecast for the month of March is

Possible Answers

Selected	Possible Answer
	431
	9587
	10706
	11000

Question

Little’s law is relationship between

Possible Answers

Selected	Possible Answer
	stock level and lead time in an inventory system
	waiting time and length of the queue in a queuing system
	number of machines and job due dates in a scheduling problem
	uncertainty in the activity time and project completion time

Question

Vehicle manufacturing assembly line is an example of

Possible Answers

Selected	Possible Answer
	product layout
	process layout
	manual layout
	fixed layout

Question

Simplex method of solving linear programming problem uses

Possible Answers

Selected	Possible Answer
	all the points in the feasible region
	only the corner points of the feasible region
	intermediate points within the infeasible region
	only the interior points in the feasible region.

Question

Note: All length dimensions shown in the figures are in mm unless otherwise specified. Figures are not drawn to scale.

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson’s rule is

Possible Answers

Selected	Possible Answer
	542
	993
	1444
	1986

Question

One of the eigen vectors of the matrix A = $\Big[ {}_1 ^ 2\!\ {}_3 ^ 2\! \Big]$ is

Possible Answers

Selected	Possible Answer
	$\Big\{ \overset{2}{-1} \Big\}$
	$\Big\{ \overset{2}{1} \Big\}$
	$\Big\{ \overset{4}{1} \Big\}$
	$\Big\{ \overset{1}{-1} \Big\}$

Question

Velocity vector of a flow field is given as $\vec V = 2xy \hat i - x^2z \hat j$ . the velocity vector at (1,1,1) is

Possible Answers

Selected	Possible Answer
	$4 \hat i - \hat j$
	$4 \hat i - \hat k$
	$\hat i - 4 \hat j$
	$\hat i - 4 \hat k$

Question

The Laplace Transform of a function f (t) = $\cfrac{1}{s^2\ (s + 1)}$ . The f (t) is

Possible Answers

Selected	Possible Answer
	$t - 1 + e^{-t}$
	$t + 1 + e^{-t}$
	$- 1 + e^{-t}$
	$2t + e^{-t}$

Question

A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is

Possible Answers

Selected	Possible Answer
	2/315
	1/630
	1/1260
	1/2520

Question

A band brake having band-width of 80mm, drum diameter of 250mm, coefficient of friction of 0.25 and angle of wrap of 270 degrees is required to exert a friction torque of 1000N-m. The maximum tension (in kN) developed in the band is

Possible Answers

Selected	Possible Answer
	1.88
	3.56
	6.12
	11.56

Question

A bracket (shown in figure) is rigidly mounted on wall using four rivets. Each rivet is 6mm in diameter and has an effective length of 12mm.

Direct shear stress (in MPa) in the most heavily loaded rivet is

Possible Answers

Selected	Possible Answer
	4.4
	8.8
	17.6
	35.2

Question

A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50mm. the value of m (in kg) is

Possible Answers

Selected	Possible Answer
	0.1
	1.0
	0.3
	0.5

Question

For the epicyclic gear arrangement shown in the figure, $\omega_2$ = 100rad / s clockwise (CW) and $\omega_{arm}$ = 80rad / s counter clockwise (CCW). The angular velocity $\omega_s$ (in rad/s) is

Possible Answers

Selected	Possible Answer
	0
	70CW
	140CCW
	140CW

Question

A lightly loaded full journal bearing has a journal of 50mm, bush bore of 50.05mm and bush length of 20mm. if rotational speed of journal is 1200rpm and average viscosity of liquid lubricant is 0.03 Pa s, the power loss (in W) will be

Possible Answers

Selected	Possible Answer
	37
	74
	118
	237

Question

For the configuration shown, the angular velocity of link AB is 10 rad/s counterclockwise. The magnitude of the relative sliding velocity $(in\ ms^{-1})$ of slider B with respect to rigid link CD is

Possible Answers

Selected	Possible Answer
	0
	0.86
	1.25
	2.5

Question

A smooth pipe of diameter 200mm carries water. The pressure in the pipe at section S1 (elevation: 10m) is 50kPa. At Section S2 (elevation: 12m) the pressure is 20kPa and velocity is $2ms^{-1}$ . Density of water is 1000kg $m^{-3}$ and acceleration due to gravity is $9.8ms^{-2}$ . Which of the following is TRUE?

Possible Answers

Selected	Possible Answer
	flow from S1 to S2 and head loss is 0.53m
	flow from S2 to S1 and head loss is 0.53m
	flow from S1 to S2 and head loss is 1.06m
	flow from S2 to S1 and head loss is 1.06m

Question

Match the following

P:Compressible flow	U: Reynolds number
Q: Free surface flow	V: Nusselt number
R: Boundary layer flow	W: Weber number
S: Pipe flow	X: Froude number
T: Heat convection	Y: Mach number
.	Z: Skin friction coefficient

Possible Answers

Selected	Possible Answer
	P-U; Q-X; R-V; S-Z; T-W
	P-W; Q-X; R-Z; S-U; T-V
	P-Y; Q-W; R-Z; S-U; T-X
	P-Y; Q-W; R-Z; S-U; T-V

Question

A mono-atomic ideal gas ( $\gamma$ = 1.67, molecular weight = 40) is compressed adiabatically from 0.1MPa, 300K to 0.2MPa . The universal gas constant is $8.314kJkmol^{-1} k^{-1}$ . The work of compression of the gas $(in\ kJ\ kg^{-1})$ is

Possible Answers

Selected	Possible Answer
	29.7
	19.9
	13.3
	0

Question

Consider the following two processes:
a. A heat source at 1200K loses 2500kJ of heat to sink at 800K
b. A heat source at 800K loses 2000kJ of heat to sink at 500K
Which of the following statements is TRUE?

Possible Answers

Selected	Possible Answer
	Process I is more irreversible than Process II
	Process II is more irreversible than Process I
	Irreversibility associated in both the processes is equal
	Both the processes are reversible

Question

A fin has 5mm diameter and 100mm length. The thermal conductivity of fin material is 400W $m^{-1}K^{-1}$ . One end of the fin is maintained at $130^\circ C$ and its remaining surface is exposed to ambient air at $30^\circ C$ . if the convective heat transfer coefficient is 40W $m^{-2}K^{-1}$ , the heat loss (in W) from the fin is

Possible Answers

Selected	Possible Answer
	0.08
	5.0
	7.0
	7.8

Question

A moist air sample has dry bulb temperature of $30^\circ C$ and specific humidity of 11.5g water vapour per kg dry air. Assume molecular weight of air as 28.93. If the saturation vapour pressure of water at $30^\circ C$ is 4.24kPa and the total pressure is 90kPa, then the relative humidity (in %) of air sample is

Possible Answers

Selected	Possible Answer
	50.5
	38.5
	56.5
	68.5

Question

Two pipes of inner diameter 100mm and outer diameter 110mm each joined by flash butt welding using 30V power supply. At the interface, 1mm of material melts from each pipe which has a resistance of $42.4 \Omega$ . If the unit melt energy is 64.4MJ $m^{-3}$ , then time required for welding in seconds is

Possible Answers

Selected	Possible Answer
	1
	5
	10
	20

Question

For tool A, Taylor’s tool life exponent (n) is 0.45 and constant (K) is 90. Similarly for tool B, n=0.3 and K=60. The cutting speed (in m/min) above which tool A will have a higher tool life than tool B is

Possible Answers

Selected	Possible Answer
	26.7
	42.5
	80.7
	142.9

Question

A taper hole is inspected using a CMM, with a probe of 2mm diameter. At a height, Z=10mm from the bottom, 5 points are touched and a diameter of circle (not compensated for probe size) is obtained as 20mm. similarly, a 40mm diameter is obtained at a height Z=40mm. the smaller diameter (in mm) of hole at Z=0 is

Possible Answers

Selected	Possible Answer
	13.334
	15.334
	15.442
	15.542

Question

Annual demand for window frames is 10000. Each frame costs Rs. 200 and ordering cost is Rs. 300 per order. Inventory holding cost is Rs. 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should

Possible Answers

Selected	Possible Answer
	order 200 frames every time
	accept 2% discount
	accept 4% discount
	order Economic Order Quantity

Question

The project activities, precedence relationships and durations are described in the table. The critical path of the project is

Activity	Precedence	Duration (in days)
P	-	3
Q	-	4
R	P	5
S	Q	5
T	R,S	7
U	R,S	5
V	T	2
W	U	10

Possible Answers

Selected	Possible Answer
	P-R-T-V
	Q-S-T-V
	P-R-U-W
	Q-S-U-W

Question

Directions for next two questions: Common Data Questions
In a steam power plant operating on the Rankine cycle, steam enters the turbine at 4MPa, $350^\circ C$ and exits at a pressure of 15kPa. Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is 90%. The thermodynamic states of water and steam are given in the table.

h is specific enthalpy, s is specific entropy and v the specific volume; subscripts f and g denote saturated liquid state and saturated vapour state.

The net work output $(kJ\ kg^{-1} )$ of the cycle is

Possible Answers

Selected	Possible Answer
	498
	775
	860
	957

Question

Heat supplied $(kJ\ kg^{-1} )$ to the cycle is

Possible Answers

Selected	Possible Answer
	2372
	2576
	2863
	3092

Question

Directions for next two questions: Common Data Questions
Four jobs are to be processed on a machine as per data listed in the table.

If the Earliest Due Date (EDD) rule is used to sequence the jobs, the number of jobs delayed is

Possible Answers

Selected	Possible Answer
	1
	2
	3
	4

Question

Using the Shortest Processing Time (SPT) rule, total tardiness is

Possible Answers

Selected	Possible Answer
	0
	2
	3
	4

Question

Directions for next two questions Statement for Linked Answer Questions:
A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross-section with a width of 30mm and height of 100mm.

The maximum bending moment occurs at

Possible Answers

Selected	Possible Answer
	Location B
	2675mm to the right of A
	2500mm to the right of A
	3225mm to the right of A

Question

The maximum magnitude of bending stress (in MPa) is given by

Possible Answers

Selected	Possible Answer
	60.0
	67.5
	200.0
	225.0

Question

Directions for next two questions Statement for Linked Answer Questions:
In a shear cutting operation, a sheet of 5mm thickness is cut along a length of 200mm. The cutting blade is 400mm long and zero-shear (S=0) is provided on the edge. The ultimate shear strength of the sheet is 100MPa and penetration to thickness ratio is 0.2. Neglect friction.

Assuming force vs displacement curve to be rectangular, the work done (in J) is

Possible Answers

Selected	Possible Answer
	100
	200
	250
	300
	None of the above.

Question

A shear of 20mm (S=20mm) is now provided on the blade. Assuming force vs displacement curve to be trapezoidal, the maximum force (in kN) exerted is

Possible Answers

Selected	Possible Answer
	5
	10
	20
	40
	None of the above.

Question

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Possible Answers

Selected	Possible Answer
	2
	17
	13
	3

Question

Choose the most appropriate word from the options given below to complete the following sentence:
If we manage to ______ our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	uphold
	restrain
	cherish
	conserve

Question

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.
Unemployed: Worker

Possible Answers

Selected	Possible Answer
	fallow: land
	unaware: sleeper
	wit: jester
	renovated: house

Question

Which of the following options is the closest in meaning to the word below:
Circuitous

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

Choose the most appropriate word from the options given below to the complete the following sentence:
His rather casual remarks on politics _____ his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they born (oldest first)?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

Question

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Possible Answers

Selected	Possible Answer
	20 days
	18 days
	16 days
	15 days

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the above passage:

Possible Answers

Selected	Possible Answer
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable
	People in military establishments like to use chemical agents in war.

Question

Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

Question

If 137+276=435 how much is 731+672?

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

GATE Mechanical Engineering Mock Test Papers

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