GATE 2023 Question Paper XE Engineering Sciences

The Graduate Aptitude Test in Engineering

GATE 2023
Question Paper
GATE is an entrance examination conducted in India that
primarily tests the comprehensive understanding of
undergraduate subjects in engineering and sciences for
admission into technical postgraduate programs.

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(C) at

(D) between

Q.2 Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(C) Recommend

(D) Refute

Page 1 of 100

Q.3 A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two
adjacent digits being the same. For example, 137 is a frabjous number, while 133
is not. How many such frabjous numbers exist?

(A) 125

(B) 720

(C) 60

(D) 80

Q.4 Which one among the following statements must be TRUE about the mean and
the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(C) At most half the candidates have a score that is larger than the median.

(D) At most half the candidates have a score that is larger than the mean.

Page 2 of 100

Q.5 In the given diagram, ovals are marked at different heights (h) of a hill. Which one
of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(C) R

(D) S

Page 3 of 100

Q.6 – Q.10 Carry TWO marks Each

Q.6 Residency is a famous housing complex with many well-established individuals
among its residents. A recent survey conducted among the residents of the
complex revealed that all of those residents who are well established in their
respective fields happen to be academicians. The survey also revealed that most of
these academicians are authors of some best-selling books.

Based only on the information provided above, which one of the following
statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also
authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(C) Some authors of best-selling books are residents of the complex who are well
established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Page 4 of 100

Q.7 Ankita has to climb 5 stairs starting at the ground, while respecting the following
rules:

1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.

Let 𝐹(𝑁) denote the number of possible ways in which Ankita can reach the 𝑁 𝑡ℎ
stair. For example, 𝐹(1) = 1, 𝐹(2) = 2, 𝐹(3) = 3.

The value of 𝐹(5) is _______.

(A) 8

(B) 7

(C) 6

(D) 5

Page 5 of 100

Q.8 The information contained in DNA is used to synthesize proteins that are
necessary for the functioning of life. DNA is composed of four nucleotides:
Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information
contained in DNA can then be thought of as a sequence of these four nucleotides:
A, T, C, and G. DNA has coding and non-coding regions. Coding regions—where
the sequence of these nucleotides are read in groups of three to produce individual
amino
acids—constitute only about 2% of human DNA. For example, the triplet of
nucleotides CCG codes for the amino acid glycine, while the triplet GGA codes
for the amino acid proline. Multiple amino acids are then assembled to form a
protein.

Based only on the information provided above, which of the following statements
can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.
(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(C) both (i) and (ii)

(D) neither (i) nor (ii)

Page 6 of 100

Q.9 Which one of the given figures P, Q, R and S represents the graph of the following
function?

𝑓(𝑥) = | |𝑥 + 2| − |𝑥 − 1| |

(A) P

(B) Q

(C) R

(D) S

Page 7 of 100

Q.10 An opaque cylinder (shown below) 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 cylinder 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

Page 8 of 100

Engineering Mathematics: XE-A (Compulsory)
XE-A: Q.11 – Q.17 Carry ONE mark Each

Q.11 Let 𝐴 be a 3 × 3 real matrix having eigenvalues 1, 2, and 3. If 𝐵 = 𝐴2 + 2𝐴 + 𝐼,
where 𝐼 is the 3 × 3 identity matrix, then the eigenvalues of 𝐵 are

(A) 4, 9, 16

(B) 1, 2, 3

(C) 1, 4, 9

(D) 4, 16, 25

Q.12 Let 𝑓: ℝ2 → ℝ be a function defined by

𝑥𝑦
, 𝑦 ≠ −|𝑥|
𝑓(𝑥, 𝑦) = { |𝑥| + 𝑦
0 , otherwise.

Then which one of the following statement is TRUE?

(A) 𝑓 is NOT continuous at (0,0).

(B) 𝜕𝑓 𝜕𝑓
(0,0) = 0, and (0,0) = 1.
𝜕𝑥 𝜕𝑦

(C) 𝜕𝑓 𝜕𝑓
(0,0) = 1, and (0,0) = 0.
𝜕𝑥 𝜕𝑦

(D) 𝜕𝑓 𝜕𝑓
(0,0) = 1, and (0,0) = 1.
𝜕𝑥 𝜕𝑦

Page 9 of 100

Q.13 If the quadrature formula

1
1 1
∫ 𝑓(𝑥)𝑑𝑥 ≈ (𝑐1 𝑓(−1) + 𝑐2 𝑓 ( ) + 𝑐3 𝑓(1))
9 2
−1

is exact for all polynomials of degree less than or equal to 2, then

𝑐
(A) 𝑐1 + 42 + 𝑐3 = 6

𝑐
(B) 𝑐1 + 32 + 𝑐3 = 4

𝑐2
(C) 𝑐1 + + 𝑐3 = 2
2

(D) 𝑐1 + 𝑐2 + 𝑐3 = 5

Q.14 The second smallest eigenvalue of the eigenvalue problem

𝑑2 𝑦
+ (𝜆 − 3)𝑦 = 0, 𝑦(0) = 𝑦(𝜋) = 0,
𝑑𝑥 2

is

(A) 4

(B) 3

(C) 7

(D) 9

Page 10 of 100

Q.15 Which one of the following functions is differentiable at 𝑧 = 0 but NOT
differentiable at any other point in the complex plane ℂ?

(A) 𝑓(𝑧) = 𝑧|𝑧|, 𝑧 ∈ ℂ

(B) 𝑓(𝑧) = sin(𝑧), 𝑧 ∈ ℂ

1
(C)
𝑓(𝑧) = {𝑒 𝑧 , 𝑧 ≠ 0 for 𝑧 ∈ ℂ
0, 𝑧 = 0

2
(D) 𝑓(𝑧) = 𝑒 −𝑧 , 𝑧∈ℂ

Q.16 If the polynomial

𝑃(𝑥) = 𝑎0 + 𝑎1 𝑥 + 𝑎2 𝑥(𝑥 − 1) + 𝑎3 𝑥(𝑥 − 1)(𝑥 − 2)

5
interpolates the points (0, 2), (1, 3), (2, 2), and (3, 5), then the value of 𝑃 (2) is
_________ (round off to 2 decimal places).

Q.17 The value of 𝑚 for which the vector field

𝐹⃗ (𝑥, 𝑦) = (4𝑥 𝑚 𝑦 2 − 2 𝑥 𝑦 𝑚 )𝑖̂ + (2𝑥 4 𝑦 − 3𝑥 2 𝑦 2 )𝑗̂

is a conservative vector field, is _________________ (in integer).

Page 11 of 100

XE-A: Q.18 – Q.21 Carry TWO marks Each

Q.18 Let

4 −2 2 3 −2 2
𝑃 = [6 −3 4], and 𝑄 = [4 −4 6] .
3 −2 3 2 −3 5

The eigenvalues of both 𝑃 and 𝑄 are 1, 1, and 2. Which one of the following
statements is TRUE?

(A) Both 𝑃 and 𝑄 are diagonalizable

(B) 𝑃 is diagonalizable but 𝑄 is NOT diagonalizable

(C) 𝑃 is NOT diagonalizable but 𝑄 is diagonalizable

(D) Both 𝑃 and 𝑄 are NOT diagonalizable

Q.19 The surface area of the portion of the paraboloid

𝑧 = 𝑥2 + 𝑦2

1
that lies between the planes 𝑧 = 0 and 𝑧 = 4 is

𝜋
(A) (2√2 − 1)
6

𝜋
(B) (2√2 − 1)
2

(C) 𝜋(2√2 − 1)

𝜋
(D) (2√2 − 1)
3

Page 12 of 100

Q.20 4
The probability of a person telling the truth is 6 . An unbiased die is thrown by
the same person twice and the person reports that the numbers appeared in both
the throws are same. Then the probability that actually the numbers appeared in
both the throws are same is __________ (round off to 2 decimal places).

Q.21 Let 𝑢(𝑥, 𝑡) be the solution of the initial boundary value problem

𝜕𝑢 𝜕2 𝑢
− = 0, 𝑥 ∈ (0, 2), 𝑡 > 0
𝜕𝑡 𝜕𝑥 2

𝑢(𝑥, 0) = sin(𝜋𝑥), 𝑥 ∈ (0, 2)

𝑢(0, 𝑡) = 𝑢(2, 𝑡) = 0.

2 1 3
Then the value of 𝑒 𝜋 (𝑢 (2 , 1) − 𝑢 (2 , 1)) is __________ (in integer).

Page 13 of 100

Fluid Mechanics (XE-B)
XE-B: Q.22 – Q.30 Carry ONE mark Each

Q.22 Match the following measuring instruments with the appropriate figures.

I – Pitot probe

II – Pitot-static probe

III – Piezometer

(A) I – P; II – Q; III – R

(B) I – R; II – Q; III – P

(C) I – R; II – P; III – Q

(D) I – Q; II – P; III – R

Page 14 of 100

Q.23 Among the following non-dimensional numbers, which one characterizes periodicity
present in a transient flow?

(A) Froude number

(B) Strouhal number

(C) Peclet number

(D) Lewis number

Q.24 For an incompressible boundary layer flow over a flat plate shown in the figure, the
momentum thickness is expressed as

∞
(A) 𝑢
∫ 𝑑𝑦
0 𝑈∞

∞
(B) 𝑢
∫ (1 − ) 𝑑𝑦
0 𝑈∞

∞
(C) 𝑢 𝑢
∫ (1 − ) 𝑑𝑦
0 𝑈∞ 𝑈∞

∞
(D) 𝑢2
∫ (1 − 2
) 𝑑𝑦
0 𝑈∞

Page 15 of 100

Q.25 Among the shear stress versus shear strain rate curves shown in the figure, which one
corresponds to a shear thinning fluid?

(A) P

(B) Q

(C) R

(D) S

Page 16 of 100

Q.26 Consider steady incompressible flow over a flat plate, where the dashed line
represents the edge of the boundary layer, as shown in the figure. Which one among
the following statements is true?

(A) Bernoulli’s equation can be applied in Region I between any two arbitrary points.

(B) Bernoulli’s equation can be applied in Region I only along a streamline.

(C) Bernoulli’s equation cannot be applied in Region II.

(D) Bernoulli’s equation cannot be applied in Region I.

Page 17 of 100

Q.27 An inviscid steady incompressible flow is formed by combining a uniform flow with
velocity 𝑈∞ and a clockwise vortex of strength 𝐾 at the origin, as shown in the
figure. Velocity potential (𝜙) for the combined flow in polar coordinate (𝑟, 𝜃) is

(A) 𝐾𝜃
𝜙= − 𝑈∞ 𝑟 cos 𝜃
2𝜋

(B) 𝐾𝜃
𝜙= − 𝑈∞ 𝑟 sin 𝜃
2𝜋

(C) 𝜙 = 𝐾 ln 𝑟 + 𝑈∞ 𝑟 cos 𝜃

(D) 𝜙 = −𝐾 ln 𝑟 + 𝑈∞ 𝑟 sin 𝜃

Page 18 of 100

Q.28 Which of the following statements are true?

(i) Conservation of mass for an unsteady incompressible flow can be represented as
∇⋅𝑉⃗⃗ = 0, where 𝑉
⃗⃗ denotes velocity vector.

(ii) Circulation is defined as the line integral of vorticity about a closed curve.

(iii) For some fluids, shear stress can be a nonlinear function of the shear strain rate.

(iv) Integration of the Bernoulli’s equation along a streamline under steady-state
leads to the Euler’s equation.

(A) (i), (ii) and (iv) only

(B) (i), (ii) and (iii) only

(C) (i) and (iii) only

(D) (ii) and (iv) only

Q.29 For a two-dimensional flow field given as 𝑉 ⃗⃗ = −𝑥𝑖̂ + 𝑦𝑗̂, a streamline passes through
points (2, 1) and (5, p). The value of p is

(A) 5

(B) 5/2

(C) 2/5

(D) 2

Page 19 of 100

Q.30 A stationary object is fully submerged in a static fluid, as shown in the figure. Here,
CG and CB stand for center of gravity and center of buoyancy, respectively. Which
one(s) among the following statements is/are true?

(A) The object is in stable equilibrium if 𝑦𝐶𝐺 > 𝑦𝐶𝐵 .

(B) The object is in stable equilibrium if 𝑦𝐶𝐺 < 𝑦𝐶𝐵 .

(C) The object is in neutral equilibrium if 𝑦𝐶𝐺 = 𝑦𝐶𝐵 .

(D) The object is in unstable equilibrium if 𝑦𝐶𝐺 = 𝑦𝐶𝐵 .

Page 20 of 100

XE-B: Q.31 – Q.43 Carry TWO marks Each

Q.31 Consider steady fully-developed incompressible flow of a Newtonian fluid
between two infinite parallel flat plates. The plates move in the opposite
directions, as shown in the figure. In the absence of body force and pressure
gradient, the ratio of shear stress at the top surface (𝑦 = 𝐻) to that at the bottom
surface (𝑦 = 0) is

(A) 1

(B) 𝑈1
𝑈2

(C) 𝑈1 − 𝑈2
𝑈2

(D) 𝑈1 + 𝑈2
𝑈2

Page 21 of 100

Q.32 A two-dimensional incompressible flow field is defined as,

⃗⃗ (𝑥, 𝑦) = (𝐴𝑥𝑦) 𝑖̂ + (𝐵𝑦 2 ) 𝑗̂
𝑉

where, 𝐴 and 𝐵 are constants. The dynamic viscosity of the Newtonian fluid is 𝜇 .
In the absence of body force, which among the following expressions represents
the pressure gradient at the location (5, 0) in the concerned flow field?

(A) 𝜇𝐴(5 𝑖̂ + 𝑗̂)

(B) 𝜇(−5𝐵 𝑖̂ + 𝐴 𝑗̂)

(C) 𝜇𝐴(−𝑗̂)

(D) 𝜇𝐴(5 𝑖̂)

Q.33 ⃗⃗ (𝑥, 𝑦) = 𝑢𝑖̂ + 𝑣𝑗̂ . The slope
For a potential flow, the fluid velocity is given by 𝑉
of the potential line at (𝑥, 𝑦) is

(A) 𝑢
𝑣

(B) 𝑣
𝑢

(C) 𝑢
−
𝑣

(D) 𝑣
−
𝑢

Page 22 of 100

Q.34 Consider steady incompressible flow of a Newtonian fluid over a horizontal flat
plate, as shown in the figure. The boundary layer thickness is proportional to

(A) 𝑥1/4

(B) 𝑥1/2

(C) 𝑥 −1/2

(D) 𝑥2

Q.35 In a steady two-dimensional compressible flow, 𝑢 and 𝑣 are the 𝑥- and 𝑦-
components of flow velocity, respectively and 𝜌 is the fluid density. Among the
following pairs of relations, which one(s) perfectly satisfies/satisfy the definition
of stream function, 𝜓, for this flow?

(A) 𝜕𝜓 𝜕𝜓
𝑢= and 𝑣 = −
𝜕𝑦 𝜕𝑥

(B) 𝜕𝜓 𝜕𝜓
𝑢=− and 𝑣 = −
𝜕𝑥 𝜕𝑦

(C) 𝜕𝜓 𝜕𝜓
𝜌𝑢 = and 𝜌𝑣 = −
𝜕𝑦 𝜕𝑥

(D) 𝜕𝜓 𝜕𝜓
𝜌𝑢 = − and 𝜌𝑣 =
𝜕𝑦 𝜕𝑥

Page 23 of 100

Q.36 A water jet (density = 1000 kg/m3) is approaching a vertical plate, having an
orifice at the center, as shown in the figure. While a part of the jet passes through
the orifice, remainder flows along the plate. Neglect friction and assume both the
inlet and exit jets to have circular cross-sections. If V = 5 m/s, 𝐷 = 100 mm and
𝑑 = 25 mm, magnitude of the horizontal force (in N, rounded off to one decimal
place) required to hold the plate in its position is ___________.

Q.37 Water (density = 1000 kg/m3 ) and alcohol (specific gravity = 0.7) enter a
Y-shaped channel at flow rates of 0.2 m3 /s and 0.3 m3 /s, respectively. Their
mixture leaves through the other end of the channel, as shown in the figure. The
average density (in kg/m3 ) of the mixture is _______.

Page 24 of 100

Q.38 ⃗⃗ = (−𝑖̂ + 2𝑗̂) m/s
The velocity and acceleration of a fluid particle are given as 𝑉
2
and 𝑎⃗ = (−2𝑖̂ − 4𝑗̂) m/s , respectively. The magnitude of the component of
acceleration (in m/s2 , rounded off to two decimal places) of the fluid particle
along the streamline is _______.

Q.39 A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power
while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed
of
1500 rpm. Consider both turbines to operate with the same fluid (identical density
and viscosity), and neglect any gravitational effect. Then the power (in W,
rounded off to nearest integer) produced by the second turbine is
_______________.

Q.40 Water (density = 1000 kg/m3) flows steadily with a flow rate of 0.05 m3/s through
a venturimeter having throat diameter of 100 mm. If the pipe diameter is 200 mm
and losses are negligible, the pressure drop (in kPa, rounded off to one decimal
place) between an upstream location in the pipe and the throat (both at the same
elevation) is _______.

Q.41 Water flows around a thin flat plate (0.25 m long, 2 m wide) with a free stream
velocity (𝑈∞ ) of 1 m/s, as shown in the figure. Consider linear velocity profile
𝑢 𝑦
(𝑈 = 𝛿 ) for which the laminar boundary layer thickness is expressed as
∞
3.5𝑥
𝛿= . For water, density = 1000 kg/m3 and dynamic viscosity = 0.001
√𝑅𝑒𝑥
kg/m.s. Net drag force (in N, rounded off to two decimal places) acting on the
plate, neglecting the end effects, is ________.

Page 25 of 100

Q.42 Axial velocity profile 𝑢(𝑟) for an axisymmetric flow through a circular tube of
radius 𝑅 is given as,

𝑢(𝑟) 𝑟 1⁄𝑛
= (1 − )
𝑈 𝑅
where 𝑈 is the centerline velocity. If 𝑉 refers to the area-averaged velocity
(volume flow rate per unit area), then the ratio 𝑉/𝑈 for 𝑛 = 1 (rounded off to two
decimal places) is ______________.

Q.43 A stationary circular pipe of radius 𝑅 = 0.5 m is half filled with water (density =
1000 kg/m3 ), whereas the upper half is filled with air at atmospheric pressure, as
shown in the figure. Acceleration due to gravity is 𝑔 = 9.81 m/s2 . The magnitude
of the force per unit length (in kN/m, rounded off to one decimal place) applied by
water on the pipe section AB is _______.

Page 26 of 100

Material Science (XE-C)
XE-C: Q.44 – Q.52 Carry ONE mark Each

Q.44 In age-hardening of an aluminium alloy, the purpose of solution treatment
followed by quenching is to

(A) form martensitic structure

(B) increase the size of the precipitates

(C) form supersaturated solid solution

(D) form precipitates at the grain boundaries

Page 27 of 100

Q.45 The magnetization (M) – magnetic field (H) curves for four different materials are
given below. Which one of these materials is most suitable for use as a permanent
magnet?

M
(A)
3

1

0
1 3 H

(B) M
3

1

0
1 3 H

(C) M
3

1

0
1 3 H

M
(D)
3

1

0
1 3 H

Page 28 of 100

Q.46 The band gap of a semiconducting material is ~ 2 eV. Which one of the following
absorption (A) vs. energy (in eV) curves is correct?

(A)
90 %

A

1 2 3
Energy (eV)

(B)
90 %

A

1 2 3
Energy (eV)

(C)

A

10 %

1 2 3
Energy (eV)

(D)
90 %

A

1 2 3
Energy (eV)

Page 29 of 100

Q.47 Figures (i) and (ii) show a binary phase diagram and the corresponding Gibbs free
energy (𝐺) vs. composition (𝑋𝐵 ) diagram, respectively. Figure (ii) corresponds to
which one of the temperatures shown in Figure (i)?

(i) (ii)
T1

T2 G

T T3

T4

A B A B
XB XB

(A) T1

(B) T2

(C) T3

(D) T4

Page 30 of 100

Q.48 Aliovalent doping of 𝑀𝑔𝐶𝑙2 in 𝑁𝑎𝐶𝑙 leads to the formation of defects. Which one
of the following is the correct defect reaction?

(A)

(B)

(C)

(D)

𝑎
Q.49 A screw dislocation in a FCC crystal has Burgers vector of 2 [110], where 𝑎 is the
lattice constant. The possible slip plane(s) is/are:

(A) (111̅)

(B) (111)

(C) (1̅11)

(D) (11̅1)

Page 31 of 100

The tensile true stress (𝜎) – true strain (𝜖) curve follows the Hollomon equation:
Q.50
𝜎 = 500𝜖 0.15 MPa
𝑑𝜎
At the maximum load, the work-hardening rate ( 𝑑𝜖 ) is (in MPa):
_______________ (rounded off to nearest integer)

Q.51 A metal has a certain vacancy fraction at a temperature of 600 K. On increasing
the temperature to 900 K, the vacancy fraction increases by a factor of
______________ (rounded off to one decimal place)

Given: Gas constant, R = 8.31 J mol−1 K −1 and activation energy for vacancy
formation, Q = 68 kJ mol−1

Q.52 In a semiconductor, the ratio of electronic mobility to hole mobility is 10. The
density of electrons and holes are 1015 𝑚−3 and 1016 𝑚−3, respectively. If the
conductivity of the material is 1.6 Ω−1 𝑚−1, then the mobility of holes is
(in 𝑚2 𝑉 −1 𝑠 −1) : ____________ (rounded off to nearest integer)

Given: Charge of an electron: 1.6 × 10−19 𝐶

Page 32 of 100

XH-C: Q.53 – Q.65 Carry TWO marks Each

Q.53 A student performed X-ray diffraction experiment on a FCC polycrystalline pure
metal. The following 𝑠𝑖𝑛2 𝜃 values were calculated from the diffraction peaks.

𝑠𝑖𝑛2 𝜃 = 0.136, 0.185, 0.504, 0.544

However, the student was negligent and missed noting one of the peaks. Which
one of the following Miller indices corresponds to the missing peak?

(A) (200)

(B) (220)

(C) (311)

(D) (222)

Page 33 of 100

Q.54 Match the lattice planes and directions (in Column I) with the corresponding Miller
indices (in Column II):

Column I Column II

c

(P) 1. (1̅11)
b
a

c

(Q) 2. [1̅12]
b
a

c

(R) 3. [2̅21]
b
a
c

(S) 4. (1̅10)
b
a

(A) P-2, Q-4, R-1, S-3

(B) P-3, Q-1, R-4, S-2

(C) P-2, Q-4, R-3, S-1

(D) P-3, Q-4, R-2, S-1

Page 34 of 100

Q.55 Match the hardness test (in Column I) with its indenter type (in Column II).

Column I Column II

(P) Brinell 1. Diamond pyramidal

(Q) Rockwell 2. Diamond cone

(R) Vickers 3. Tungsten carbide sphere

4. Steel sphere

(A) P-2, Q-4, R-1

(B) P-4, Q-2, R-3

(C) P-3, Q-4, R-2

(D) P-4, Q-2, R-1

Page 35 of 100

Q.56 TTT diagram of a eutectoid steel is shown below. Match the heat treatment cycle (in
Column I) with its microstructure (in Column II).

Austenite
727

P
Temperature (oC)

R

Q

Time (s)

Column I Column II

P 1. Bainite only

Q 2. Pearlite only

R 3. Pearlite + Bainite + Martensite

4. Pearlite + Martensite

(A) P-1, Q-2, R-4

(B) P-2, Q-3, R-2

(C) P-2, Q-4, R-1

(D) P-2, Q-3, R-1

Page 36 of 100

Q.57 Which of the following statement(s) is/are true for an optical microscope?

(A) Increasing the aperture of the objective lens deteriorates the resolution

(B) Reducing the wavelength of illuminating light improves the resolution

(C) Increasing the refractive index of the medium in between the sample and the
objective lens improves the resolution

(D) Reducing the wavelength of illuminating light decreases the depth of field

Q.58 Among the 14 Bravais lattices, there is no base centred cubic unit cell. Which of
the following statement(s) is/are true?

(A) The base-centred cubic unit cell is same as the simple tetragonal unit cell

(B) The base-centred cubic unit cell is same as the body centred tetragonal unit cell

(C) The base-centred cubic unit cell is same as the simple orthorhombic unit cell

(D) The base-centred cubic unit cell does not have any 3-fold rotation axis

Page 37 of 100

Q.59 Specific heat (𝐶𝑣 ) of a material was found to depend on temperature as shown
below. Which of the following statement(s) is/are true?

(J kg-1 K-2)

(A) The material is metallic

(B) The material is insulating

(C) The material is three dimensional

(D) The material is one dimensional

Q.60 A pure Silicon wafer is doped with Boron by exposing it to B2O3 vapour at an
elevated temperature. It takes 1000 seconds to reach a Boron concentration of
1020 𝑎𝑡𝑜𝑚𝑠 𝑚−3 at a depth of 1 µm. The time taken to reach the same
concentration of Boron at a depth of 2 µm is (in seconds): _________ (rounded
off to nearest integer)

Given: Boron concentration on the wafer surface remains constant.

Q.61 The Young’s modulus of a quartz piezoelectric crystal is 100 GPa. The uniaxial
stress required to change its polarization by 1% is (give absolute value in GPa)
_________ (rounded off to nearest integer)

Page 38 of 100

Q.62 A one-dimensional nanowire has a linear electron density of 108 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑐𝑚−1.
The Fermi energy of the system is (in eV) ______ (rounded off to two decimal
places)

ℏ2
Given: = 0.24 (eV)2 s2 kg-1 where ‘m’ is the mass of an electron
2𝑚

Q.63 Two moles of a monoatomic ideal gas at 10 atm and 300 K is expanded
isothermally and reversibly to a pressure of 2 atm. The absolute value of work
done by the system is (in kJ) ____________ (rounded off to two decimal places)

Given: R = 8.31 J mol−1 K −1, 1 atm = 101 kPa

Q.64 An electrochemical cell consists of pure Zn electrode (anode) and a hydrogen
electrode (cathode) in a dilute Zn+2 solution. The overall reaction is:

Zn (s) + 2H+ = H2 + Zn+2

[𝑍𝑛+2 ]
If the overall cell potential is +0.690 V, then the value of 𝑙𝑛 is
[𝐻 + ]2
________ (rounded off to two decimal places)

Given: Pressure of hydrogen gas = 1 atm; Temperature = 298 K;
𝑅𝑇
= 0.0256 V, where R is gas constant and F is Faraday constant
𝐹

The standard reduction potential of:

Zn+2 + 2e = Zn (Eo = ̶ 0.762 V) versus Standard Hydrogen Electrode

2H+ + 2e = H2 (Eo = 0 V)

Page 39 of 100

Q.65 In a Raman spectroscopy experiment done at 300 K, a Raman line is observed at
200 𝑐𝑚−1 (~25 𝑚𝑒𝑉). The ratio of the intensity of the Stokes line to that of the
Anti-Stokes line is ____________ (rounded off to two decimal places)

Given: Boltzmann constant, k = 8.62 × 10−5 𝑒𝑉 𝐾 −1

Page 40 of 100

Solid Mechanics (XE-D)
XE-D: Q.66 – Q.74 Carry ONE mark Each

Q.66 A plane truss is simply supported at P and R as shown. A downward force F is
applied at hinge Q. The axial force developed in member PS is

(A) √5
𝐹 Tensile
2

(B) √5
𝐹 Compressive
2

(C) √5 𝐹 Tensile

(D) √5 𝐹 Compressive

Page 41 of 100

Q.67 A massless rigid rod OP of length L is hinged frictionlessly at O. A concentrated
mass m is attached to end P of the rod. Initially, the rod OP is horizontal. Then, it
is released from rest. There is gravity as shown. The rod acquires an angular
velocity as it swings. The clockwise angular velocity of the rod, when it first
reaches the vertical position as shown, is

(A) 𝑔
2√
𝐿

(B)
2𝑔
√
𝐿

(C) 𝑔
√
𝐿

(D) 1 𝑔
√
2 𝐿

Page 42 of 100

Q.68 Two equivalent descriptions of the state of stress at a point are shown in the
figure. The normal stresses 𝜎1 and 𝜎2 as shown on the right must be, respectively,

(A) 𝜏o and −𝜏o

(B) −𝜏o and 𝜏o

𝜏o 𝜏
(C) and − o
√2 √2

𝜏 𝜏o
(D) − o and
√2 √2

Q.69 The state of strain at a point in a machine component is given as

𝜀𝑥𝑥 = 2.5 × 10−4, 𝜀𝑦𝑦 = 2.0 × 10−4, 𝜀𝑧𝑧 = −1.5 × 10−4, 𝜀𝑥𝑦 = 2.5 × 10−4,

𝜀𝑦𝑧 = −0.5 × 10−4, 𝜀𝑧𝑥 = −1.0 × 10−4 . The volumetric strain at this point is

(A) 4 × 10−4

(B) 3 × 10−4

(C) −5 × 10−4

(D) −3 × 10−4

Page 43 of 100

Q.70 A thin walled, closed cylindrical vessel of inside diameter 𝑑 and wall thickness 𝑡
contains a fluid under pressure 𝑝. The figure below shows a part of the cylindrical
vessel; end caps are not shown. Consider the small element shown with sides
parallel and perpendicular to the axis of the cylinder. The stresses 𝜎1 and 𝜎2 are

(A) 𝑝𝑑 𝑝𝑑
𝜎1 = ; 𝜎2 =
2𝑡 4𝑡

(B) 𝑝𝑑 𝑝𝑑
𝜎1 = ; 𝜎2 =
𝑡 2𝑡

(C) 𝑝𝑑 𝑝𝑑
𝜎1 = ; 𝜎2 =
4𝑡 2𝑡

(D) 𝑝𝑑
𝜎1 = ; 𝜎 =0
2𝑡 2

Page 44 of 100

Q.71 A spring mass system is shown in the figure below. Take the acceleration due to
gravity as 𝑔 = 9.81 m/s2. The static deflection due to weight and the time period of
oscillations, respectively, are

(A) 0.392 m and 1.26 s

(B) 0.392 m and 3.52 s

(C) 0.626 m and 1.26 s

(D) 0.626 m and 3.52 s

Page 45 of 100

Q.72 A rod is subjected to three forces as shown in the figure on the left. An equivalent
force system with forces F1, F2 and moment M is shown in the figure on the right.
The value of M (in N-m) is______(rounded off to one decimal place).

Q.73 A simply supported beam of length 3 m is loaded as shown in the figure. The
magnitude of the shear force (in kN) at the mid-point of the beam
is______(rounded off to one decimal place).

Q.74 For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The
magnitude of maximum shear stress (in MPa) in the material is______(rounded
off to one decimal place).

Page 46 of 100

XE-D: Q.75 – Q.87 Carry TWO marks Each

Q.75 A solid uniform rigid disk of mass 𝑚 and radius 𝑅 rolls without slipping along a
horizontal surface PQ. The speed of the center of the disk is 𝑣. The disk then
3𝑅
strikes a hurdle of height 20 at point S. During the impact, there is no rebound or
slip at S and no impulse from the surface PQ. The magnitude of the velocity of the
center of the disk immediately after the impact is

(A) 0.1𝑣

(B) 0.3𝑣

(C) 0.7𝑣

(D) 0.9𝑣

Page 47 of 100

Q.76 A cylinder made of rubber (length = L and diameter = d) is inserted in a rigid
container as shown in the figure. The rubber cylinder fits snugly in the rigid
container. There is no wall friction. The modulus of elasticity of the rubber is E
and its Poisson’s ratio is ν. The cylinder is subjected to a small uniform pressure 𝑝
as shown in the figure. The resulting axial strain (𝜀𝑧𝑧 ) is

(A) 𝑝
−
𝐸

(B) 𝑝
− (1 − 2ν)
𝐸

(C) 𝑝 (1 + ν)(1 − 2ν)
− [ ]
𝐸 (1 − ν)

(D) 𝑝 (1 − ν)(1 − 2ν)
− [ ]
𝐸 (1 + ν)

Page 48 of 100

Q.77 The state of stress at the critical location in a structure is 𝜎𝑥𝑥 = 420 MPa,
𝜎𝑦𝑦 = 100 MPa, 𝜎𝑧𝑧 = 𝜎𝑥𝑦 = 𝜎𝑦𝑧 = 𝜎𝑧𝑥 = 0. The yield stress of the material in
uniaxial tension is 400 MPa. Select the correct statement among the following.

(A) The structure is safe by both Tresca (maximum shear stress) theory and von-Mises
(distortion energy) theory.

(B) The structure is safe by Tresca (maximum shear stress) theory and unsafe by
von-Mises (distortion energy) theory.

(C) The structure is unsafe by Tresca (maximum shear stress) theory and safe by
von-Mises (distortion energy) theory.

(D) The structure is unsafe by both Tresca (maximum shear stress) theory and
von-Mises (distortion energy) theory.

Page 49 of 100

Q.78 The figure shows a column of rectangular cross section 100 mm × 80 mm. It
carries a load of 60 kN at a point 30 mm from the edge 𝑃𝑄. The values of stress
component 𝜎𝑧𝑧 on surfaces 𝑃𝑄𝑄 ′ 𝑃′ and 𝑆𝑅𝑅 ′ 𝑆 ′ , at points far away from both
ends of the column, are respectively

(A) 18.75 N/mm2 (Compressive) and 3.75 N/mm2 (Tensile)

(B) 18.75 N/mm2 (Compressive) and 3.75 N/mm2 (Compressive)

(C) 13.13 N/mm2 (Compressive) and 1.88 N/mm2 (Tensile)

(D) 13.13 N/mm2 (Compressive) and 1.88 N/mm2 (Compressive)

Page 50 of 100

Q.79 Consider an electric pole with dimensions as shown in the figure. Let the end R be
subjected to a vertical force F. The flexural rigidity of both vertical and horizontal
bars is EI. Neglect the axial deflection of the vertical bar, and all effects of
self-weight. The vertical deflection at end R is

(A) 7𝐹𝐿3
3𝐸𝐼

(B) 10𝐹𝐿3
3𝐸𝐼

(C) 5𝐹𝐿3
3𝐸𝐼

(D) 8𝐹𝐿3
3𝐸𝐼

Page 51 of 100

Q.80 A uniform cantilever beam has flexural rigidity 𝐸𝐼 and length 𝐿. It is subjected to
a concentrated force 𝐹 and moment 𝑀 = 2𝐹𝐿 at the free end as shown. The
deflection (𝛿) at the free end is

(A) 11𝐹𝐿3
12𝐸𝐼

(B) 8𝐹𝐿3
9𝐸𝐼

(C) 4𝐹𝐿3
3𝐸𝐼

(D) 7𝐹𝐿3
6𝐸𝐼

Page 52 of 100

Q.81 A steel ball of mass 𝑚 = 10 kg is suspended from the ceiling of a moving carriage
by two inextensible strings making 60° with the horizontal as shown. The carriage
has an acceleration 𝑎 such that the tension in the string on the right is double the
tension in the string on the left. Take the acceleration due to gravity (g) as 10 m/s2.
The acceleration 𝑎 (in m/s2) is______(rounded off to one decimal place).

Q.82 A block of mass 𝑚 = 10 kg is lying on an inclined plane PQ. The mass is
restrained from sliding down the inclined plane by a force 𝐹. The coefficient of
friction between the block and the inclined plane is 0.3. Take the acceleration due
to gravity as 10 m/s2. The smallest force 𝐹 (in N) required to prevent the block
from sliding down is______(rounded off to one decimal place).

Page 53 of 100

Q.83 A spherical rigid ball of mass 10 kg is moving with a speed of 2 m/s in the
direction shown. The ball collides with a rigid frictionless wall and rebounds at an
angle 𝛼 with a speed of 𝑣, as shown. The coefficient of restitution is 0.9. The
angle 𝛼 (in degrees) is______(rounded off to one decimal place).

Q.84 A thin steel plate is loaded in the x-y plane as shown in the figure. Take the
Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200
GPa. The strain along the 𝑧-direction is 𝜀𝑧𝑧 = −3 × 10−4 . The value of 𝜎𝑦𝑦 (in
MPa) is______(rounded off to one decimal place).

Page 54 of 100

Q.85 A composite rod made of steel and copper is fixed immovably at its ends as shown
in the figure. The length of each portion of the rod is 1 m as shown. The
cross-sections of both portions are the same. The moduli of elasticity of steel and
copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal
expansion of steel and copper are 12 × 10−6 /℃ and 18 × 10−6 /℃, respectively.
The composite rod is initially stress free. Then, the temperature of the composite
rod is increased by 100 ℃. The magnitude of axial stress (in MPa) developed in
the steel rod is______(rounded off to one decimal place).

Q.86 A slender uniform elastic rod of length 1 m and of solid circular cross-section of
diameter 50 mm is originally straight. It is then loaded by equal and opposite end
moments as indicated in the figure. The resulting lateral displacement of the
mid-point of the rod is 10 mm (displacements are exaggerated in the figure). The
maximum longitudinal strain in the rod is 𝑝 × 10−3, where 𝑝 is______(rounded
off to one decimal place).

Q.87 Consider a solid cylindrical shaft and a hollow cylindrical shaft. Both shafts are
axisymmetric and elastic, and have the same cross-sectional area. The hollow
shaft has an outside diameter of 150 mm and an inside diameter of 120 mm. When
both the shafts are twisted by the same twisting moment, the ratio of maximum
shear stress developed in the hollow shaft (𝜏ℎ ) to maximum shear stress
developed in the solid shaft (𝜏𝑠 ) will be______(rounded off to three decimal

places).

Page 55 of 100

Thermodynamics (XE-E)
Q.88 – Q.96 Carry ONE mark Each

Q.88 A The number of properties required to fix the state of a system is given by
‘state postulate’.

R The state of a simple compressible system is completely specified by two
independent, intensive properties.

About the statements A and R applied to a single-phase system,

(A) A is correct and R is incorrect.

(B) A is incorrect and R is correct.

(C) Both A and R are incorrect.

(D) Both A and R are correct.

Q.89 Which of the following is an extensive property of a system?

(A) Density

(B) Pressure

(C) Temperature

(D) Total mass

Page 56 of 100

Q.90 A tank of volume V contains homogeneous mixture of two ideal gases, A and B at
a temperature T and a pressure P. The mixture contains nA moles of gas A and nB
moles of gas B. If PA and PB are the partial pressures of gas A and gas B,
respectively, then

(A) 𝑛𝐴 𝑛𝐵
𝑃𝐴 = 𝑃, 𝑃𝐵 = 𝑃
𝑛𝐴 + 𝑛𝐵 𝑛𝐴 + 𝑛𝐵

(B) 𝑛𝐵 𝑛𝐴
𝑃𝐴 = 𝑃, 𝑃𝐵 = 𝑃
𝑛𝐴 𝑛𝐵

(C) 𝑛𝐴 𝑛𝐵
𝑃𝐴 = 𝑃, 𝑃𝐵 = 𝑃
𝑛𝐵 𝑛𝐴

(D) 𝑛𝐵 𝑛𝐴
𝑃𝐴 = 𝑃, 𝑃𝐵 = 𝑃
𝑛𝐴 + 𝑛𝐵 𝑛𝐴 + 𝑛𝐵

Q.91 If an ideal air-standard Otto cycle and an ideal air-standard Diesel cycle operate
on the same compression ratio, then the relation between the thermal efficiencies
(ηth) of the cycles is

(A) 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜 = 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙 and 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜 < 1

(B) 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜 > 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙

(C) 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜 < 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙

(D) 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜 = 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙 = 1

Page 57 of 100

Q.92 The following statements are given:

(i) The third law of thermodynamics deals with the entropy of a substance
at the absolute zero temperature.
(ii) Entropy of any non-crystalline structure is zero at absolute zero
temperature.
(iii) At the absolute zero temperature, the crystal structure has maximum
degree of order.
(iv) The thermal energy of the substance at absolute zero temperature is
maximum.

The correct option describing these statements is

(A) Only (i) is correct

(B) Only (ii) is correct

(C) Both (i) and (iii) are correct

(D) Both (i) and (iv) are correct

Page 58 of 100

Q.93 Adiabatic bulk modulus of a substance is defined as

(A) 1 𝜕𝑣
− ( )
𝑣 𝜕𝑃 𝑇

(B) 𝜕𝑃
−𝑣 ( )
𝜕𝑣 𝑇

(C) 1 𝜕𝑣
− ( )
𝑣 𝜕𝑃 𝑠

(D) 𝜕𝑃
−𝑣 ( )
𝜕𝑣 𝑠

Q.94 An insulated rigid closed tank of 2 m3 internal volume contains saturated liquid-
vapor mixture of water at 200 ℃. The quality of the mixture is 0.75. The mass of
the mixture in the tank is ____________ kg (rounded off to one decimal place).

Use the following data for water:

At 200 ℃: vf = 0.001156 m3/kg, vfg = 0.12620 m3/kg, vg = 0.12736 m3/kg

Q.95 A rigid closed tank contains 2 kg of an ideal gas at 500 kPa and 350 K. A valve is
opened, and half of the mass of the gas is allowed to escape. Then the valve is
closed. If the final pressure in the tank is 300 kPa, the final temperature in the tank
is ____________ K (in integer).

Page 59 of 100

Q.96 Air at 400 K and 200 kPa is heated at constant pressure to 600 K. Assuming that
the internal energy is a function of temperature only, the magnitude of change in
internal energy during this process is ____________ kJ/kmol (rounded off to one
decimal place).

Use the following data:
Molar specific heat of air at constant volume: 𝑐̅𝑣 (kJ/kmol-K) = 𝑎 + 𝑏𝑇 + 𝑐𝑇 2
where 𝑇 is temperature in K, 𝑎 = 19.686 kJ/kmol-K, 𝑏 = 0.002 kJ/kmol-K2
and 𝑐 = 0.5 × 10−5 kJ/kmol-K3.

Page 60 of 100

XE-XE: Q.97 – Q.109 Carry TWO marks Each

Q.97 A rigid closed tank having a volume of 2 m3 contains 0.1 m3 of saturated liquid
water and 1.9 m3 of saturated water vapor at 100 kPa. Heat is transferred to the
tank until the final tank pressure reaches 2 MPa.

Following data for water is given:

At 100 kPa: vf = 0.001043 m3/kg, vg = 1.694 m3/kg,
uf = 417.33 kJ/kg, ug = 2506.06 kJ/kg
At 2 MPa: vf = 0.001177 m3/kg, vg = 0.09963 m3/kg,
uf = 906.42 kJ/kg, ug = 2600.26 kJ/kg

The magnitude of heat transfer in this process is

(A) 34670 kJ

(B) 55842 kJ

(C) 67906 kJ

(D) 77470 kJ

Page 61 of 100

Q.98 An ideal Diesel cycle has a compression ratio of 20 and cut-off ratio of 1.5. At the
beginning of the compression stroke, air is at 100 kPa, 300 K. Use the
cold-air-standard assumptions with property value cp = 1.005 kJ/kg-K. Assume
cp / cv = 1.4. For this cycle, the net work output per unit mass is

(A) 335 kJ/kg

(B) 395 kJ/kg

(C) 500 kJ/kg

(D) 165 kJ/kg

Q.99 A 5 kg metal block (cp = 0.5 kJ/kg-K) at 373 K is submerged into 10 kg of water
(cp = 4.2 kJ/kg-K) at 293 K in an insulated rigid container without spilling.
Assuming thermal equilibrium is reached, the approximate entropy change of the
universe is

(A) −0.565 kJ/K

(B) 0.073 kJ/K

(C) 0.642 kJ/K

(D) 0.963 kJ/K

Page 62 of 100

Q.100 Match the following:

Thermodynamic function/equation Expression
A1 Helmholtz function (a) B1 d ℎ𝑔 − ℎ𝑓
( (ln 𝑃)) =
d𝑇 𝑅𝑇 2
𝑠𝑎𝑡

A2 Gibbs function (g) B2 𝑢 − 𝑇𝑠
A3 T-ds equation B3 d𝑢 = 𝑇d𝑠 − 𝑃d𝑣
A4 Clapeyron-Clausius equation B4 ℎ − 𝑇𝑠

.

(A) A1→B2, A2→B4, A3→B1, A4→B3

(B) A1→B4, A2→B2, A3→B1, A4→B3

(C) A1→B2, A2→B4, A3→B3, A4→B1

(D) A1→B4, A2→B2, A3→B3, A4→B1

Q.101 A piston-cylinder device initially contains 1 m3 of air at 200 kPa and 25 ℃. Air
expands at constant pressure while a heater of 250 W is switched on for 10
minutes. There is a heat loss of 4 kJ during this process. Assuming air as an ideal
gas, the final temperature of air is ____________ ℃ (rounded off to one decimal
place).

Use the following data for air: R = 0.287 kJ/kg-K, cp = 1.005 kJ/kg-K

Page 63 of 100

Q.102 Steam at 2 MPa and 300 ℃ steadily enters a nozzle of inlet diameter of 20 cm.
Steam leaves the nozzle with a velocity of 300 m/s. The mass flow rate of steam
through the nozzle is 10 kg/s. Assume no work interaction and no change in
potential energy. If the heat loss from the nozzle per kg of steam is 3 kJ,
the exit enthalpy per kg of steam is ____________ kJ (rounded off to nearest
integer).

Use the following data for steam:
At 2 MPa and 300 ℃: v = 0.12551 m3/kg, h = 3024.2 kJ/kg

Q.103 A rigid tank of 2 m3 internal volume contains 5 kg of water as a saturated
liquid-vapor mixture at 400 kPa. Half of the mass of the saturated liquid in the
tank is drained-off while maintaining constant pressure of 400 kPa in the tank.
The final quality of the mixture remaining in the tank is ____________ (rounded
off to two decimal places).

Use the following data for water:
At 400 kPa: vf = 0.001084 m3/kg, vfg = 0.46138 m3/kg, vg = 0.46246 m3/kg

Q.104 Consider a spark ignition engine which operates on an ideal air-standard Otto
cycle. It uses a fuel which produces 44 MJ/kg of heat in the engine. If the engine
requires 40 mg of fuel to produce 1 kJ of work output, then the compression ratio
of the Otto cycle is ____________ (rounded off to two decimal places).

For the entire cycle, use cp / cv = 1.4

Q.105 A refrigerator operates on an ideal vapor compression cycle between the pressure
limits of 140 kPa and 800 kPa. The working fluid is the refrigerant R-134a. The
refrigerant enters the compressor as saturated vapor at 140 kPa and exits at 800
kPa and 60 ℃. It leaves the condenser as a saturated liquid at 800 kPa. The
coefficient of performance (COP) of the refrigerator is ____________ (rounded
off to two decimal places).

Use the following property data for R-134a:
At 140 kPa: hf = 27.06 kJ/kg, hg = 239.19 kJ/kg
At 800 kPa: hf = 95.48 kJ/kg, hg = 267.34 kJ/kg
At 800 kPa and 60 ℃: h = 296.82 kJ/kg

Page 64 of 100

Q.106 A steam power plant operates on a simple ideal Rankine cycle. The condenser
pressure is 10 kPa and the boiler pressure is 5 MPa. The steam enters the turbine
at 600 ℃. Mass flow rate of the steam is 50 kg/s. Neglecting the pump work, the
net power output of the plant is ____________ MW (rounded off to one decimal
place).

Use the following property data for water:

At 10 kPa:
hf = 191.81 kJ/kg, hfg = 2392.82 kJ/kg, hg = 2584.63 kJ/kg
sf = 0.6492 kJ/kg-K, sfg = 7.5010 kJ/kg-K, sg = 8.1502 kJ/kg-K

At 5 MPa and 600 ℃:
h = 3666.47 kJ/kg, s = 7.2588 kJ/kg-K

Q.107 In an air-conditioning system, air enters at 20 ℃ and 30% relative humidity at a
steady rate of 30 m3/min in a humidifier and it is conditioned to 25 ℃ and
60% relative humidity. Assuming entire process takes place at pressure of 100
kPa, the mass flow rate of the steam added to air in the humidifier
is ____________ kg/min (rounded off to three decimal places).

Use the following property data:

At 20 ℃ and 25 ℃, saturation pressures of water are 2.3392 kPa and
3.1698 kPa, respectively.

For air, R = 0.287 kJ/kg-K

Q.108 An office uses a heat pump to receive 500 kJ/day heat in winter to maintain its
temperature at 300 K. The ambient temperature is 280 K. If the COP of the heat
pump is 60% of its theoretical maximum value, the ratio of actual work input to
the minimum theoretical work input to the heat pump is ____________ (rounded
off to one decimal place).

Q.109 d𝑃
In a liquid-vapour phase change process, (d𝑇 ) at 100 C for saturated water is
𝑠𝑎𝑡
3750 Pa/K. If the resulting change in specific volume (𝑣𝑔 − 𝑣𝑓 ) is 1.672 m3/kg,
the enthalpy of vaporization (ℎ𝑓𝑔 ) will be ____________ kJ/kg (in integer).

Page 65 of 100

Polymer Science and Engineering (XE-F)
XE-F: Q.110 – Q.118 Carry ONE mark Each

Q.110 Which one of the monomers given is used in the synthesis of cellulose?

(A) Fructose

(B) Lactic acid

(C) Galactose

(D) Glucose

Q.111 A copper wire upon loading instantaneously increases in length to l, and then
continues to elongate gradually. Upon unloading, the wire retracts to length l.
According to the Maxwell model, which one of the options given correctly relates
the total strain E, the applied stress S, the modulus G, the material’s resistance to
flow ƞ, and the elapsed time t between loading and unloading?

(A) E = (S/G) – (S/ƞ)t

(B) E = (S/G) × (S/ƞ)t

(C) E = (S/G) + (S/ƞ)t

(D) E = (S/G) / (S/ƞ)t

Page 66 of 100

Q.112 Consider the structure of a crosslinked polymer shown in the figure. From the
options given, identify the monomers that are used in the synthesis of the polymer.

NH

N N

N N N
H H n

(A) Melamine and Benzaldehyde

(B) Melamine and Acetone

(C) Melamine and Formaldehyde

(D) Melamine and Ethanol

Q.113 Among the options given, choose the most suitable compatibilizer for blending
Polyvinylidene fluoride (PVDF) and Acrylonitrile butadiene styrene (ABS).

(A) Styrene-acrylonitrile (SAN)

(B) Polybutadiene (PB)

(C) Polymethyl methacrylate (PMMA)

(D) Nylon 6

Page 67 of 100

Q.114 A high molecular weight polymer passes through different zones from the hopper
to the die in an extruder. Among the options given, identify the correct match
between the zones and their key functions.

Zones Key functions

P Metering zone 1 High shear forces for effective
mixing

Q Compression zone 2 Receives the charge or feed

R Feed zone 3 Melts the charge or feed through
heat conducted by the heating
element

S Working zone 4 The charge or feed acquires a
constant flow rate imparted by the
helical flight of the screw

.

(A) P-4; Q-3; R-2; S-1

(B) P-3; Q-4; R-1; S-2

(C) P-4; Q-1; R-2; S-3

(D) P-3; Q-1; R-2; S-4

Page 68 of 100

Q.115 Polymer wetting is improved by the addition of fillers with functional groups. In a
typical case-study, natural-clay was modified with hydroxyl groups and
compounded with Nylon 6 along with an antioxidant. The resulting composite
exhibited poor mechanical properties. Which one among the options given
explains this observation?

(A) The surface functional groups of the filler reacted with Nylon 6

(B) The antioxidant degraded during the processing

(C) The surface functional groups of the filler formed hydrogen bonds with the
antioxidant

(D) The antioxidant reacted with Nylon 6

Page 69 of 100

Q.116 Among the options given, identify the correct match between the polymers and
their glass transition temperatures (Tg).

Polymer Glass transition temperature (°C)

P High density polyethylene 1 >200

Q Poly(vinyl carbazole) 2 145 to 155

R Polymethyl methacrylate 3 -100 to -80

S Polycarbonate 4 90 to 100

(A) P-2; Q-4; R-3; S-1

(B) P-3; Q-1; R-4; S-2

(C) P-3; Q-4; R-1; S-2

(D) P-4, Q-2; R-1; S-3

Page 70 of 100

Q.117 What is the correct order of decreasing crystallinity of the given polymers?

P atactic-Polypropylene

Q syndiotactic-Polystyrene

R Nylon 6

S Polyethylene terephthalate

(A) P>R>S>Q

(B) S>Q>P>R

(C) Q>S>R>P

(D) S>R>Q>P

Page 71 of 100

Q.118 Choose the correct option that best correlates the graphs with the polymerization
methods.

(A) P – living polymerization; Q – chain growth; R – step growth

(B) P – chain growth; Q – living polymerization; R – step growth

(C) P – step growth; Q – living polymerization; R – chain growth

(D) P – living polymerization; Q – step growth; R – chain growth

Page 72 of 100

XE-F: Q.119 – Q.131 Carry TWO marks Each

Q.119 From the options given, identify the correct match(es) between the polymer
products with the most appropriate processing technique.

Polymer product Processing technique

P Fishing rods 1 Compression moulding

Q Soft drink bottles 2 Thermoforming

R Plastic sheets 3 Pultrusion

S Plastic trays 4 Blow moulding

(A) P-3; Q-4; R-1; S-2

(B) P-3; Q-2; R-1; S-4

(C) P-1; Q-2; R-3; S-4

(D) P-3; Q-4; R-1; S-1

Q.120 Among the options given, which agents are used to vulcanize or cure rubbers?

(A) Dicumyl peroxide

(B) Zinc stearate

(C) Carbon black

(D) Dinitrobenzene

Page 73 of 100

Q.121 Lipase is a natural enzyme, which cleaves carboxylic ester bonds. Among the
options given, identify the polymer(s) degraded by lipase.

(A) Polypropylene (PP)

(B) Polycaprolactone (PCL)

(C) Polyvinylidene fluoride (PVDF)

(D) Polyethylene terephthalate (PET)

Q.122 Among the options given, identify the correct pair(s) of catalyst and co-catalyst
that form a Ziegler-Natta catalyst.

(A) TiCl3 and Al(CH3CH2)2Cl

(B) ZnCl2 and Al(CH3)3

(C) TiO2 and Al(CH3)3

(D) VCl4 and Al(CH3CH2)2Cl

Page 74 of 100

Q.123 Mechanical stress is applied on a polymer. Identify the correct match(es)
between the statements (1, 2, 3, 4, 5) that describe the deformations and
the regimes (P, Q, R).

P Rubbery regime 1 Stress-relaxation takes place and the excess
free energy is dissipated

Q Region around 2 The motions of the molecules are long-
glass transition range
temperature (Tg)

R Sample under 3 Segmental motion of the molecules is
deformed state important

4 The maximum relaxation time is strongly
dependent on the molecular weight

5 The deformations are independent of the
molecular weight and primarily depend on
the local structure

(A) P-2; Q-5; R-1

(B) P-1; Q-5; R-1

(C) P-2; Q-3; R-4

(D) P-4; Q-3; R-1

Page 75 of 100

Q.124 Stress versus elongation profiles for different polymeric materials are shown in the
figure. Choose the combination that best describes these profiles.

(A) 1-Nylon fibers; 2-Polyethylene; 3-Vulcanized rubber; 4-Polystyrene

(B) 1-Polyethylene; 2-Vulcanized rubber; 3-Polystyrene; 4-Nylon fibers

(C) 1-Polystyrene; 2-Nylon fibers; 3-Polyethylene; 4-Vulcanized rubber

(D) 1-Vulcanized rubber; 2-Polyethylene; 3-Nylon fibers; 4-Polystyrene

Q.125 Among the options given, which method(s) is/are used for the synthesis of atactic
polystyrene?

(A) Free radical polymerization

(B) Ring opening polymerization

(C) Polycondensation

(D) Ionic polymerization

Page 76 of 100

Q.126 A nylon sample of 0.03 m2 cross-sectional area is subjected to a creep load of
10 kN. The load is removed after a duration of 60 s. Young’s modulus and the
viscosity for nylon are 1 GPa and 300 Giga Poise. The compliance of the
specimen is ________×10-9 m2/N. (Answer in integer)

Q.127 Polyvinylidine fluoride (PVDF) was quenched from the melt in one case and in
the other case, it was slowly cooled from the melt at 10 °C/min. The percentage
crystallinity of the slowly cooled PVDF is 60%. The heat of fusion for the
quenched PVDF is 0.5ΔHm (ΔHm is the heat of fusion for the slowly cooled
PVDF), and the heat of fusion for 100% crystalline PVDF is 100 J/g. The
percentage crystallinity of the quenched PVDF is ______%. (Answer in integer)

Q.128 A polymeric material of density 0.9 g/cc and melt volume of 10 cc in an extruder
has a residence time of 100 s. The output of the extruder is _____ kg/h.
(Rounded off to two decimal places)

Q.129 A polymer weighing 0.2 g is dissolved in 100 ml of benzene and has a relative
viscosity of 1.5. The polymer obeys Mark-Houwink equation with constants
a = 0.5 and K = 0.001. The molecular weight of the polymer is _____ ×1010 g/mol.
(Rounded off to two decimal places)

Q.130 A continuous and aligned glass-fiber reinforced composite consists of 40 vol% of
glass-fiber having a modulus of elasticity of 69 GPa and 60 vol% of a polyester
resin, which when hardened, displays a modulus of 3.4 GPa. The modulus of
elasticity of this composite in the longitudinal direction is___________GPa.
(Rounded off to two decimal places)

Page 77 of 100

Q.131 The molar mass distribution of a polymer is

Number of molecules Molar mass (g/mol)

100 7500

50 5000

The resulting weight average molecular weight of the polymer is _______ g/mol.
(Answer in integer)

Page 78 of 100

Food Technology (XE-G)
XE-G: Q.132 – Q.140 Carry ONE mark Each

Q.132 Choose the correct group of fat soluble vitamins

(A) Cholecalciferol, α-Tocopherol, Menadione

(B) Thiamine, Cholecalciferol, α-Tocopherol

(C) Niacin, α-Tocopherol, Menadione

(D) Biotin, Thiamin, Niacin

Q.133 The synthesis of thyroxine T4 in human body requires

(A) Selenium

(B) Iodine

(C) Iron

(D) Zinc

Page 79 of 100

Q.134 Which among the followings is NOT an essential amino acid?

(A) L-Phenylalanine

(B) L-Valine

(C) L-Lysine

(D) L-Arginine

Q.135 The time required for stipulated destruction of a microbial population at a given
temperature is

(A) D-value

(B) F-value

(C) z-value

(D) Q10 value

Page 80 of 100

Q.136 Which among the following statements is NOT correct?

(A) Cod fish is a major source of ω-3 fatty acids.

(B) Beetroot is a good source of β-carotene.

(C) Apple is a good source of vitamin B12.

(D) Fresh sugarcane juice is a good source of polyphenol oxidase.

Q.137 Which of the following statements is NOT correct?

(A) As the shear rate increases, the apparent viscosity decreases for a pseudoplastic
fluid.

(B) As the shear rate increases, the apparent viscosity increases for a dilatant fluid.

(C) A Bingham fluid requires application of yield stress prior to any response.

(D) Rheopectic and thixotropic are two time independent fluids.

Page 81 of 100

Q.138 Calculate the efficiency in percent (rounded off to 1 decimal place) of an oil
expeller which yields 37 kg oil containing 5% solid impurities from 100 kg
mustard seeds. The oil content of the mustard seed is 38%.

Q.139 Orange juice is packaged aseptically and stored under ambient conditions. The
degradation of vitamin C in the juice occurs during storage and it follows first
order reaction kinetics. The degradation rate constant is 5.2×10-3 day-1. The half-
life of vitamin C in days is ____________ (in integer).

Q.140 The weight of 10 kg dried cauliflower containing 5% moisture (wet basis) after
rehydration is 60 kg. If the fresh cauliflower contained 87% moisture (wet basis),
calculate the coefficient of rehydration (rounded off to 2 decimal places).

Page 82 of 100

XE-G: Q.141 – Q.153 Carry TWO marks Each

Q.141 Match the industrial product in Column I with fermentative organism in Column
II.

Column I Column II

P. Vinegar 1. Enterbacter aerogenes

Q. Citric acid 2. Saccharomyces cerevisiae

R. Ethanol 3. Acetobacter aceti

S. L-Lysine 4. Aspergillus niger

(A) P-3, Q-4, R-2, S-1

(B) P-1, Q-3, R-2, S-4

(C) P-3, Q-1, R-4, S-2

(D) P-2, Q-1, R-3, S-4

Page 83 of 100

Q.142 Match the enzyme in Column I with its application in food processing/reaction
given in Column II.

Column I Column II

P. Chymosin 1. Acyl glycerol restructuring

Q. Thermolysin 2. Lactose hydrolysis

R. β-Galactosidase 3. Aspartame synthesis

S. Lipase 4. Cheese manufacturing

(A) P-4, Q-3, R-2, S-1

(B) P-3, Q-1, R-2, S-4

(C) P-4, Q-2, R-3, S-1

(D) P-1, Q-4, R-2, S-3

Page 84 of 100

Q.143 Identify the Gram +ve bacteria responsible for causing food borne diseases among
the followings

(A) Campylobacter jejuni

(B) Clostridium botulinum

(C) Vibrio cholerae

(D) Salmonella typhi

Q.144 Extrusion cooking is accomplished in four different stages, which are indicated as
I, II, III and IV in the figure given below. Choose the correct option representing
the name of each stage.

Te
m
pe
rat III
ur
e/ IV
II
Pr I
ess
ur
e Extrusion cooking stages

(A) I – Feeding, II – Cooking, III – Kneading, IV – Expansion

(B) I – Kneading, II – Feeding, III – Cooking, IV – Expansion

(C) I – Feeding, II – Kneading, III – Cooking, IV – Expansion

(D) I – Cooking, II – Kneading, III – Feeding, IV – Expansion

Page 85 of 100

Q.145 Match the method/ value used for measuring lipid characteristics in Column I with
the corresponding properties indicated by them, in Column II.

Column I Column II

P. Thiobarbituric acid test 1. Induction time

Q. Rancimat method 2. Degree of unsaturation

R. Peroxide value 3. Carbonyl content

S. Iodine value 4. Hydroperoxide content

(A) P-3, Q-1, R-4, S-2

(B) P-1, Q-3, R-4, S-2

(C) P-3, Q-1, R-2, S-4

(D) P-3, Q-4, R-1, S-2

Page 86 of 100

Q.146 Match the peeling technique in Column I with the vegetable, for which it is used
in industry, given in Column II.

Column I Column II

P. Knife peeling 1. Brinjal

Q. Abrasion peeling 2. Tomato

R. Flame peeling 3. Potato

S. Flash peeling 4. Cucumber

(A) P-3, Q-4, R-1, S-2

(B) P-4, Q-1, R-3, S-2

(C) P-4, Q-3, R-2, S-1

(D) P-4, Q-3, R-1, S-2

Page 87 of 100

Q.147 Match the process in Column I with the related food component in Column II.

Column I Column II

P. Caramelization 1. Lipid

Q. Denaturation 2. Sugar

R. Oxidation 3. Pigment

S. Bleaching 4. Enzyme

(A) P-2, Q-4, R-1, S-3

(B) P-2, Q-1, R-4, S-3

(C) P-1, Q-3, R-2, S-4

(D) P-2, Q-1, R-3, S-4

Page 88 of 100

Q.148 Identify the correct statement(s) related to grain polysaccharides among the
followings.

(A) Dextrin are a group of low molecular weight polysaccharides produced by dry
hydrolysis of starch.

Amylose is a linear polymer of D-glucose units joined by α (1→6) glycoside
(B)
linkages.

(C) Amylopectin is a branched chain polymer of D-galactose monomer units.

Retrogradation is a process of reassociation of amylose and formation of
(D)
crystalline structure by gelatinized starch upon cooling.

Q.149 Identify the correct pair(s) of governing law with respective process operation.

(A) Stoke’s law - Mass transfer

(B) Kirchhoff’s law - Radiation heat transfer

(C) Fourier’s law –Conduction heat transfer

(D) Fick’s law - Molecular diffusion

Q.150 A hammer mill is used to grind blackgram. The size distribution of the blackgram
is such that 80% passes through a 6-mesh (particle size = 3.36 mm) screen. The
power requirement to produce a powder, 80% of which passes through a 45-mesh
(particle size = 0.354 mm) screen is 4.5 kW. The power in kW required to produce

a finer powder 80% of which passes through a 60-mesh (particle size = 0.25 mm)
will be ____________ (rounded off to 2 decimal places). Assume the feed rate to
the mill is constant in both the cases. Use Bond’s law of size reduction.

Page 89 of 100

Q.151 If D10 for Salmonella in egg yolk is 0.75 kGy, calculate the radiation dose in kGy
(rounded off to 2 decimal places) required for reducing the Salmonella count in
egg yolk by 8 log cycles.

Q.152 The average moisture binding energy of a plant protein based snack at 8%
moisture content (dry basis) is 3200 cal.mol-1. If the water activity of the snack at
the above moisture content is 0.30 at 30 ℃, the water activity of the sample at 45
℃ is _____________ (rounded off to 2 decimal places). The value of Gas
constant R = 1.987 cal.mol-1.K-1.

Q.153 Cow milk is pasteurized at a flow rate of 1 kg.s-1 in a counter-current heat
exchanger using hot water as the heating medium. The milk enters the heat
exchanger at 15 ℃ and exits at 50 ℃. The specific heat of cow milk is 3.5 kJ.kg-
1
.℃-1 and remains constant at the inlet and exit of the heat exchanger. The inlet
and exit temperatures of the hot water are 75 ℃ and 60 ℃ respectively. If the
overall heat transfer coefficient is 1800 W.m-2.℃-1, the heat transfer surface area
in m2 is ______ (rounded off to 2 decimal places). Assume steady state conditions.

Page 90 of 100

Atmospheric and Ocean Science (XE-H)
XE-H: Q.154 – Q.162 Carry ONE mark Each

Q.154 The net water level elevation near the coast arising due to a tropical-cyclone-
induced storm is a combination of the following factors _________.

(A) astronomical tides, and distant cyclonic storm

(B) wind-induced waves, astronomical tides, and distant cyclonic storm

(C) astronomical tides, coastal currents, and distant cyclonic storm

(D) riverine flow, astronomical tides, and distant cyclonic storm

Q.155 The typical speeds of a tsunami wave in water depths of 10 m, 100 m, and 1000
m, respectively, are ________.

(A) approximately 100 m s-1, 31 m s-1 and 10 m s-1

(B) approximately 50 m s-1, 75 m s-1 and 100 m s-1

(C) approximately 10 m s-1, 31 m s-1 and 100 m s-1

(D) approximately 100 m s-1, 10 m s-1 and 31 m s-1

Page 91 of 100

Q.156 Which classification of tides best represents the west coast of India?

(A) Diurnal and Mixed

(B) Semidiurnal and Mixed

(C) only Diurnal

(D) only Mixed

Q.157 The variation in geostrophic winds with height, in particular, at the atmospheric
boundary layer, considering the variation in pressure gradient as a function of
height, is referred to as __________.

(A) Isallobaric winds

(B) Gradient winds

(C) Thermal winds

(D) Cyclostrophic winds

Q.158 Consider the following options and pick out the right choice. The solubility of a
gas in sea water increases with ________.

(A) the increase of temperature, salinity and pressure

(B) the decrease of temperature, salinity and pressure

(C) the increase of temperature, and the decrease of salinity and pressure

(D) the decrease of temperature and salinity, and the increase of pressure

Page 92 of 100

Q.159 From the list given below, identify the organism type in the biological pump that
takes up carbon dioxide from the atmosphere into the ocean.

(A) Zooplankton

(B) Fish

(C) Phytoplankton

(D) Radiolarians

Q.160 The amount of CO2 that can be absorbed _______ when the temperature of
seawater decreases.

(A) Remains the same

(B) Increases

(C) Decreases

(D) Can either increase or decrease

Q.161 Which among the following gases has the highest global warming potential?

(A) CO2

(B) Water vapor

(C) Methane

(D) N2O

Page 93 of 100

Q.162 What will happen to the speed of a balanced flow as one moves across the isobar
along a particular latitude?

(A) The speed changes for a geostrophic flow and remains constant for a cyclostrophic
flow

(B) The speed remains constant for a geostrophic flow and changes for a cyclostrophic
flow

(C) The speed remains constant for both (geostrophic and cyclostrophic) types of flow

(D) The speed changes for both (geostrophic and cyclostrophic) types of flow

Page 94 of 100

XE-H: Q.163 – Q.175 Carry TWO marks Each

Q.163 The following illustration depicts the circulation pattern in the North Indian Ocean
during the southwest (June-August) monsoon. Identify the markers numbered
from 1-5 in the illustration and pick out the right choice.

(A) 1. Great Whirl, 2. East India Coastal Current, 3. East African Coastal Current, 4.
Summer (Southwest) Monsoon Current, and 5. West India Coastal Current.

(B) 1. East African Coastal Current, 2. Summer (Southwest) Monsoon Current, 3.
Great Whirl, 4. South Equatorial Counter Current, and 5. East India Coastal
Current.

(C) 1. Great Whirl, 2. Summer (Southwest) Monsoon Current, 3. West India Coastal
Current, 4. Somali Current, and 5. East India Coastal Current.

(D) 1. East African Coastal Current, 2. West India Coastal Current, 3. Somali Current,
4. East India Coastal Current, and 5. South Equatorial Counter Current.

Page 95 of 100

Q.164 From the following list identify the region that has low chlorophyll and low
nutrients.

(A) Upwelling, anticyclonic eddy

(B) Upwelling, cyclonic eddy

(C) Downwelling, anticyclonic eddy

(D) Downwelling, cyclonic eddy

Q.165 Match the following physical phenomena from the perspective of monsoonal
circulation:

Column-1 Column-2
a) Reversal of East-West temperature i) Over the tropics
gradient with seasons
b) Reversal of North-South ii) Indian Ocean
temperature gradient with seasons
c) Surface cooling and deepening of iii) Over mid-latitudes
mixed layer
d) Northward movement of south iv) Arabian Sea
equatorial current

(A) a-i, b-iii, c-ii, d-iv

(B) a-iii, b-i, c-iv, d-ii

(C) a-iii, b-ii, c-iv, d-i

(D) a-ii, b-i, c-ii, d-iv

Page 96 of 100

Q.166 Choose the correct statement(s) in context to Ekman spiral from the following:

(A) The balance of Coriolis force and pressure

(B) The balance of Coriolis force, wind shear, and frictional force

(C) Deflection of surface current to the right of the wind direction in the Northern
hemisphere

(D) The increase of current velocity with depth

Q.167 Which of the following is/are associated with winter rainfall over India?

(A) Northeast monsoon

(B) Southwest monsoon

(C) Western disturbances

(D) Agulhas Current

Q.168 If the global albedo is increased from 0.3 to 0.4, the global radiative equilibrium
temperature (in K) would decrease by ________.

(consider no greenhouse effect, solar constant = 1360 W m-2 and Stefan-
Boltzmann constant = 5.67 × 10-8 W m-2 K-4, rounded off to one decimal place).

Page 97 of 100

Q.169 When a parcel of dry air rises at a rate of 2 cm s -1 vertically, what should be the
rate of heating per unit mass in J s-1 kg-1 (due to the radiation, conduction, etc.) in
order to maintain the air parcel at a constant temperature?

(consider the acceleration due to gravity as 9.8 m s-2, rounded off to three decimal
places).

Q.170 Two balls each of 5 cm in diameter are placed 200 m apart on a horizontal
frictionless plane at 45º N. The balls are impulsively propelled directly at each
other with equal speeds. What must be the speed in m s-1 so that the two balls just
miss each other?

(consider the value of Ω as 7.29 × 10-5 rad s-1, rounded off to two decimal places).

Q.171 A parcel of dry air having an initial temperature of 30 ºC at 1000 hPa level is
lifted adiabatically. At what pressure (in hPa) its density reduces by half?

(consider the ratio of the specific heat of dry air at a constant pressure to the
specific heat of dry air at a constant volume, Cp/Cv = 0.71, rounded off to two
decimal places).

Page 98 of 100

Q.172 A cylindrical tank containing water is rotating about the z-axis at a constant
angular velocity of 10 rad s-1. The schematic of the isobaric surface is shown in
the following illustration, where ‘A’ and ‘B’ are two points on the isobaric surface
at heights ‘z1 ’ and ‘z2 ’, respectively. Assuming the atmospheric pressure to be
negligible and no transient flow, estimate the elevation difference in m between
‘z1 ’ and ‘z2 ’.

(consider r1 = 0.5 m, r2 = 1.0 m and gravitational acceleration g = 9.8 m s-2,
rounded off to two decimal places)

Q.173 Consider that there are 295 million vehicles across India and they drive about
12000 km yr-1. Each vehicle consumes about 25 km lit-1 of petrol and the amount
of carbon released per litre is 5.5 gm. What is the amount of carbon emitted into
the atmosphere in mega ton per year (rounded off to two decimal places)?

Q.174 Consider the two parallel isobars separated by a spacing of 250 km at 30º N
(air density = 0.70 kg m-3, 2Ω = 14.6×10-5 rad s-1) with a pressure gradient of 5

hPa. Calculate the geostrophic velocity in m s-1 (rounded off to two decimal
places).

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Q.175 Considering a gyre system in the following illustration (where ‘L’ and ‘H’
represent low- and high-pressure regions along 45º N), the average slope between
the points ‘A’ and ‘B’ is 2.1 cm km-1 under no wind condition. For a steady
southerly wind of 10 m s-1 over these regions, find out the magnitude of the
current velocity in m s-1 (rounded off to two decimal places).

END OF QUESTION PAPER

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