GATE ME 2022: Mechanical Engineering Session 2
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SESSION - 1
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GATE 2022 (ME Set-1) Mechanical Engineering
GATE 2022 General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark each.
Q.1 After playing _________ hours of tennis, I am feeling _________ tired to walk
back.
(A) too / too
(B) too / two
(C) two / two
(D) two / too
Q.2 The average of the monthly salaries of M, N and S is ₹ 4000. The average of the
monthly salaries of N, S and P is ₹ 5000. The monthly salary of P is ₹ 6000.
What is the monthly salary of M as a percentage of the monthly salary of P?
(A) 50%
(B) 75%
(C) 100%
(D) 125%
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.3 A person travelled 80 km in 6 hours. If the person travelled the first part with a
uniform speed of 10 kmph and the remaining part with a uniform speed of 18
kmph.
What percentage of the total distance is travelled at a uniform speed
of 10 kmph?
(A) 28.25
(B) 37.25
(C) 43.75
(D) 50.00
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.4 Four girls P, Q, R and S are studying languages in a University. P is learning
French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish
and French. S is learning Dutch and Japanese.
Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch
is easier than Japanese, and Spanish is easier than French.
Based on the above information, which girl is learning the most difficult pair of
languages?
(A) P
(B) Q
(C) R
(D) S
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.5
A block with a trapezoidal cross-section is placed over a block with rectangular
cross section as shown above.
Which one of the following is the correct drawing of the view of the 3D object
as viewed in the direction indicated by an arrow in the above figure?
(A)
(B)
(C)
(D)
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GATE 2022 (ME Set-1) Mechanical Engineering
Q. 6 – Q. 10 Carry TWO marks each.
Q.6 Humans are naturally compassionate and honest. In a study using strategically
placed wallets that appear “lost”, it was found that wallets with money are more
likely to be returned than wallets without money. Similarly, wallets that had a key
and money are more likely to be returned than wallets with the same amount of
money alone. This suggests that the primary reason for this behavior is
compassion and empathy.
Which one of the following is the CORRECT logical inference based on the
information in the above passage?
(A) Wallets with a key are more likely to be returned because people do not care
about money
(B) Wallets with a key are more likely to be returned because people relate to
suffering of others
(C) Wallets used in experiments are more likely to be returned than wallets that are
really lost
(D) Money is always more important than keys
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GATE 2022 (ME Set-1) Mechanical Engineering
A rhombus is formed by joining the midpoints of the sides of a unit square.
Q.7
What is the diameter of the largest circle that can be inscribed within the
rhombus?
(A) 1
√2
(B) 1
2√2
(C) √2
(D) 2√2
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.8 An equilateral triangle, a square and a circle have equal areas.
What is the ratio of the perimeters of the equilateral triangle to square to circle?
(A) 3√3 ∶ 2 ∶ √π
(B)
3 √3 : 2 ∶ √π
(C)
3 √3 : 4 ∶ 2√π
(D)
3 √3 : 2 ∶ 2√π
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.9 Given below are three conclusions drawn based on the following three
statements.
Statement 1: All teachers are professors.
Statement 2: No professor is a male.
Statement 3: Some males are engineers.
Conclusion I: No engineer is a professor.
Conclusion II: Some engineers are professors.
Conclusion III: No male is a teacher.
Which one of the following options can be logically inferred?
(A) Only conclusion III is correct
(B) Only conclusion I and conclusion II are correct
(C) Only conclusion II and conclusion III are correct
(D) Only conclusion I and conclusion III are correct
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Q.10 In a 12-hour clock that runs correctly, how many times do the second, minute,
and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day
to 3 AM the next day?
(A) 11
(B) 12
(C) 144
(D) 2
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.11 - 35 Carry ONE mark each.
Q.11 The limit
x + αx + 2π
p = lim
→ x − π + 2 sin x
has a finite value for a real α. The value of α and the corresponding limit p are
(A) α = −3π, and p = π
(B) α = −2π, and p = 2π
(C) α = π, and p = π
(D) α = 2π, and p = 3π
Q.12 Solution of ∇ T = 0 in a square domain (0 < x < 1 and 0 < y < 1) with
boundary conditions:
T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1, y) = 1 + y
is
(A) T(x, y) = x − xy + y
(B) T(x, y) = x + y
(C) T(x, y) = −x + y
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GATE 2022 (ME Set-1) Mechanical Engineering
(D) T(x, y) = x + xy + y
Q.13 Given a function φ = (x + y + z ) in three-dimensional Cartesian space, the
value of the surface integral
n ∙ ∇φ dS ,
where S is the surface of a sphere of unit radius and n is the outward unit normal
vector on S, is
(A) 4π
(B) 3π
(C) 4π/3
(D) 0
Q.14 The Fourier series expansion of x in the interval −1 ≤ x < 1 with periodic
continuation has
(A) only sine terms
(B) only cosine terms
(C) both sine and cosine terms
(D) only sine terms and a non-zero constant
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.15 If A =
10 2k + 5
is a symmetric matrix, the value of k is ___________.
3k − 3 k + 5
(A) 8
(B) 5
(C) −0.4
1 + √1561
(D)
12
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.16 A uniform light slender beam AB of section modulus EI is pinned by a frictionless
joint A to the ground and supported by a light inextensible cable CB to hang a
weight W as shown. If the maximum value of W to avoid buckling of the beam AB
is obtained as βπ EI, where π is the ratio of circumference to diameter of a circle,
then the value of β is
C
g
A 30° B
2.5 m
W
(A) 0.0924 m-2
(B) 0.0713 m-2
(C) 0.1261 m-2
(D) 0.1417 m-2
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.17 The figure shows a schematic of a simple Watt governor mechanism with the
spindle O1O2 rotating at an angular velocity ω about a vertical axis. The balls at P
and S have equal mass. Assume that there is no friction anywhere and all other
components are massless and rigid. The vertical distance between the horizontal
plane of rotation of the balls and the pivot O1 is denoted by h. The value of
h = 400 mm at a certain ω. If ω is doubled, the value of h will be _________ mm.
(A) 50
(B) 100
(C) 150
(D) 200
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.18 A square threaded screw is used to lift a load W by applying a force F. Efficiency
of square threaded screw is expressed as
(A) The ratio of work done by W per revolution to work done by F per revolution
(B) W/F
(C) F/W
(D) The ratio of work done by F per revolution to work done by W per revolution
Q.19 A CNC worktable is driven in a linear direction by a lead screw connected
directly to a stepper motor. The pitch of the lead screw is 5 mm. The stepper
motor completes one full revolution upon receiving 600 pulses. If the worktable
speed is 5 m/minute and there is no missed pulse, then the pulse rate being
received by the stepper motor is
(A) 20 kHz
(B) 10 kHz
(C) 3 kHz
(D) 15 kHz
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.20 .
The type of fit between a mating shaft of diameter 25.0 . mm and a hole of
.
diameter 25.015 . mm is __________.
(A) Clearance
(B) Transition
(C) Interference
(D) Linear
Q.21 In a linear programming problem, if a resource is not fully utilized, the shadow
price of that resource is
(A) positive
(B) negative
(C) zero
(D) infinity
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GATE 2022 (ME Set-1) Mechanical Engineering Q.22 Which one of the following is NOT a form of inventory? (A) Raw materials (B) Work-in-process materials (C) Finished goods (D) CNC Milling Machines Q.23 The Clausius inequality holds good for (A) any process (B) any cycle (C) only reversible process (D) only reversible cycle ME-1 Page 18 of 46
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Q.24 A tiny temperature probe is fully immersed in a flowing fluid and is moving with
zero relative velocity with respect to the fluid. The velocity field in the fluid is
V⃗ = (2x) ̂ + (y + 3t) ̂, and the temperature field in the fluid is
T = 2x + xy + 4t, where x and y are the spatial coordinates, and t is the time. The
time rate of change of temperature recorded by the probe at
(x = 1, y = 1, t = 1) is _______.
(A) 4
(B) 0
(C) 18
(D) 14
Q.25 In the following two-dimensional momentum equation for natural convection over
a surface immersed in a quiescent fluid at temperature T (g is the gravitational
acceleration, β is the volumetric thermal expansion coefficient, ν is the kinematic
viscosity, u and v are the velocities in x and y directions, respectively, and T is the
temperature)
u +v = gβ(T − T ) + ν ,
the term gβ(T − T ) represents
(A) Ratio of inertial force to viscous force.
(B) Ratio of buoyancy force to viscous force.
(C) Viscous force per unit mass.
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(D) Buoyancy force per unit mass.
Q.26 Assuming the material considered in each statement is homogeneous, isotropic, linear
elastic, and the deformations are in the elastic range, which one or more of the
following statement(s) is/are TRUE?
(A) A body subjected to hydrostatic pressure has no shear stress.
(B) If a long solid steel rod is subjected to tensile load, then its volume increases.
(C) Maximum shear stress theory is suitable for failure analysis of brittle materials.
(D) If a portion of a beam has zero shear force, then the corresponding portion of the
elastic curve of the beam is always straight.
Q.27 Which of the following heat treatment processes is/are used for surface hardening
of steels?
(A) Carburizing
(B) Cyaniding
(C) Annealing
(D) Carbonitriding
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Q.28 Which of the following additive manufacturing technique(s) can use a wire as a
feedstock material?
(A) Stereolithography
(B) Fused deposition modeling
(C) Selective laser sintering
(D) Directed energy deposition processes
Q.29 Which of the following methods can improve the fatigue strength of a circular mild
steel (MS) shaft?
(A) Enhancing surface finish
(B) Shot peening of the shaft
(C) Increasing relative humidity
(D) Reducing relative humidity
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Q.30 The figure shows a purely convergent nozzle with a steady, inviscid compressible
flow of an ideal gas with constant thermophysical properties operating under
choked condition. The exit plane shown in the figure is located within the nozzle.
If the inlet pressure (P0) is increased while keeping the back pressure (Pback)
unchanged, which of the following statements is/are true?
(A) Mass flow rate through the nozzle will remain unchanged.
(B) Mach number at the exit plane of the nozzle will remain unchanged at unity.
(C) Mass flow rate through the nozzle will increase.
(D) Mach number at the exit plane of the nozzle will become more than unity.
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Q.31 The plane of the figure represents a horizontal plane. A thin rigid rod at rest is
pivoted without friction about a fixed vertical axis passing through O. Its mass
moment of inertia is equal to 0.1 kg∙cm2 about O. A point mass of 0.001 kg hits it
normally at 200 cm/s at the location shown, and sticks to it. Immediately after the
impact, the angular velocity of the rod is ___________ rad/s (in integer).
O
10 cm
200 cm/s
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Q.32 A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational
field as shown, such that it can execute small amplitude simple harmonic motion in
the plane of the figure without slip at the pivot point. The inner radius r and outer
radius R are such that r = R /2, and the acceleration due to gravity is g. If the
time period of small amplitude simple harmonic motion is given by T = βπ R/g,
where π is the ratio of circumference to diameter of a circle, then β = ________
(round off to 2 decimal places).
A
g
r G
R
Q.33 Electrochemical machining operations are performed with tungsten as the tool, and
copper and aluminum as two different workpiece materials. Properties of copper
and aluminum are given in the table below.
Material Atomic mass Valency Density (g/cm3)
(amu)
Copper 63 2 9
Aluminum 27 3 2.7
Ignore overpotentials, and assume that current efficiency is 100% for both the
workpiece materials. Under identical conditions, if the material removal rate (MRR)
of copper is 100 mg/s, the MRR of aluminum will be ________________ mg/s
(round-off to two decimal places).
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GATE 2022 (ME Set-1) Mechanical Engineering
Q.34 A polytropic process is carried out from an initial pressure of 110 kPa and volume
of 5 m3 to a final volume of 2.5 m3. The polytropic index is given by n = 1.2. The
absolute value of the work done during the process is _______ kJ (round off to 2
decimal places).
Q.35 A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient
temperature of 25 C. Assume that the entire solar flux is absorbed by the plate.
Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann
constant = 5.669 10-8 W/m2-K4. Neglect all other modes of heat transfer except
radiation.
Under the aforementioned conditions, the radiation equilibrium temperature of the
plate is __________ C (round off to the nearest integer).
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Q.36 – Q.65 Carry TWO marks Each
Q.36 The value of the integral
6z
dz
2z − 3z + 7z − 3z + 5
evaluated over a counter-clockwise circular contour in the complex plane enclosing
only the pole z = i, where i is the imaginary unit, is
(A) (−1 + i) π
(B) (1 + i) π
(C) 2(1 − i)π
(D) (2 + i)π
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Q.37 An L-shaped elastic member ABC with slender arms AB and BC of uniform cross-
section is clamped at end A and connected to a pin at end C. The pin remains in
continuous contact with and is constrained to move in a smooth horizontal slot. The
section modulus of the member is same in both the arms. The end C is subjected to
a horizontal force P and all the deflections are in the plane of the figure. Given the
length AB is 4a and length BC is a, the magnitude and direction of the normal force
on the pin from the slot, respectively, are
A
4a B
a P
C
(A) 3P/8, and downwards
(B) 5P/8, and upwards
(C) P/4, and downwards
(D) 3P/4, and upwards
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Q.38 A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1
prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ CE. The
T-shaped link CDEF is constructed such that the slider B can cross the point D, and
CE is sufficiently long. For the given lengths as shown, the mechanism is
E
G 3 cm
F D
1.5 cm
5 cm
B
A 3 cm
C
a Grashof chain with links AG, AB, and CDEF completely rotatable about the
(A)
ground link FG
(B) a non-Grashof chain with all oscillating links
a Grashof chain with AB completely rotatable about the ground link FG, and
(C)
oscillatory links AG and CDEF
(D) on the border of Grashof and non-Grashof chains with uncertain configuration(s)
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Q.39 Consider a forced single degree-of-freedom system governed by
ẍ (t) + 2ζω ẋ (t) + ω x(t) = ω cos(ωt), where ζ and ω are the
damping ratio and undamped natural frequency of the system, respectively, while
ω is the forcing frequency. The amplitude of the forced steady state response of this
system is given by [(1 − r ) + (2ζr) ] / , where r = ω/ω . The peak
amplitude of this response occurs at a frequency ω = ω . If ω denotes the
damped natural frequency of this system, which one of the following options is
true?
(A) ω <ω <ω
(B) ω =ω <ω
(C) ω <ω =ω
(D) ω <ω <ω
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Q.40 A bracket is attached to a vertical column by means of two identical rivets U and V
separated by a distance of 2a = 100 mm, as shown in the figure. The permissible
shear stress of the rivet material is 50 MPa. If a load P = 10 kN is applied at an
eccentricity e = 3√7 a, the minimum cross-sectional area of each of the rivets to
avoid failure is ___________ mm2.
(A) 800
(B) 25
(C) 100√7
(D) 200
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Q.41 In Fe-Fe3C phase diagram, the eutectoid composition is 0.8 weight % of carbon at
725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of
carbon. A steel sample, having no other alloying element except 0.5 weight % of
carbon, is slowly cooled from 1000 ºC to room temperature. The fraction of
pro-eutectoid α-ferrite in the above steel sample at room temperature is
(A) 0.387
(B) 0.864
(C) 0.475
(D) 0.775
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Q.42 Activities A to K are required to complete a project. The time estimates and the
immediate predecessors of these activities are given in the table. If the project is to
be completed in the minimum possible time, the latest finish time for the activity G
is ____________ hours.
Activity Time (hours) Immediate predecessors
A 2 ─
B 3 ─
C 2 ─
D 4 A
E 5 B
F 4 B
G 3 C
H 10 D, E
I 5 F
J 8 G
K 3 H, I, J
(A) 5
(B) 10
(C) 8
(D) 9
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Q.43 A solid spherical bead of lead (uniform density = 11000 kg/m3) of diameter
d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid
(dynamic viscosity = 1.1 × 10 kg∙m∙s). The coefficient of drag is given by
c = , where the Reynolds number (Re) is defined on the basis of the diameter
of the bead. The drag force acting on the bead is expressed as
D = (c )(0.5ρV ) , where ρ is the density of the liquid. Neglect the
buoyancy force. Using g = 10 m/s2, the velocity V is __________ m/s.
(A) 1
24
(B) 1
6
(C) 1
18
(D) 1
12
Q.44 Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter
1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s,
respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the
pressure drop between these two locations is 10 kPa, the force exerted by the gas
on the pipe between these two locations is ____________ N.
(A) 350π
(B) 750π
(C) 1000π
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GATE 2022 (ME Set-1) Mechanical Engineering
(D) 3000
Q.45 Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated
and the other end (x = L) is exposed to flow of air at temperature T∞ with
convective heat transfer coefficient h. The cylindrical surface of the rod is insulated
so that the heat transfer is strictly along the axis of the rod. The rate of internal heat
generation per unit volume inside the rod is given as
2πx
q̇ = cos .
L
The steady state temperature at the mid-location of the rod is given as TA. What
will be the temperature at the same location, if the convective heat transfer
coefficient increases to 2h?
q̇ L
(A) T +
2ℎ
(B) 2T
(C) T
(D) q̇ L q̇ L
T 1− + T
4πℎ 4πℎ
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Q.46 The system of linear equations in real (x, y) given by
2 5 − 2α
(x y) = (0 0 )
α 1
involves a real parameter α and has infinitely many non-trivial solutions for special
value(s) of α. Which one or more among the following options is/are non-trivial
solution(s) of (x, y) for such special value(s) of α?
(A) x = 2, y = −2
(B) x = −1, y=4
(C) x = 1, y=1
(D) x = 4, y = −2
Q.47 Let a random variable X follow Poisson distribution such that
Prob(X = 1) = Prob(X = 2).
The value of Prob(X = 3) is __________ (round off to 2 decimal places).
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Q.48 Consider two vectors:
a⃗ = 5 i + 7 j + 2 k
b⃗ = 3 i − j + 6 k
Magnitude of the component of a⃗ orthogonal to b⃗ in the plane containing the vectors
a⃗ and b⃗ is __________ (round off to 2 decimal places).
Q.49 A structure, along with the loads applied on it, is shown in the figure. Self-weight
of all the members is negligible and all the pin joints are friction-less. AE is a single
member that contains pin C. Likewise, BE is a single member that contains pin D.
Members GI and FH are overlapping rigid members. The magnitude of the force
carried by member CI is ________ kN (in integer).
A
3.5 m 3m
C I H
2 kN
3m
G
B D E F
2m 2m 3m 3m
4 kN
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Q.50 Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are
resting on ground at P and Q, respectively, as shown in the figure. A vertical force
F acts on the pin R as shown. When the included angle θ < 90°, the rods remain in
static equilibrium due to Coulomb friction between the rods and ground at locations
P and Q. At θ = 90°, impending slip occurs simultaneously at points P and Q. Then
the ratio of the coefficient of friction at Q to that at P (µQ /µP) is _________ (round
off to two decimal places).
F
R
5m θ 12 m
P Q
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Q.51 A cylindrical disc of mass m = 1 kg and radius r = 0.15 m was spinning at
ω = 5 rad/s when it was placed on a flat horizontal surface and released (refer to
the figure). Gravity g acts vertically downwards as shown in the figure. The
coefficient of friction between the disc and the surface is finite and positive.
Disregarding any other dissipation except that due to friction between the disc and
the surface, the horizontal velocity of the center of the disc, when it starts rolling
without slipping, will be _________ m/s (round off to 2 decimal places).
r
m ω
g
Q.52 A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal
radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected
to some internal pressure, its nominal perimeter in the cylindrical portion increased
by 0.1% and the corresponding wall thickness became t̅. The corresponding change
in the wall thickness of the cylindrical portion, i.e. 100 × (t̅ − t)/t, is ________%
(round off to 3 decimal places).
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Q.53 A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and
planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and
arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot
joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3
has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter
clockwise (ccw), the magnitude of angular velocity of arm OP is __________rpm
(in integer).
Q.54 Under orthogonal cutting condition, a turning operation is carried out on a
metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the
cutting tool is 5º. The uncut chip thickness and width of cut are 0.2 mm and 3 mm,
respectively. In this turning operation, the resulting friction angle and shear angle
are 45º and 25º, respectively. If the dynamic yield shear strength of the workpiece
material under this cutting condition is 1000 MPa, then the cutting force is
______________ N (round off to one decimal place).
Q.55 A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such
that the entire wall thickness of the tube is cut in a single pass. The axial feed of the
tool is 1 m/minute and the specific cutting energy (u) of the tube material is
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6 J⁄mm . Neglect contribution of feed force towards power. The power required to
carry out this operation is _________ kW (round off to one decimal place).
Q.56 A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of
roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which
gives a coefficient of friction, µ = 0.1. The flow stress (σ ) of the material in MPa
is σ = 207 + 414 ε, where ε is the true strain. Assuming rolling to be a plane strain
deformation process, the roll separation force (F) for maximum permissible draft
(thickness reduction) is _________ kN (round off to the nearest integer).
Use:
µ
F = 1.15 σ 1 + wL, where σ is average flow stress, L is roll-workpiece
contact length, and ℎ is the average sheet thickness.
Q.57 Two mild steel plates of similar thickness, in butt-joint configuration, are welded
by gas tungsten arc welding process using the following welding parameters.
Welding voltage 20 V
Welding current 150 A
Welding speed 5 mm/s
A filler wire of the same mild steel material having 3 mm diameter is used in this
welding process. The filler wire feed rate is selected such that the final weld bead
is composed of 60% volume of filler and 40% volume of plate material. The heat
required to melt the mild steel material is 10 J/mm3. The heat transfer factor is 0.7
and melting factor is 0.6. The feed rate of the filler wire is __________ mm/s (round
off to one decimal place).
Q.58 An assignment problem is solved to minimize the total processing time of four jobs
(1, 2, 3 and 4) on four different machines such that each job is processed exactly by
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GATE 2022 (ME Set-1) Mechanical Engineering
one machine and each machine processes exactly one job. The minimum total
processing time is found to be 500 minutes. Due to a change in design, the
processing time of Job 4 on each machine has increased by 20 minutes. The revised
minimum total processing time will be _____________ minutes (in integer).
Q.59 The product structure diagram shows the number of different components required
at each level to produce one unit of the final product P. If there are 50 units of on-
hand inventory of component A, the number of additional units of component A
needed to produce 10 units of product P is _________ (in integer).
Q.60 Consider a one-dimensional steady heat conduction process through a solid slab of
thickness 0.1 m. The higher temperature side A has a surface temperature of 80 C,
and the heat transfer rate per unit area to low temperature side B is 4.5 kW/m2. The
thermal conductivity of the slab is 15 W/m.K. The rate of entropy generation per
unit area during the heat transfer process is ________ W/m2.K (round off to 2
decimal places).
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Q.61 In a steam power plant based on Rankine cycle, steam is initially expanded in a
high-pressure turbine. The steam is then reheated in a reheater and finally expanded
in a low-pressure turbine. The expansion work in the high-pressure turbine is
400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work
is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser
is ________ kJ/kg (round off to 2 decimal places).
Q.62 An engine running on an air standard Otto cycle has a displacement volume
250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the
beginning of the compression process are 100 kPa and 300 K, respectively. Heat
transfer during constant-volume heat addition process is 800 kJ/kg. The specific
heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant
pressure and constant volume is 1.4. Assume the specific heats to remain constant
during the cycle. The maximum pressure in the cycle is ______ kPa (round off to
the nearest integer).
Q.63 A steady two-dimensional flow field is specified by the stream function
ψ = kx y,
where x and y are in meter and the constant k = 1 ms. The magnitude of
acceleration at a point (x, y) = (1 m, 1 m) is ________ m/s2 (round off to 2 decimal
places).
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Q.64 Consider a solid slab (thermal conductivity, k = 10 W∙m∙K) with thickness
0.2 m and of infinite extent in the other two directions as shown in the figure.
Surface 2, at 300 K, is exposed to a fluid flow at a free stream temperature (T∞) of
293 K, with a convective heat transfer coefficient (h) of 100 W∙m∙K. Surface 2
is opaque, diffuse and gray with an emissivity () of 0.5 and exchanges heat by
radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid
slab is neglected. The Stefan-Boltzmann constant is 5.67×108 W∙m∙K. The
temperature T1 of Surface 1 of the slab, under steady-state conditions,
is _________ K (round off to the nearest integer).
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Q.65 During open-heart surgery, a patient’s blood is cooled down to 25 C from 37 C
using a concentric tube counter-flow heat exchanger. Water enters the heat
exchanger at 4 C and leaves at 18 C. Blood flow rate during the surgery is
5 L/minute.
Use the following fluid properties:
Fluid Density (kg/m3) Specific heat (J/kg-K)
Blood 1050 3740
Water 1000 4200
Effectiveness of the heat exchanger is _________ (round off to 2 decimal places).
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Q. No. Session Question Subject Key/Range Mark
Type Name
1 7 MCQ GA D 1
2 7 MCQ GA A 1
3 7 MCQ GA C 1
4 7 MCQ GA B 1
5 7 MCQ GA A 1
6 7 MCQ GA B 2
7 7 MCQ GA A 2
8 7 MCQ GA B 2
9 7 MCQ GA A 2
10 7 MCQ GA MTA 2
11 7 MCQ ME A 1
12 7 MCQ ME B 1
13 7 MCQ ME A 1
14 7 MCQ ME A 1
15 7 MCQ ME A 1
16 7 MCQ ME A 1
17 7 MCQ ME B 1
18 7 MCQ ME A 1
19 7 MCQ ME B 1
20 7 MCQ ME B 1
21 7 MCQ ME C 1
22 7 MCQ ME D 1
23 7 MCQ ME B 1
24 7 MCQ ME C 1
25 7 MCQ ME D 1
26 7 MSQ ME A,B 1
27 7 MSQ ME A,B,D 1
28 7 MSQ ME B,D 1
29 7 MSQ ME A,B,D OR A, B 1
30 7 MSQ ME B,C 1
31 7 NAT ME 10 to 10 1
32 7 NAT ME 2.62 to 2.70 1
33 7 NAT ME 27.00 to 30.00 1
34 7 NAT ME 404.00 to 414.00 1
35 7 NAT ME 210 to 225 1
36 7 MCQ ME A 2
37 7 MCQ ME A 2
38 7 MCQ ME A 2
39 7 MCQ ME A 2
40 7 MCQ ME A 2
41 7 MCQ ME A 2
42 7 MCQ ME B 2
43 7 MCQ ME C 2
44 7 MCQ ME B 2
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45 7 MCQ ME C 2 46 7 MSQ ME A,B 2 47 7 NAT ME 0.17 to 0.19 2 48 7 NAT ME 7.90 to 8.70 2 49 7 NAT ME 18 to 18 2 50 7 NAT ME 5.70 to 5.80 2 51 7 NAT ME 0.24 to 0.26 2 52 7 NAT ME -0.062 to -0.058 2 53 7 NAT ME 600 to 600 2 54 7 NAT ME 2570.0 to 2576.0 2 55 7 NAT ME 30.0 to 32.0 2 56 7 NAT ME 340 to 360 2 57 7 NAT ME 10.5 to 10.9 2 58 7 NAT ME 520 to 520 2 59 7 NAT ME 110 to 110 2 60 7 NAT ME 1.12 to 1.24 2 61 7 NAT ME 2620.00 to 2630.00 2 62 7 NAT ME 4780 to 4825 2 63 7 NAT ME 4.20 to 4.28 2 64 7 NAT ME 315 to 323 2 65 7 NAT ME 0.40 to 0.44 2
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SESSION - 2
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GATE 2022 (ME Set-2) Mechanical Engineering
GATE 2022 General Aptitude
Q.1 – Q.5 Carry ONE mark each.
Q.1 Writing too many things on the ________ while teaching could make the
students get _________.
(A) bored / board
(B) board / bored
(C) board / board
(D) bored / bored
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Q.2 Which one of the following is a representation (not to scale and in bold) of all
values of x satisfying the inequality 2 − 5x ≤ − on the real number
line?
(A)
(B)
(C)
(D)
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Q.3 If f(x) = 2 ln √e , what is the area bounded by f(x) for the interval [0, 2]
on the x-axis?
(A) 1
2
(B) 1
(C) 2
(D) 4
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Q.4 A person was born on the fifth Monday of February in a particular year.
Which one of the following statements is correct based on the above
information?
(A) The 2nd February of that year is a Tuesday
(B) There will be five Sundays in the month of February in that year
(C) The 1st February of that year is a Sunday
(D) All Mondays of February in that year have even dates
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Q.5
Which one of the groups given below can be assembled to get the shape that is
shown above using each piece only once without overlapping with each other?
(rotation and translation operations may be used).
(A)
(B)
(C)
(D)
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Q. 6 – Q. 10 Carry TWO marks each.
Q.6 Fish belonging to species S in the deep sea have skins that are extremely black
(ultra-black skin). This helps them not only to avoid predators but also sneakily
attack their prey. However, having this extra layer of black pigment results in
lower collagen on their skin, making their skin more fragile.
Which one of the following is the CORRECT logical inference based on the
information in the above passage?
(A) Having ultra-black skin is only advantageous to species S
(B) Species S with lower collagen in their skin are at an advantage because it helps
them avoid predators
(C) Having ultra-black skin has both advantages and disadvantages to species S
(D) Having ultra-black skin is only disadvantageous to species S but advantageous
only to their predators
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Q.7 For the past m days, the average daily production at a company was 100 units
per day.
If today’s production of 180 units changes the average to 110 units per day,
what is the value of m?
(A) 18
(B) 10
(C) 7
(D) 5
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Q.8 Consider the following functions for non-zero positive integers, p and q.
f(p, q) = p × p × p × … … … × p = p ; f(p, 1) = p
terms
⫶( )
⫶⫶
g(p, q ) = p ; g(p, 1) = p
Which one of the following options is correct based on the above?
(A) f(2,2) = g(2,2)
(B) f(g(2,2), 2) < f 2, g(2,2)
(C) g(2,1) ≠ f(2,1)
(D) f(3,2) > g(3,2)
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Q.9 Four cities P, Q, R and S are connected through one-way routes as shown in the
figure. The travel time between any two connected cities is one hour. The boxes
beside each city name describe the starting time of first train of the day and their
frequency of operation. For example, from city P, the first trains of the day start
at 8 AM with a frequency of 90 minutes to each of R and S. A person does not
spend additional time at any city other than the waiting time for the next
connecting train.
If the person starts from R at 7 AM and is required to visit S and return to R,
what is the minimum time required?
(A) 6 hours 30 minutes
(B) 3 hours 45 minutes
(C) 4 hours 30 minutes
(D) 5 hours 15 minutes
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Q.10 Equal sized circular regions are shaded in a square sheet of paper of 1 cm side
length. Two cases, case M and case N, are considered as shown in the figures
below. In the case M, four circles are shaded in the square sheet and in the case
N, nine circles are shaded in the square sheet as shown.
What is the ratio of the areas of unshaded regions of case M to that of case N?
case M case N
(A) 2 : 3
(B) 1 : 1
(C) 3 : 2
(D) 2 : 1
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Q.11 - 35 Carry ONE mark each.
Q.11 F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0,
and stays at each of these values for 1 second before changing. What is the constant
term in the Fourier series expansion of F(t)?
F(t)
4
−3 −2 −1 0 1 2 3 4
t (seconds)
(A) 1
(B) 2
(C) 3
(D) 4
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Q.12 Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its
centroid at the point (1, 2, 3). The surface integral ∫ F⃗ ⋅ dA⃗ of a vector field
F⃗ = 3x ̂ + 5y ̂ + 6zk over the entire surface A of the cube is ______.
(A) 14
(B) 27
(C) 28
(D) 31
Q.13 Consider the definite integral
(4x + 2x + 6)dx.
Let I be the exact value of the integral. If the same integral is estimated using
Simpson’s rule with 10 equal subintervals, the value is I . The percentage error is
defined as e = 100 × (I − I )/I . The value of e is
(A) 2.5
(B) 3.5
(C) 1.2
(D) 0
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Q.14 Given ∫ e dx = √π .
( )
If a and b are positive integers, the value of ∫ e dx is ________.
(A) √πa
(B) π
a
(C) b√πa
(D) π
b
a
Q.15 A polynomial φ(s) = a s + a s + ⋯ + a s + a of degree n > 3 with
constant real coefficients a , a , …a has triple roots at s = −σ. Which one of
the following conditions must be satisfied?
(A) φ(s) = 0 at all the three values of s satisfying s + σ = 0
(B) φ(s) = 0,
( )
= 0, and
( )
= 0 at s = −σ
(C) φ(s) = 0,
( )
= 0, and
( )
= 0 at s = −σ
(D) φ(s) = 0, and
( )
= 0 at s = −σ
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Q.16 Which one of the following is the definition of ultimate tensile strength (UTS)
obtained from a stress-strain test on a metal specimen?
(A) Stress value where the stress-strain curve transitions from elastic to plastic behavior
(B) The maximum load attained divided by the original cross-sectional area
(C) The maximum load attained divided by the corresponding instantaneous cross-
sectional area
(D) Stress where the specimen fractures
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Q.17 A massive uniform rigid circular disc is mounted on a frictionless bearing at the end
E of a massive uniform rigid shaft AE which is suspended horizontally in a uniform
gravitational field by two identical light inextensible strings AB and CD as shown,
where G is the center of mass of the shaft-disc assembly and g is the acceleration
due to gravity. The disc is then given a rapid spin ω about its axis in the positive x-
axis direction as shown, while the shaft remains at rest. The direction of rotation is
defined by using the right-hand thumb rule. If the string AB is suddenly cut,
assuming negligible energy dissipation, the shaft AE will
B D
g
L L
z
y A G C
x E
ω
(A) rotate slowly (compared to ω) about the negative z-axis direction
(B) rotate slowly (compared to ω) about the positive z-axis direction
(C) rotate slowly (compared to ω) about the positive y-axis direction
(D) rotate slowly (compared to ω) about the negative y-axis direction
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Q.18 A structural member under loading has a uniform state of plane stress which in usual
notations is given by σ = 3P, σ = −2P and τ = √2 P, where P > 0. The yield
strength of the material is 350 MPa. If the member is designed using the maximum
distortion energy theory, then the value of P at which yielding starts (according to
the maximum distortion energy theory) is
(A) 70 MPa
(B) 90 MPa
(C) 120 MPa
(D) 75 MPa
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Q.19 Fluidity of a molten alloy during sand casting depends on its solidification range.
The phase diagram of a hypothetical binary alloy of components A and B is shown
in the figure with its eutectic composition and temperature. All the lines in this phase
diagram, including the solidus and liquidus lines, are straight lines. If this binary
alloy with 15 weight % of B is poured into a mould at a pouring temperature of
800 ºC, then the solidification range is
(A) 400 ºC
(B) 250 ºC
(C) 800 ºC
(D) 150 ºC
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Q.20 A shaft of diameter 25 .. mm is assembled in a hole of diameter 25 .. mm.
Match the allowance and limit parameter in Column I with its corresponding
quantitative value in Column II for this shaft-hole assembly.
Allowance and limit parameter (Column I) Quantitative value (Column II)
P Allowance 1 0.09 mm
Q Maximum clearance 2 24.96 mm
R Maximum material limit for hole 3 0.04 mm
4 25.0 mm
(A) P-3, Q-1, R-4
(B) P-1, Q-3, R-2
(C) P-1, Q-3, R-4
(D) P-3, Q-1, R-2
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Q.21 Match the additive manufacturing technique in Column I with its corresponding
input material in Column II.
Additive manufacturing technique Input material (Column II)
(Column I)
P Fused deposition modelling 1 Photo sensitive liquid resin
Q Laminated object manufacturing 2 Heat fusible powder
R Selective laser sintering 3 Filament of polymer
4 Sheet of thermoplastic or
green compacted metal sheet
(A) P-3, Q-4, R-2
(B) P-1, Q-2, R-4
(C) P-2, Q-3, R-1
(D) P-4, Q-1, R-4
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GATE 2022 (ME Set-2) Mechanical Engineering Q.22 Which one of the following CANNOT impart linear motion in a CNC machine? (A) Linear motor (B) Ball screw (C) Lead screw (D) Chain and sprocket Q.23 Which one of the following is an intensive property of a thermodynamic system? (A) Mass (B) Density (C) Energy (D) Volume ME-2 Page 20 of 49
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Q.24 Consider a steady flow through a horizontal divergent channel, as shown in the
figure, with supersonic flow at the inlet. The direction of flow is from left to right.
Pressure at location B is observed to be higher than that at an upstream location A.
Which among the following options can be the reason?
(A) Since volume flow rate is constant, velocity at B is lower than velocity at A
(B) Normal shock
(C) Viscous effect
(D) Boundary layer separation
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Q.25 Which of the following non-dimensional terms is an estimate of Nusselt number?
(A) Ratio of internal thermal resistance of a solid to the boundary layer thermal
resistance
(B) Ratio of the rate at which internal energy is advected to the rate of conduction
heat transfer
(C) Non-dimensional temperature gradient
(D) Non-dimensional velocity gradient multiplied by Prandtl number
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Q.26 A square plate is supported in four different ways (configurations (P) to (S) as shown
in the figure). A couple moment C is applied on the plate. Assume all the members
to be rigid and mass-less, and all joints to be frictionless. All support links of the plate
are identical.
C C C C
(P) (Q) (R) (S)
The square plate can remain in equilibrium in its initial state for which one or more
of the following support configurations?
(A) Configuration (P)
(B) Configuration (Q)
(C) Configuration (R)
(D) Configuration (S)
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Q.27 Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the
top of the casting. Assume solidification time, t ∝ V ⁄A , where V is the volume
and A is the total surface area dissipating heat. If the top of the riser is insulated,
which of the following radius/radii of riser is/are acceptable?
(A) a
3
(B) a
2
(C) a
4
(D) a
6
Q.28 Which of these processes involve(s) melting in metallic workpieces?
(A) Electrochemical machining
(B) Electric discharge machining
(C) Laser beam machining
(D) Electron beam machining
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Q.29 The velocity field in a fluid is given to be V⃗ = (4xy) ̂ + 2(x − y ) ̂.
Which of the following statement(s) is/are correct?
(A) The velocity field is one-dimensional.
(B) The flow is incompressible.
(C) The flow is irrotational.
(D) The acceleration experienced by a fluid particle is zero at (x = 0, y = 0).
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Q.30 A rope with two mass-less platforms at its two ends passes over a fixed pulley as
shown in the figure. Discs with narrow slots and having equal weight of 20 N each
can be placed on the platforms. The number of discs placed on the left side platform
is n and that on the right side platform is m.
It is found that for n = 5 and m = 0, a force F= 200 N (refer to part (i) of the figure)
is just sufficient to initiate upward motion of the left side platform. If the force F is
removed then the minimum value of m (refer to part (ii) of the figure) required to
prevent downward motion of the left side platform is______ (in integer).
Fixed pulley Fixed pulley
(i) (ii)
g
m discs
n discs n discs
F
Mass-less platforms Mass-less platforms
Q.31 For a dynamical system governed by the equation,
ẍ (t) + 2ζω ẋ (t) + ω x(t) = 0,
the damping ratio ζ is equal to log 2. The displacement x of this system is
measured during a hammer test. A displacement peak in the positive displacement
direction is measured to be 4 mm. Neglecting higher powers (>1) of the damping
ratio, the displacement at the next peak in the positive direction will be
___________ mm (in integer).
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Q.32 An electric car manufacturer underestimated the January sales of car by 20 units,
while the actual sales was 120 units. If the manufacturer uses exponential smoothing
method with a smoothing constant of α = 0.2, then the sales forecast for the month
of February of the same year is ___________units (in integer).
Q.33 The demand of a certain part is 1000 parts/year and its cost is ₹1000/part. The orders
are placed based on the economic order quantity (EOQ). The cost of ordering is
₹100/order and the lead time for receiving the orders is 5 days. If the holding cost
is ₹20/part/year, the inventory level for placing the orders is _________ parts
(round off to the nearest integer).
Q.34 Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly
insulated container. The specific heat of the gas at constant volume cv is equal to
750 J∙kg∙K. A stirrer performs 225 kJ of work on the gas. Assume that the
container does not participate in the thermodynamic interaction. The final pressure
of the gas will be ___________ bar (in integer).
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Q.35 Wien’s law is stated as follows: λ T = C, where C is 2898 µm∙K and λ is the
wavelength at which the emissive power of a black body is maximum for a given
temperature T. The spectral hemispherical emissivity (ε ) of a surface is shown in
the figure below (1Å = 10–10m). The temperature at which the total hemispherical
emissivity will be highest is __________ K (round off to the nearest integer).
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Q. 36 - 65 Carry TWO marks each.
Q.36 For the exact differential equation,
,
which one of the following is the solution?
(A) u + 2x = constant
(B) xu + u = constant
(C) 1
x u + 2u = constant
2
(D) 1
ux + 2x = constant
2
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Q.37 A rigid homogeneous uniform block of mass 1 kg, height ℎ = 0.4 m and width
b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field
(g = 9.81 m/s2), supported by a roller in the configuration shown in the figure. A
short duration (impulsive) force F, producing an impulse I , is applied at a height
of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The
minimum value of I required to topple the block is
b g
F
h
d
(A) 0.953 Ns
(B) 1.403 Ns
(C) 0.814 Ns
(D) 1.172 Ns
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Q.38 A linear elastic structure under plane stress condition is subjected to two sets of
loading, I and II. The resulting states of stress at a point corresponding to these two
loadings are as shown in the figure below. If these two sets of loading are applied
simultaneously, then the net normal component of stress σ is ________.
(A) 3σ/2
(B) σ 1 + 1⁄√2
(C) σ/2
(D) σ 1 − 1⁄√2
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Q.39 A rigid body in the X-Y plane consists of two point masses (1 kg each) attached to
the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates
at 30 RPM counter-clockwise about the Z-axis passing through point O. A point
mass of √2 kg, attached to one end of a third massless rod, is used for balancing the
body by attaching the free end of the rod to point O. The length of the third rod
is ________ cm.
(A) 1
(B) √2
(C) 1/√2
(D) 1/2√2
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Q.40 A spring mass damper system (mass m, stiffness k, and damping coefficient c)
excited by a force F(t) = B sin ωt, where B, ω and t are the amplitude, frequency
and time, respectively, is shown in the figure. Four different responses of the system
(marked as (i) to (iv)) are shown just to the right of the system figure. In the figures
of the responses, A is the amplitude of response shown in red color and the dashed
lines indicate its envelope. The responses represent only the qualitative trend and
those are not drawn to any specific scale.
F(t)
(i) (ii)
A A
m t t
(iii) (iv)
A A
c
t t
Four different parameter and forcing conditions are mentioned below.
(P) c > 0 and ω = k/m (Q) c < 0 and ω ≠ 0
(R) c = 0 and ω = k/m (S) c = 0 and ω ≅ k/m
Which one of the following options gives correct match (indicated by arrow →) of
the parameter and forcing conditions to the responses?
(A) (P) → (i), (Q) → (iii), (R) → (iv), (S) → (ii)
(B) (P) → (ii), (Q) → (iii), (R) → (iv), (S) → (i)
(C) (P) → (i), (Q) → (iv), (R) → (ii), (S) → (iii)
(D) (P) → (iii), (Q) → (iv), (R) → (ii), (S) → (i)
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.41 Parts P1-P7 are machined first on a milling machine and then polished at a separate
machine. Using the information in the following table, the minimum total
completion time required for carrying out both the operations for all 7 parts
is __________ hours.
Part Milling (hours) Polishing (hours)
No.
P1 8 6
P2 3 2
P3 3 4
P4 4 6
P5 5 7
P6 6 4
P7 2 1
(A) 31
(B) 33
(C) 30
(D) 32
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.42 A manufacturing unit produces two products P1 and P2. For each piece of P1 and
P2, the table below provides quantities of materials M1, M2, and M3 required, and
also the profit earned. The maximum quantity available per day for M1, M2 and M3
is also provided. The maximum possible profit per day is ₹__________.
M1 M2 M3 Profit per piece
(₹)
P1 2 2 0 150
P2 3 1 2 100
Maximum quantity 70 50 40
available per day
(A) 5000
(B) 4000
(C) 3000
(D) 6000
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.43 A tube of uniform diameter D is immersed in a steady flowing inviscid liquid stream
of velocity V, as shown in the figure. Gravitational acceleration is represented by g.
The volume flow rate through the tube is ______.
(A) π
D V
4
(B) π
D 2gℎ
4
(C) π
D 2g(ℎ + ℎ )
4
(D) π
D V − 2gℎ
4
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.44 The steady velocity field in an inviscid fluid of density 1.5 is given to be
V⃗ = (y − x ) ̂ + (2xy) ̂. Neglecting body forces, the pressure gradient at
(x = 1, y = 1) is __________ .
(A) 10 ̂
(B) 20 ̂
(C) −6 ̂ − 6 ̂
(D) −4 ̂ − 4 ̂
Q.45 In a vapour compression refrigeration cycle, the refrigerant enters the compressor
in saturated vapour state at evaporator pressure, with specific enthalpy equal to
250 kJ/kg. The exit of the compressor is superheated at condenser pressure with
specific enthalpy equal to 300 kJ/kg. At the condenser exit, the refrigerant is
throttled to the evaporator pressure. The coefficient of performance (COP) of the
cycle is 3. If the specific enthalpy of the saturated liquid at evaporator pressure is
50 kJ/kg, then the dryness fraction of the refrigerant at entry to evaporator
is _________.
(A) 0.2
(B) 0.25
(C) 0.3
(D) 0.35
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.46 A is a 3×5 real matrix of rank 2. For the set of homogeneous equations Ax = 0,
where 0 is a zero vector and x is a vector of unknown variables, which of the
following is/are true?
(A) The given set of equations will have a unique solution.
(B) The given set of equations will be satisfied by a zero vector of appropriate size.
(C) The given set of equations will have infinitely many solutions.
(D) The given set of equations will have many but a finite number of solutions.
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.47 The lengths of members BC and CE in the frame shown in the figure are equal. All
the members are rigid and lightweight, and the friction at the joints is negligible.
Two forces of magnitude Q > 0 are applied as shown, each at the mid-length of the
respective member on which it acts.
Q
D F
C E
Q
G H
A B
Which one or more of the following members do not carry any load (force)?
(A) AB
(B) CD
(C) EF
(D) GH
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GATE 2022 (ME Set-2) Mechanical Engineering
3 p
Q.48 If the sum and product of eigenvalues of a 2 × 2 real matrix are 4 and −1
p q
respectively, then |p| is ______ (in integer).
Q.49 Given z = x + iy, i = √−1. C is a circle of radius 2 with the centre at the origin.
If the contour C is traversed anticlockwise, then the value of the integral
∫ ( )( )
dz is _______ (round off to one decimal place).
Q.50 A shaft of length L is made of two materials, one in the inner core and the other in
the outer rim, and the two are perfectly joined together (no slip at the interface) along
the entire length of the shaft. The diameter of the inner core is d and the external
diameter of the rim is d , as shown in the figure. The modulus of rigidity of the core
and rim materials are G and G , respectively. It is given that d = 2d and
G = 3G . When the shaft is twisted by application of a torque along the shaft axis,
the maximum shear stress developed in the outer rim and the inner core turn out to
be τ and τ , respectively. All the deformations are in the elastic range and stress-
strain relations are linear. Then the ratio τ /τ is ______ (round off to 2 decimal
places).
d
d
Shaft cross-section
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.51 A rigid beam AD of length 3a = 6 m is hinged at frictionless pin joint A and
supported by two strings as shown in the figure. String BC passes over two small
frictionless pulleys of negligible radius. All the strings are made of the same material
and have equal cross-sectional area. A force F = 9 kN is applied at C and the
resulting stresses in the strings are within linear elastic limit. The self-weight of the
beam is negligible with respect to the applied load. Assuming small deflections, the
tension developed in the string at C is _________ kN (round off to 2 decimal places).
Q.52 In the configuration of the planar four-bar mechanism at a certain instant as shown
in the figure, the angular velocity of the 2 cm long link is ω = 5 rad/s. Given the
dimensions as shown, the magnitude of the angular velocity ω of the 4 cm long
link is given by _____ rad/s (round off to 2 decimal places).
5 cm 4 cm
ω
2 cm ω
10 cm
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.53 A shaft AC rotating at a constant speed carries a thin pulley of radius r = 0.4 m at
the end C which drives a belt. A motor is coupled at the end A of the shaft such that
it applies a torque M about the shaft axis without causing any bending moment.
The shaft is mounted on narrow frictionless bearings at A and B where
AB = BC = L = 0.5 m. The taut and slack side tensions of the belt are T = 300 N
and T = 100 N, respectively. The allowable shear stress for the shaft material is
80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value
of π available in the on-screen virtual calculator. Neglecting shock and fatigue
loading and assuming maximum shear stress theory, the minimum required shaft
diameter is _______ mm (round off to 2 decimal places).
A B r
M C
x L L
y z T T
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.54 A straight-teeth horizontal slab milling cutter is shown in the figure. It has 4 teeth
and diameter (D) of 200 mm. The rotational speed of the cutter is 100 rpm and the
linear feed given to the workpiece is 1000 mm/minute. The width of the workpiece
(w) is 100 mm, and the entire width is milled in a single pass of the cutter. The
cutting force/tooth is given by F = Kt w, where specific cutting force
K = 10 N/mm , w is the width of cut, and t is the uncut chip thickness.
The depth of cut (d) is D/2, and hence the assumption of ≪ 1 is invalid. The
maximum cutting force required is ________ kN (round off to one decimal place).
Q.55 In an orthogonal machining operation, the cutting and thrust forces are equal in
magnitude. The uncut chip thickness is 0.5 mm and the shear angle is 15°. The
orthogonal rake angle of the tool is 0° and the width of cut is 2 mm. The workpiece
material is perfectly plastic and its yield shear strength is 500 MPa. The cutting
force is _________ N (round off to the nearest integer).
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.56 The best size wire is fitted in a groove of a metric screw such that the wire touches
the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and
included angle of the thread are 4 mm and 60º, respectively. The diameter of the
best size wire is ___________ mm (round off to 2 decimal places).
Q.57 In a direct current arc welding process, the power source has an open circuit voltage
of 100 V and short circuit current of 1000 A. Assume a linear relationship between
voltage and current. The arc voltage (V) varies with the arc length (l) as
V = 10 + 5l, where V is in volts and l is in mm. The maximum available arc power
during the process is _________ kVA (in integer).
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.58 A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct
extrusion process to produce a bar of L-section. The cross sectional dimensions of
this L-section bar are shown in the figure. The total extrusion pressure (p) in MPa
for the above process is related to extrusion ratio (r) as
2l
p=K σ 0.8 + 1.5 ln (r) + ,
d
where σ is the mean flow strength of the billet material in MPa, l is the portion of
the billet length remaining to be extruded in mm, d is the initial diameter of the
billet in mm, and K is the die shape factor.
If the mean flow strength of the billet material is 50 MPa and the die shape factor
is 1.05, then the maximum force required at the start of extrusion is ________ kN
(round off to one decimal place).
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.59 A project consists of five activities (A, B, C, D and E). The duration of each activity
follows beta distribution. The three time estimates (in weeks) of each activity and
immediate predecessor(s) are listed in the table. The expected time of the project
completion is __________ weeks (in integer).
Time estimates (in weeks)
Optimistic Most likely Pessimistic Immediate
Activity time time time predecessor(s)
A 4 5 6 None
B 1 3 5 A
C 1 2 3 A
D 2 4 6 C
E 3 4 5 B, D
Q.60 A rigid tank of volume of 8 m3 is being filled up with air from a pipeline connected
through a valve. Initially the valve is closed and the tank is assumed to be
completely evacuated. The air pressure and temperature inside the pipeline are
maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by
opening the valve and the process ends when the tank pressure is equal to the
pipeline pressure. During the filling process, heat loss to the surrounding
is 1000 kJ. The specific heats of air at constant pressure and at constant volume
are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic
energy and potential energy.
The final temperature of the tank after the completion of the filling process
is _________ K (round off to the nearest integer).
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.61 At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal
to 3500 kJ/kg and specific entropy equal to 6.5 kJ∙kg∙K. It expands reversibly in
the turbine to the condenser pressure. Heat loss occurs reversibly in the turbine at a
temperature of 500 K. If the exit specific enthalpy and specific entropy
are 2500 kJ/kg and 6.3 kJ∙kg∙K, respectively, the work output from the turbine
is ________ MW (in integer).
Q.62 A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and
length = 8 m) is immersed in the water and is hinged without friction at point A on
the waterline as shown in the figure. A solid spherical ball made of lead (specific
gravity = 11.4) is attached to the free end of the rod to keep the assembly in static
equilibrium inside the water. For simplicity, assume that the radius of the ball is
much smaller than the length of the rod.
Assume density of water = 103 kg/m3 and π = 3.14.
Radius of the ball is _______ cm (round off to 2 decimal places).
A
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.63 Consider steady state, one-dimensional heat conduction in an infinite slab of
thickness 2L (L = 1 m) as shown in the figure. The conductivity (k) of the material
varies with temperature as k = CT, where T is the temperature in K, and C is a
constant equal to 2 W∙m∙K. There is a uniform heat generation of 1280 kW/m3
in the slab. If both faces of the slab are maintained at 600 K, then the temperature
at x = 0 is ________ K (in integer).
600 K 600 K
x = −L x=L
x=0
Q.64 Saturated vapor at 200 oC condenses to saturated liquid at the rate of 150 kg/s on
the shell side of a heat exchanger (enthalpy of condensation ℎ = 2400 kJ/kg). A
fluid with c = 4 kJ∙kg∙K enters at 100 oC on the tube side. If the effectiveness
of the heat exchanger is 0.9, then the mass flow rate of the fluid in the tube side
is ________ kg/s (in integer).
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GATE 2022 (ME Set-2) Mechanical Engineering
Q.65 Consider a hydrodynamically and thermally fully-developed, steady fluid flow
of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A
constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the
pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200 oC.
The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the
fluid is 5. The thermal conductivity and the specific heat of the fluid
are 0.08 W∙m∙Kand 2600 J∙kg∙K, respectively. The correlation
Nu = 0.023 Re . Pr . is applicable, where the Nusselt Number (Nu) is defined on
the basis of the pipe diameter. The pipe surface temperature at the exit
is ________ oC (round off to the nearest integer).
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Q. No. Session Question Subject Key/Range Mark
Type Name
1 8 MCQ GA B 1
2 8 MCQ GA C 1
3 8 MCQ GA C 1
4 8 MCQ GA A 1
5 8 MCQ GA B OR C 1
6 8 MCQ GA C 2
7 8 MCQ GA C 2
8 8 MCQ GA A 2
9 8 MCQ GA A 2
10 8 MCQ GA B 2
11 8 MCQ ME B 1
12 8 MCQ ME A 1
13 8 MCQ ME D 1
14 8 MCQ ME B 1
15 8 MCQ ME B 1
16 8 MCQ ME B 1
17 8 MCQ ME A 1
18 8 MCQ ME A 1
19 8 MCQ ME D 1
20 8 MCQ ME A 1
21 8 MCQ ME A 1
22 8 MCQ ME D 1
23 8 MCQ ME B 1
24 8 MCQ ME B 1
25 8 MCQ ME C 1
26 8 MSQ ME B,C,D 1
27 8 MSQ ME A,B OR B 1
28 8 MSQ ME B,C,D 1
29 8 MSQ ME B,C,D 1
30 8 NAT ME 3 to 3 1
31 8 NAT ME 1.95 to 2.05 1
32 8 NAT ME 104 to 104 1
33 8 NAT ME 13 to 15 1
34 8 NAT ME 2 to 2 1
35 8 NAT ME 4825 to 4835 1
36 8 MCQ ME C 2
37 8 MCQ ME A 2
38 8 MCQ ME A 2
39 8 MCQ ME A 2
40 8 MCQ ME C 2
41 8 MCQ ME B 2
42 8 MCQ ME B 2
43 8 MCQ ME D 2
44 8 MCQ ME C 2
Text of page 101
45 8 MCQ ME B 2 46 8 MSQ ME B,C 2 47 8 MSQ ME B,D 2 48 8 NAT ME 2 to 2 2 49 8 NAT ME 0.2 to 0.2 2 50 8 NAT ME 1.48 to 1.52 2 51 8 NAT ME 1.48 to 1.52 2 52 8 NAT ME 1.24 to 1.26 2 53 8 NAT ME 23.60 to 24.20 2 54 8 NAT ME 2.4 to 2.6 2 55 8 NAT ME 2700 to 2750 2 56 8 NAT ME 2.29 to 2.33 2 57 8 NAT ME 25 to 25 2 58 8 NAT ME 2426.0 to 2432.0 2 59 8 NAT ME 15 to 15 2 60 8 NAT ME 385 to 405 2 61 8 NAT ME 450 to 450 2 62 8 NAT ME 3.48 to 3.70 2 63 8 NAT ME 1000 to 1000 2 64 8 NAT ME 1000 to 1000 2 65 8 NAT ME 317 to 324 2
Text of page 1
Q. No. Session Question Subject Key/Range Mark
Type Name
1 7 MCQ GA D 1
2 7 MCQ GA A 1
3 7 MCQ GA C 1
4 7 MCQ GA B 1
5 7 MCQ GA A 1
6 7 MCQ GA B 2
7 7 MCQ GA A 2
8 7 MCQ GA B 2
9 7 MCQ GA A 2
10 7 MCQ GA MTA 2
11 7 MCQ ME A 1
12 7 MCQ ME B 1
13 7 MCQ ME A 1
14 7 MCQ ME A 1
15 7 MCQ ME A 1
16 7 MCQ ME A 1
17 7 MCQ ME B 1
18 7 MCQ ME A 1
19 7 MCQ ME B 1
20 7 MCQ ME B 1
21 7 MCQ ME C 1
22 7 MCQ ME D 1
23 7 MCQ ME B 1
24 7 MCQ ME C 1
25 7 MCQ ME D 1
26 7 MSQ ME A,B 1
27 7 MSQ ME A,B,D 1
28 7 MSQ ME B,D 1
29 7 MSQ ME A,B,D OR A, B 1
30 7 MSQ ME B,C 1
31 7 NAT ME 10 to 10 1
32 7 NAT ME 2.62 to 2.70 1
33 7 NAT ME 27.00 to 30.00 1
34 7 NAT ME 404.00 to 414.00 1
35 7 NAT ME 210 to 225 1
36 7 MCQ ME A 2
37 7 MCQ ME A 2
38 7 MCQ ME A 2
39 7 MCQ ME A 2
40 7 MCQ ME A 2
41 7 MCQ ME A 2
42 7 MCQ ME B 2
43 7 MCQ ME C 2
44 7 MCQ ME B 2
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45 7 MCQ ME C 2 46 7 MSQ ME A,B 2 47 7 NAT ME 0.17 to 0.19 2 48 7 NAT ME 7.90 to 8.70 2 49 7 NAT ME 18 to 18 2 50 7 NAT ME 5.70 to 5.80 2 51 7 NAT ME 0.24 to 0.26 2 52 7 NAT ME -0.062 to -0.058 2 53 7 NAT ME 600 to 600 2 54 7 NAT ME 2570.0 to 2576.0 2 55 7 NAT ME 30.0 to 32.0 2 56 7 NAT ME 340 to 360 2 57 7 NAT ME 10.5 to 10.9 2 58 7 NAT ME 520 to 520 2 59 7 NAT ME 110 to 110 2 60 7 NAT ME 1.12 to 1.24 2 61 7 NAT ME 2620.00 to 2630.00 2 62 7 NAT ME 4780 to 4825 2 63 7 NAT ME 4.20 to 4.28 2 64 7 NAT ME 315 to 323 2 65 7 NAT ME 0.40 to 0.44 2
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Q. No. Session Question Subject Key/Range Mark
Type Name
1 8 MCQ GA B 1
2 8 MCQ GA C 1
3 8 MCQ GA C 1
4 8 MCQ GA A 1
5 8 MCQ GA B OR C 1
6 8 MCQ GA C 2
7 8 MCQ GA C 2
8 8 MCQ GA A 2
9 8 MCQ GA A 2
10 8 MCQ GA B 2
11 8 MCQ ME B 1
12 8 MCQ ME A 1
13 8 MCQ ME D 1
14 8 MCQ ME B 1
15 8 MCQ ME B 1
16 8 MCQ ME B 1
17 8 MCQ ME A 1
18 8 MCQ ME A 1
19 8 MCQ ME D 1
20 8 MCQ ME A 1
21 8 MCQ ME A 1
22 8 MCQ ME D 1
23 8 MCQ ME B 1
24 8 MCQ ME B 1
25 8 MCQ ME C 1
26 8 MSQ ME B,C,D 1
27 8 MSQ ME A,B OR B 1
28 8 MSQ ME B,C,D 1
29 8 MSQ ME B,C,D 1
30 8 NAT ME 3 to 3 1
31 8 NAT ME 1.95 to 2.05 1
32 8 NAT ME 104 to 104 1
33 8 NAT ME 13 to 15 1
34 8 NAT ME 2 to 2 1
35 8 NAT ME 4825 to 4835 1
36 8 MCQ ME C 2
37 8 MCQ ME A 2
38 8 MCQ ME A 2
39 8 MCQ ME A 2
40 8 MCQ ME C 2
41 8 MCQ ME B 2
42 8 MCQ ME B 2
43 8 MCQ ME D 2
44 8 MCQ ME C 2
Text of page 4
45 8 MCQ ME B 2 46 8 MSQ ME B,C 2 47 8 MSQ ME B,D 2 48 8 NAT ME 2 to 2 2 49 8 NAT ME 0.2 to 0.2 2 50 8 NAT ME 1.48 to 1.52 2 51 8 NAT ME 1.48 to 1.52 2 52 8 NAT ME 1.24 to 1.26 2 53 8 NAT ME 23.60 to 24.20 2 54 8 NAT ME 2.4 to 2.6 2 55 8 NAT ME 2700 to 2750 2 56 8 NAT ME 2.29 to 2.33 2 57 8 NAT ME 25 to 25 2 58 8 NAT ME 2426.0 to 2432.0 2 59 8 NAT ME 15 to 15 2 60 8 NAT ME 385 to 405 2 61 8 NAT ME 450 to 450 2 62 8 NAT ME 3.48 to 3.70 2 63 8 NAT ME 1000 to 1000 2 64 8 NAT ME 1000 to 1000 2 65 8 NAT ME 317 to 324 2
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Source: GATE. Question paper published by GATE.