GATE ME 2023: Mechanical Engineering
Text of page 1
Mechanical Engineering (ME)
General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each
Q.1 He did not manage to fix the car himself, so he _______ in the garage.
(A) got it fixed
(B) getting it fixed
(C) gets fixed
(D) got fixed
Q.2 Planting : Seed : : Raising : _____
(By word meaning)
(A) Child
(B) Temperature
(C) Height
(D) Lift
Page 1 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.3 A certain country has 504 universities and 25951 colleges. These are categorised into
Grades I, II, and III as shown in the given pie charts.
What is the percentage, correct to one decimal place, of higher education institutions
(colleges and universities) that fall into Grade III?
(A) 22.7
(B) 23.7
(C) 15.0
(D) 66.8
Page 2 of 56
Organizing Institute: IIT Kanpur
Text of page 3
Mechanical Engineering (ME)
Q.4 The minute-hand and second-hand of a clock cross each other _______ times
between 09:15:00 AM and 09:45:00 AM on a day.
(A) 30
(B) 15
(C) 29
(D) 31
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.5 The symbols , , , and are to be filled, one in each box, as shown below.
The rules for filling in the four symbols are as follows.
1) Every row and every column must contain each of the four symbols.
2) Every 2×2 square delineated by bold lines must contain each of the four
symbols.
Which symbol will occupy the box marked with ‘ ’ in the partially filled figure?
(A)
(B)
(C)
(D)
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.6 – Q.10 Carry TWO marks Each
Q.6 In a recently held parent-teacher meeting, the teachers had very few complaints
about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost
all of Ravi’s friends at school were hardworking and kind too. But the teachers drew
attention to Ravi’s complete lack of interest in sports. The teachers believed that,
along with some of his friends who showed similar disinterest in sports, Ravi needed
to engage in some sports for his overall development.
Based only on the information provided above, which one of the following
statements can be logically inferred with certainty?
(A) All of Ravi’s friends are hardworking and kind.
(B) No one who is not a friend of Ravi is hardworking and kind.
(C) None of Ravi’s friends are interested in sports.
(D) Some of Ravi’s friends are hardworking and kind.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.7 Consider the following inequalities
p2 − 4q < 4
3p + 2q < 6
where p and q are positive integers.
The value of (p + q) is _______.
(A) 2
(B) 1
(C) 3
(D) 4
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.8 Which one of the sentence sequences in the given options creates a coherent
narrative?
(i) I could not bring myself to knock.
(ii) There was a murmur of unfamiliar voices coming from the big drawing
room and the door was firmly shut.
(iii) The passage was dark for a bit, but then it suddenly opened into a bright
kitchen.
(iv) I decided I would rather wander down the passage.
(A) (iv), (i), (iii), (ii)
(B) (iii), (i), (ii), (iv)
(C) (ii), (i), (iv), (iii)
(D) (i), (iii), (ii), (iv)
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.9 How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6}
that satisfy the condition that S is a subset of T?
(A) 729
(B) 728
(C) 665
(D) 664
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.10 An opaque pyramid (shown below), with a square base and isosceles faces, is
suspended in the path of a parallel beam of light, such that its shadow is cast on a
screen oriented perpendicular to the direction of the light beam. The pyramid can
be reoriented in any direction within the light beam. Under these conditions, which
one of the shadows P, Q, R, and S is NOT possible?
(A) P
(B) Q
(C) R
(D) S
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.11 – Q.35 Carry ONE mark Each
Q.11 A machine produces a defective component with a probability of 0.015. The
number of defective components in a packed box containing 200 components
produced by the machine follows a Poisson distribution. The mean and the
variance of the distribution are
(A) 3 and 3, respectively
(B) √3 and √3 , respectively
(C) 0.015 and 0.015, respectively
(D) 3 and 9, respectively
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.12 The figure shows the plot of a function over the interval [-4, 4]. Which one of the
options given CORRECTLY identifies the function?
(A) |2 − x|
(B) |2 − |x||
(C) |2 + |x||
(D) 2 − |x|
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Organizing Institute: IIT Kanpur
Text of page 12
Mechanical Engineering (ME)
Q.13 With reference to the Economic Order Quantity (EOQ) model, which one of the
options given is correct?
(A) Curve P1: Total cost, Curve P2: Holding cost,
Curve P3: Setup cost, and Curve P4: Production cost.
(B) Curve P1: Holding cost, Curve P2: Setup cost,
Curve P3: Production cost, and Curve P4: Total cost.
(C) Curve P1: Production cost, Curve P2: Holding cost,
Curve P3: Total cost, and Curve P4: Setup cost.
(D) Curve P1: Total cost, Curve P2: Production cost,
Curve P3: Holding cost, and Curve P4: Setup cost.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.14 Which one of the options given represents the feasible region of the linear
programming model:
Maximize 45X1 + 60X2
X1 ≤ 45
X2 ≤ 50
10X1 + 10X2 ≥ 600
25X1 + 5X2 ≤ 750
(A) Region P
(B) Region Q
(C) Region R
(D) Region S
Page 13 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
A cuboidal part has to be accurately positioned first, arresting six degrees of
Q.15 freedom and then clamped in a fixture, to be used for machining. Locating pins in
the form of cylinders with hemi-spherical tips are to be placed on the fixture for
positioning. Four different configurations of locating pins are proposed as shown.
Which one of the options given is correct?
Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are
(A) over-constrained and Configuration P3 is under-constrained.
Configuration P2 arrests 6 degrees of freedom, while Configurations P1 and P3 are
(B) over-constrained and Configuration P4 is under-constrained.
Configuration P3 arrests 6 degrees of freedom, while Configurations P2 and P4 are
(C) over-constrained and Configuration P1 is under-constrained.
Configuration P4 arrests 6 degrees of freedom, while Configurations P1 and P3 are
(D) over-constrained and Configuration P2 is under-constrained.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.16 The effective stiffness of a cantilever beam of length L and flexural rigidity EI
subjected to a transverse tip load W is
(A) 3EI
L3
(B) 2EI
L3
(C) L3
2EI
(D) L3
3EI
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.17 The options show frames consisting of rigid bars connected by pin joints. Which
one of the frames is non-rigid?
(A)
(B)
(C)
(D)
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.18 The S-N curve from a fatigue test for steel is shown. Which one of the options gives
the endurance limit?
(A) Sut
(B) S2
(C) S3
(D) S4
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Organizing Institute: IIT Kanpur
Text of page 18
Mechanical Engineering (ME)
Q.19 Air (density = 1.2 kg/m3, kinematic viscosity = 1.5×10-5 m2/s) flows over a flat
plate with a free-stream velocity of 2 m/s. The wall shear stress at a location
15 mm from the leading edge is w. What is the wall shear stress at a location
30 mm from the leading edge?
(A) w / 2
(B) √2 w
(C) 2 w
(D) w / √2
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.20 Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as
shown in the figure.
The variations in the flow across the cross-section are negligible. The flow
conditions at Location 1 are given as follows:
P1 = 100 kPa, ρ1 = 1.2 kg/m3, u1 = 400 m/s
The duct cross-sectional area at Location 2 is given by A2 = 2A1, where A1
denotes the duct cross-sectional area at Location 1. Which one of the given
statements about the velocity u2 and pressure P2 at Location 2 is TRUE?
(A) u2 < u1 , P2 < P1
(B) u2 < u1 , P2 > P1
(C) u2 > u1 , P2 < P1
(D) u2 > u1 , P2 > P1
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.21 Consider incompressible laminar flow of a constant property Newtonian fluid in
an isothermal circular tube. The flow is steady with fully-developed temperature
and velocity profiles. The Nusselt number for this flow depends on
(A) neither the Reynolds number nor the Prandtl number
(B) both the Reynolds and Prandtl numbers
(C) the Reynolds number but not the Prandtl number
(D) the Prandtl number but not the Reynolds number
Page 20 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.22 A heat engine extracts heat (Q H) from a thermal reservoir at a temperature of
1000 K and rejects heat (Q L) to a thermal reservoir at a temperature of 100 K,
while producing work (W). Which one of the combinations of [Q H, Q L and W]
given is allowed?
(A) Q H = 2000 J, Q L = 500 J, W = 1000 J
(B) Q H = 2000 J, Q L = 750 J, W = 1250 J
(C) Q H = 6000 J, Q L = 500 J, W = 5500 J
(D) Q H = 6000 J, Q L = 600 J, W = 5500 J
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.23 Two surfaces P and Q are to be joined together. In which of the given joining
operation(s), there is no melting of the two surfaces P and Q for creating the joint?
(A) Arc welding
(B) Brazing
(C) Adhesive bonding
(D) Spot welding
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.24 A beam is undergoing pure bending as shown in the figure. The stress (σ)-strain
(ε) curve for the material is also given. The yield stress of the material is σY .
Which of the option(s) given represent(s) the bending stress distribution at cross-
section AA after plastic yielding?
(A)
(B)
(C)
(D)
Page 23 of 56
Organizing Institute: IIT Kanpur
Text of page 24
Mechanical Engineering (ME)
Q.25 In a metal casting process to manufacture parts, both patterns and moulds provide
shape by dictating where the material should or should not go. Which of the
option(s) given correctly describe(s) the mould and the pattern?
(A) Mould walls indicate boundaries within which the molten part material is allowed,
while pattern walls indicate boundaries of regions where mould material is not
allowed.
(B) Moulds can be used to make patterns.
(C) Pattern walls indicate boundaries within which the molten part material is
allowed, while mould walls indicate boundaries of regions where mould material
is not allowed.
(D) Patterns can be used to make moulds.
Page 24 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.26 The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The
yield stress of the material is 100 MPa. Which prediction(s) about material failure
at P is/are CORRECT?
(A) Maximum normal stress theory predicts that the material fails
(B) Maximum shear stress theory predicts that the material fails
(C) Maximum normal stress theory predicts that the material does not fail
(D) Maximum shear stress theory predicts that the material does not fail
Page 25 of 56
Organizing Institute: IIT Kanpur
Text of page 26
Mechanical Engineering (ME)
Q.27 Which of the plot(s) shown is/are valid Mohr’s circle representations of a plane
stress state in a material? (The center of each circle is indicated by O.)
(A) M1
(B) M2
(C) M3
(D) M4
Page 26 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.28 Consider a laterally insulated rod of length L and constant thermal conductivity.
Assuming one-dimensional heat conduction in the rod, which of the following
steady-state temperature profile(s) can occur without internal heat generation?
(A)
(B)
(C)
(D)
Page 27 of 56
Organizing Institute: IIT Kanpur
Text of page 28
Mechanical Engineering (ME)
Q.29 Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an
angular velocity ratio |ω2 |/|ω1 | = 1/4, have their centers 30 mm apart. The
number of teeth on the driver (gear 1) is _______ .
(Answer in integer)
Page 28 of 56
Organizing Institute: IIT Kanpur
Text of page 29
Mechanical Engineering (ME)
Q.30 The figure shows a block of mass m = 20 kg attached to a pair of identical linear
springs, each having a spring constant k = 1000 N/m. The block oscillates on a
frictionless horizontal surface. Assuming free vibrations, the time taken by the
block to complete ten oscillations is _________ seconds. (Rounded off to two
decimal places)
Take π = 3.14.
Page 29 of 56
Organizing Institute: IIT Kanpur
Text of page 30
Mechanical Engineering (ME)
Q.31 A vector field
B(x, y, z) = x î + y ĵ − 2z k̂
is defined over a conical region having height ℎ = 2, base radius r = 3 and axis
along z, as shown in the figure. The base of the cone lies in the x-y plane and is
centered at the origin.
If n denotes the unit outward normal to the curved surface S of the cone, the
value of the integral
∫B ⋅ n dS
S
equals _________ . (Answer in integer)
Page 30 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.32 A linear transformation maps a point (x, y) in the plane to the point (x̂, ŷ)
according to the rule
x̂ = 3y, ŷ = 2x.
Then, the disc x 2 + y 2 ≤ 1 gets transformed to a region with an area equal to
_________ . (Rounded off to two decimals)
Use π = 3.14.
Q.33 The value of k that makes the complex-valued function
f(z) = e −kx (cos 2y − i sin 2y)
analytic, where z = x + iy, is _________.
(Answer in integer)
Page 31 of 56
Organizing Institute: IIT Kanpur
Text of page 32
Mechanical Engineering (ME)
Q.34 The braking system shown in the figure uses a belt to slow down a pulley rotating
in the clockwise direction by the application of a force P. The belt wraps around
the pulley over an angle α = 270 degrees. The coefficient of friction between the
belt and the pulley is 0.3. The influence of centrifugal forces on the belt is
negligible.
During braking, the ratio of the tensions T1 to T2 in the belt is equal to
__________. (Rounded off to two decimal places)
Take π = 3.14.
Q.35 Consider a counter-flow heat exchanger with the inlet temperatures of two fluids
(1 and 2) being T1, in = 300 K and T2, in = 350 K. The heat capacity rates of the
two fluids are C1= 1000 W/K and C2 = 400 W/K, and the effectiveness of the
heat exchanger is 0.5. The actual heat transfer rate is _____ kW.
(Answer in integer)
Page 32 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.36 – Q.65 Carry TWO marks Each
Q.36 1
Which one of the options given is the inverse Laplace transform of ?
s 3 −s
u(t) denotes the unit-step function.
(A) 1 1
(−1 + e −t + e t ) u(t)
2 2
(B) 1
( e −t − e t ) u(t)
3
(C) 1 1
(−1 + e −(t−1) + e (t−1) ) u(t − 1)
2 2
(D) 1 1
(−1 − e −(t−1) − e (t−1) ) u(t − 1)
2 2
Page 33 of 56
Organizing Institute: IIT Kanpur
Text of page 34
Mechanical Engineering (ME)
Q.37 A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an
immovable rigid block as shown in the figure. If the collision is perfectly elastic,
what is the momentum vector of the ball (in kg m/s) just after impact?
Take the acceleration due to gravity to be g = 9.8 m/s 2 . Options have been
rounded off to one decimal place.
(A) 19.6 î
(B) 19.6 ĵ
(C) 17.0 î + 9.8 ĵ
(D) 9.8 î + 17.0 ĵ
Page 34 of 56
Organizing Institute: IIT Kanpur
Text of page 35
Mechanical Engineering (ME)
Q.38 The figure shows a wheel rolling without slipping on a horizontal plane with
angular velocity ω1. A rigid bar PQ is pinned to the wheel at P while the end Q
slides on the floor.
What is the angular velocity ω2 of the bar PQ?
(A) ω2 = 2ω1
(B) ω2 = ω1
(C) ω2 = 0.5ω1
(D) ω2 = 0.25ω1
Page 35 of 56
Organizing Institute: IIT Kanpur
Text of page 36
Mechanical Engineering (ME)
Q.39 A beam of length L is loaded in the xy −plane by a uniformly distributed load,
and by a concentrated tip load parallel to the z −axis, as shown in the figure. The
resulting bending moment distributions about the y and the z axes are denoted by
My and Mz , respectively.
Which one of the options given depicts qualitatively CORRECT variations of
My and Mz along the length of the beam?
(A)
(B)
(C)
(D)
Page 36 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.40 The figure shows a thin-walled open-top cylindrical vessel of radius r and wall
thickness t. The vessel is held along the brim and contains a constant-density
liquid to height ℎ from the base. Neglect atmospheric pressure, the weight of the
vessel and bending stresses in the vessel walls.
Which one of the plots depicts qualitatively CORRECT dependence of the
magnitudes of axial wall stress (σ1 ) and circumferential wall stress (σ2 ) on y?
(A)
(B)
(C)
(D)
Page 37 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.41 Which one of the following statements is FALSE?
(A) For an ideal gas, the enthalpy is independent of pressure.
(B) For a real gas going through an adiabatic reversible process, the process equation is given by
PV γ = constant, where P is the pressure, V is the volume and γ is the ratio of the specific heats
of the gas at constant pressure and constant volume.
(C) For an ideal gas undergoing a reversible polytropic process PV 1.5 = constant, the equation
connecting the pressure, volume and temperature of the gas at any point along the process is
P mT
= , where R is the gas constant and m is the mass of the gas.
R V
(D) Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high
temperature.
Page 38 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.42 Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is
massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air
(considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to
the specific heat at constant volume for air. The piston is initially located at a position L1. The
initial pressure of the air inside the cylinder is P1 ≫ P0, where P0 is the atmospheric pressure.
The stop S1 is instantaneously removed and the piston moves to the position L2, where the
equilibrium pressure of air inside the cylinder is P2 ≫ P0.
What is the work done by the piston on the atmosphere during this process?
(A) 0
(B) P0 A(L2 − L1 )
(C) L1
P1 AL1 ln
L2
(D) (P2 L2 − P1 L1 )A
(1 − γ)
Page 39 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.43 A cylindrical rod of length ℎ and diameter d is placed inside a cubic enclosure of
side length L. S denotes the inner surface of the cube. The view-factor FS-S is
(A) 0
(B) 1
(C) (πdℎ + πd2 /2)
6L2
(D) (πdℎ + πd2 /2)
1−
6L2
Page 40 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.44 In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the
rake angle of the tool α = 5°, and the shear angle, φ, is known to be 45°.
Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close
to each other. As they approach the thin shear zone (shown as a thick line in the figure),
plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2).
Assuming that the perpendicular distance between PQ and RS is δ = 25 μm, what is the
value of shear strain rate (in s-1) that the material undergoes at the shear zone?
(A) 1.84 × 104
(B) 5.20 × 104
(C) 0.71 × 104
(D) 1.30 × 104
Page 41 of 56
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Mechanical Engineering (ME)
Q.45 A CNC machine has one of its linear positioning axes as shown in the figure,
consisting of a motor rotating a lead screw, which in turn moves a nut horizontally
on which a table is mounted. The motor moves in discrete rotational steps of 50
steps per revolution. The pitch of the screw is 5 mm and the total horizontal
traverse length of the table is 100 mm. What is the total number of controllable
locations at which the table can be positioned on this axis?
(A) 5000
(B) 2
(C) 1000
(D) 200
Page 42 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.46 Cylindrical bars P and Q have identical lengths and radii, but are composed of
different linear elastic materials. The Young’s modulus and coefficient of thermal
expansion of Q are twice the corresponding values of P. Assume the bars to be
perfectly bonded at the interface, and their weights to be negligible.
The bars are held between rigid supports as shown in the figure and the
temperature is raised by ΔT. Assume that the stress in each bar is homogeneous
and uniaxial. Denote the magnitudes of stress in P and Q by σ1 and σ2 ,
respectively.
Which of the statement(s) given is/are CORRECT?
(A) The interface between P and Q moves to the left after heating
(B) The interface between P and Q moves to the right after heating
(C) σ1 < σ2
(D) σ1 = σ2
Page 43 of 56
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Mechanical Engineering (ME)
Q. 47 A very large metal plate of thickness d and thermal conductivity k is cooled by a
stream of air at temperature T∞ = 300 K with a heat transfer coefficient ℎ, as
shown in the figure. The centerline temperature of the plate is TP. In which of the
following case(s) can the lumped parameter model be used to study the heat
transfer in the metal plate?
(A) ℎ = 10 Wm-2K-1, k = 100 Wm-1K-1, d = 1 mm, TP = 350 K
(B) ℎ = 100 Wm-2K-1, k = 100 Wm-1K-1, d = 1 m, TP = 325 K
(C) ℎ = 100 Wm-2K-1, k = 1000 Wm-1K-1, d = 1 mm, TP = 325 K
(D) ℎ = 1000 Wm-2K-1, k = 1 Wm-1K-1, d = 1 m, TP = 350 K
Page 44 of 56
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Mechanical Engineering (ME)
Q.48 The smallest perimeter that a rectangle with area of 4 square units can have is
______ units.
(Answer in integer)
Q.49 Consider the second-order linear ordinary differential equation
d2y dy
x2 + x − y = 0, x ≥ 1
dx 2 dx
with the initial conditions
dy
y(x = 1) = 6, | = 2.
dx x=1
The value of y at x = 2 equals _________.
(Answer in integer)
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Mechanical Engineering (ME)
Q.50 The initial value problem
dy
+ 2y = 0, y(0) = 1
dt
is solved numerically using the forward Euler’s method with a constant and
positive time step of Δt.
Let yn represent the numerical solution obtained after n steps. The condition
|yn+1 | ≤ |yn | is satisfied if and only if Δt does not exceed _____________.
(Answer in integer)
Q.51 The atomic radius of a hypothetical face-centered cubic (FCC) metal is
(√2⁄10) nm. The atomic weight of the metal is 24.092 g/mol. Taking
Avogadro’s number to be 6.023×1023 atoms/mol, the density of the metal is
____________ kg/m3.
(Answer in integer)
Page 46 of 56
Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.52 A steel sample with 1.5 wt.% carbon (no other alloying elements present) is
slowly cooled from 1100 °C to just below the eutectoid temperature (723 °C). A
part of the iron-cementite phase diagram is shown in the figure. The ratio of the
pro-eutectoid cementite content to the total cementite content in the
microstructure that develops just below the eutectoid temperature is ________.
(Rounded off to two decimal places)
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.53 A part, produced in high volumes, is dimensioned as shown. The machining
process making this part is known to be statistically in control based on sampling
data. The sampling data shows that D1 follows a normal distribution with a mean
of 20 mm and a standard deviation of 0.3 mm, while D2 follows a normal
distribution with a mean of 35 mm and a standard deviation of 0.4 mm. An
inspection of dimension C is carried out in a sufficiently large number of parts.
To be considered under six-sigma process control, the upper limit of dimension C
should be ____________ mm.
(Rounded off to one decimal place)
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Mechanical Engineering (ME)
Q.54 A coordinate measuring machine (CMM) is used to determine the distance between Surface
SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the
datum as per the engineering drawing used for manufacturing this part. The CMM is used
to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on
Surface SQ as shown. A regression procedure is used to fit the necessary planes.
The distance between the two fitted planes is ___________ mm.
(Answer in integer)
Page 49 of 56
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Mechanical Engineering (ME)
Q.55 A solid part (see figure) of polymer material is to be fabricated by additive
manufacturing (AM) in square-shaped layers starting from the bottom of the part
working upwards. The nozzle diameter of the AM machine is a/10 mm and the
nozzle follows a linear serpentine path parallel to the sides of the square layers
with a feed rate of a/5 mm/min.
Ignore any tool path motions other than those involved in adding material, and any
other delays between layers or the serpentine scan lines.
The time taken to fabricate this part is ___________ minutes.
(Answer in integer)
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.56 An optical flat is used to measure the height difference between a reference slip
gauge A and a slip gauge B. Upon viewing via the optical flat using a
monochromatic light of wavelength 0.5 µm, 12 fringes were observed over a
length of 15 mm of gauge B. If the gauges are placed 45 mm apart, the height
difference of the gauges is ______________ m.
(Answer in integer)
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Mechanical Engineering (ME)
Q.57 Ignoring the small elastic region, the true stress (σ) – true strain (ε) variation of a
material beyond yielding follows the equation σ = 400ε 0.3 MPa. The engineering
ultimate tensile strength value of this material is ________ MPa.
(Rounded off to one decimal place)
Q.58 The area moment of inertia about the y-axis of a linearly tapered section shown in
the figure is _____________ m4.
(Answer in integer)
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Mechanical Engineering (ME)
Q.59 A cylindrical bar has a length L = 5 m and cross section area S = 10 m2 . The bar
is made of a linear elastic material with a density ρ = 2700 kg/m3 and Young’s
modulus E = 70 GPa. The bar is suspended as shown in the figure and is in a state
of uniaxial tension due to its self-weight.
The elastic strain energy stored in the bar equals _________ J. (Rounded off to two
decimal places)
Take the acceleration due to gravity as g = 9.8 m/s2 .
Q.60 A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made
of a linear elastic material with a shear modulus of 80 GPa. While operating at
500 rpm, the angle of twist across its length is found to be 0.5 degrees.
The power transmitted by the shaft at this speed is _______kW. (Rounded off to
two decimal places)
Take π = 3.14.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.61 Consider a mixture of two ideal gases, X and Y, with molar masses
M̅ X = 10 kg/kmol and M̅ Y = 20 kg/kmol, respectively, in a container. The total
pressure in the container is 100 kPa, the total volume of the container is 10 m3
and the temperature of the contents of the container is 300 K. If the mass of
gas-X in the container is 2 kg, then the mass of gas-Y in the container
is ____ kg. (Rounded off to one decimal place)
Assume that the universal gas constant is 8314 J kmol-1K-1.
Q.62 The velocity field of a certain two-dimensional flow is given by
V(x, y) = k(xî − yĵ)
where k = 2 s-1. The coordinates x and y are in meters. Assume gravitational
effects to be negligible.
If the density of the fluid is 1000 kg/m3 and the pressure at the origin is 100 kPa,
the pressure at the location (2 m, 2 m) is _____________ kPa.
(Answer in integer)
Q.63 Consider a unidirectional fluid flow with the velocity field given by
V(x, y, z, t) = u(x, t) î
where u(0, t) = 1. If the spatially homogeneous density field varies with time
t as
ρ(t) = 1 + 0.2e −t
the value of u(2, 1) is ______________. (Rounded off to two decimal places)
Assume all quantities to be dimensionless.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.64 The figure shows two fluids held by a hinged gate. The atmospheric pressure is
Pa = 100 kPa. The moment per unit width about the base of the hinge is
____________ kNm/m. (Rounded off to one decimal place)
Take the acceleration due to gravity to be g = 9.8 m/s2.
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Organizing Institute: IIT Kanpur
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Mechanical Engineering (ME)
Q.65 An explosion at time t = 0 releases energy E at the origin in a space filled with
a gas of density . Subsequently, a hemispherical blast wave propagates
radially outwards as shown in the figure.
Let R denote the radius of the front of the hemispherical blast wave. The radius
R follows the relationship R = k t a E b ρc , where k is a dimensionless constant.
The value of exponent a is ___________.
(Rounded off to one decimal place)
END OF QUESTION PAPER
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Organizing Institute: IIT Kanpur
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GATE 2023 Mechanical Engineering (ME)
Q. No. Session Question Type (QT) Subject
MCQ/MSQ/NAT
Name (SN) Key/Range (KY) Mark (MK)
1 2 MCQ GA A 1
2 2 MCQ GA A 1
3 2 MCQ GA A 1
4 2 MCQ GA A 1
5 2 MCQ GA B 1
6 2 MCQ GA D 2
7 2 MCQ GA A 2
8 2 MCQ GA C 2
9 2 MCQ GA A 2
10 2 MCQ GA B 2
11 2 MCQ ME A 1
12 2 MCQ ME B 1
13 2 MCQ ME A 1
14 2 MCQ ME B 1
15 2 MCQ ME A 1
16 2 MCQ ME A 1
17 2 MCQ ME C 1
18 2 MCQ ME D 1
19 2 MCQ ME D 1
20 2 MCQ ME C 1
21 2 MCQ ME A 1
22 2 MCQ ME B 1
23 2 MSQ ME B, C 1
24 2 MSQ ME C, D 1
25 2 MSQ ME A, B, D 1
26 2 MSQ ME B, C 1
27 2 MSQ ME A, C 1
28 2 MSQ ME A, B 1
29 2 NAT ME 95.999 to 96.001 1
30 2 NAT ME 6.27 to 6.29 1
31 2 NAT ME -0.001 to 0.001 1
32 2 NAT ME 18.80 to 18.90 1
33 2 NAT ME 1.999 to 2.001 1
34 2 NAT ME 4.05 to 4.15 1
35 2 NAT ME 9.999 to 10.001 1
36 2 MCQ ME A 2
37 2 MCQ ME C 2
38 2 MCQ ME D 2
39 2 MCQ ME B 2
40 2 MCQ ME A 2
41 2 MCQ ME B 2
42 2 MCQ ME B 2
43 2 MCQ ME D 2
44 2 MCQ ME B 2
45 2 MCQ ME C 2
46 2 MSQ ME A, D 2
Text of page 2
47 2 MSQ ME A, C 2
48 2 NAT ME 7.999 to 8.001 2
49 2 NAT ME 8.999 to 9.001 2
50 2 NAT ME 0.999 to 1.001 2
51 2 NAT ME 2490 to 2510 2
52 2 NAT ME 0.53 to 0.55 2
53 2 NAT ME 16.4 to 16.6 2
54 2 NAT ME 4.999 to 5.001 2
55 2 NAT ME MTA 2
56 2 NAT ME 8.999 to 9.001 2
57 2 NAT ME 206.0 to 207.0 2
58 2 NAT ME 3023.999 to 3024.001 2
59 2 NAT ME 2.00 to 2.16 2
60 2 NAT ME 237 to 240 2
61 2 NAT ME 3.9 to 4.1 2
62 2 NAT ME 83.999 to 84.001 2
63 2 NAT ME 1.10 to 1.20 2
64 2 NAT ME 55.9 to 58.5 2
65 2 NAT ME 0.39 to 0.41 2
MTA = Marks to All
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Source: GATE. Question paper published by GATE.