GATE 2024 Question Paper for Chemical Engineering (CH)

GATE
2024
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

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

Q.1 If ‘→’ denotes increasing order of intensity, then the meaning of the words

[simmer → seethe → smolder] is analogous to [break → raze → ________ ].

Which one of the given options is appropriate to fill the blank?

(A) obfuscate

(B) obliterate

(C) fracture

(D) fissure

Page 1 of 38

Q.2 In a locality, the houses are numbered in the following way:

The house-numbers on one side of a road are consecutive odd integers starting from
301, while the house-numbers on the other side of the road are consecutive even
numbers starting from 302. The total number of houses is the same on both sides of
the road.

If the difference of the sum of the house-numbers between the two sides of the road
is 27, then the number of houses on each side of the road is

(A) 27

(B) 52

(C) 54

(D) 26

Q.3 𝑝 𝑝
𝑝 𝑝 𝑞 ( −1)
For positive integers 𝑝 and 𝑞 , with ≠ 1 , ( ) = 𝑝 𝑞 . Then,
𝑞 𝑞

(A) 𝑞 𝑝 = 𝑝𝑞

(B) 𝑞𝑝 = 𝑝2𝑞

(C) √𝑞 = √𝑝

𝑝 𝑞
(D) √𝑞 = √𝑝

Page 2 of 38

Q.4 Which one of the given options is a possible value of x in the following sequence?

3, 7, 15, x, 63, 127, 255

(A) 35

(B) 40

(C) 45

(D) 31

Q.5 On a given day, how many times will the second-hand and the minute-hand of a
clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

(A) 51

(B) 49

(C) 50

(D) 55

Page 3 of 38

Q.6 – Q.10 Carry TWO marks Each

Q.6 In the given text, the blanks are numbered (i)−(iv). Select the best match for
all the blanks.

From the ancient Athenian arena to the modern Olympic stadiums,
(i) (ii)
athletics the potential for a spectacle. The crowd with bated
breath as the Olympian artist twists his body, stretching the javelin behind him.
(iii)
Twelve strides in, he begins to cross-step. Six cross-steps in an abrupt
(iv)
stop on his left foot. As his body like a door turning on a hinge, the
javelin is launched skyward at a precise angle.

(A) (i) hold (ii) waits (iii) culminates (iv) pivot

(B) (i) holds (ii) wait (iii) culminates (iv) pivot

(C) (i) hold (ii) wait (iii) culminate (iv) pivots

(D) (i) holds (ii) waits (iii) culminate (iv) pivots

Page 4 of 38

Q.7 Three distinct sets of indistinguishable twins are to be seated at a circular table that
has 8 identical chairs. Unique seating arrangements are defined by the relative
positions of the people.

How many unique seating arrangements are possible such that each person is sitting
next to their twin?

(A) 12

(B) 14

(C) 10

(D) 28

Page 5 of 38

Q.8 The chart given below compares the Installed Capacity (MW) of four power
generation technologies, T1, T2, T3, and T4, and their Electricity Generation
(MWh) in a time of 1000 hours (h).

Installed Capacity Electricity Generation
14000 70
13000 65
12000 60
Electricity Generation (MWh)

11000 55

Installed Capacity (MW)
10000 50
9000 45
8000 40
7000 35
6000 30
5000 25
4000 20
3000 15
2000 10
1000 5
0 0
T1 T2 T3 T4
Power Generation Technology

The Capacity Factor of a power generation technology is:

Electricity Generation (MWh)
Capacity Factor =
Installed Capacity (MW) × 1000 (h)

Which one of the given technologies has the highest Capacity Factor?

(A) T1

(B) T2

(C) T3

(D) T4

Page 6 of 38

Q.9 In the 4 × 4 array shown below, each cell of the first three columns has either a
cross (X) or a number, as per the given rule.

Rule: The number in a cell represents the count of crosses around its immediate
neighboring cells (left, right, top, bottom, diagonals).

As per this rule, the maximum number of crosses possible in the empty column is

(A) 0

(B) 1

(C) 2

(D) 3

Page 7 of 38

Q.10 During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the
Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio
of the Earth-Sun and Earth-Moon distances is closest to

(A) 328

(B) 382

(C) 238

(D) 283

Page 8 of 38

Q.11 – Q.35 Carry ONE mark Each

Q.11 The first non-zero term in the Taylor series expansion of (1 − 𝑥) − 𝑒 −𝑥
about 𝑥 = 0 is

(A) 1

(B) −1

(C) 𝑥2
2

(D) 𝑥2
−
2

Q.12 Consider the normal probability distribution function

4 2
𝑓(𝑥) = 𝑒 −8(𝑥+3)
√2𝜋
If 𝜇 and 𝜎 are the mean and standard deviation of 𝑓(𝑥) respectively, then the
ordered pair (𝜇, 𝜎) is

(A) 1
(3, 4)

(B) 1
(−3, 4)

(C) (3, 4)

(D) (−3, 4)

Page 9 of 38

Q.13 If 𝑧1 = −1 + 𝑖 and 𝑧2 = 2𝑖, where 𝑖 = √−1, then Arg(𝑧1 ⁄𝑧2 ) is

(A) 3𝜋
4

(B) 𝜋
4

(C) 𝜋
2

(D) 𝜋
3

Page 10 of 38

Q.14 A homogeneous azeotropic distillation process separates an azeotropic AB binary
feed using a heavy entrainer, E, as shown in the figure. The loss of E in the two
product streams is negligible so that E circulates around the process in a closed-
circuit. For a distillation column with fully specified feed(s), given operating
pressure, a single distillate stream and a single bottoms stream, the steady-state
degrees of freedom equals 2. For the process in the figure with a fully specified AB
feed stream and given column operating pressures, the steady-state degrees of
freedom equals

(A) 3

(B) 4

(C) 5

(D) 6

Page 11 of 38

Q.15 An infinitely long cylindrical water filament of radius 𝑅 is surrounded by air.
Assume water and air to be static. The pressure outside the filament is 𝑃out and the
pressure inside is 𝑃in . If γ is the surface tension of the water-air interface, then
𝑃in − 𝑃out is

2𝛾
(A) 𝑅

(B) 0

(C) 𝛾
𝑅

(D) 4𝛾
𝑅

Q.16 ̂ , where 𝒊̂, 𝒋̂ and
The velocity field in an incompressible flow is 𝒗 = 𝛼𝑥𝑦𝒊̂ + 𝑣𝑦 𝒋̂ + 𝛽𝒌
̂ are unit-vectors in the (𝑥, 𝑦, 𝑧) Cartesian coordinate system. Given that 𝛼 and 𝛽
𝒌
are constants, and 𝑣𝑦 = 0 at 𝑦 = 0, the correct expression for 𝑣𝑦 is

(A) −𝛼𝑥𝑦
2

(B) −𝛼𝑦 2
2

(C) 𝛼𝑦 2
2

(D) 𝛼𝑥𝑦
2

Page 12 of 38

Q.17 Consider the steady, uni-directional diffusion of a binary mixture of 𝐴 and 𝐵 across
a vertical slab of dimensions 0.2 m × 0.1 m × 0.02 m as shown in the figure. The
total molar concentration of 𝐴 and 𝐵 is constant at 100 mol m−3 . The mole fraction
of 𝐴 on the left and right faces of the slab are maintained at 0.8 and 0.2, respectively.
If the binary diffusion coefficient 𝐷𝐴𝐵 = 1 × 10−5 m2 s−1 , the molar flow rate of 𝐴
in mol s−1 , along the horizontal 𝑥 direction is

(A) 6 × 10−4

(B) 6 × 10−6

(C) 3 × 10−6

(D) 3 × 10−4

Page 13 of 38

Q.18 Consider a vapour-liquid mixture of components 𝐴 and 𝐵 that obeys Raoult’s law.
The vapour pressure of 𝐴 is half that of 𝐵. The vapour phase concentrations of 𝐴
and 𝐵 are 3 mol m−3 and 6 mol m−3, respectively. At equilibrium, the ratio of the
liquid phase concentration of 𝐴 to that of 𝐵 is

(A) 1.0

(B) 0.5

(C) 2.0

(D) 1.5

Q.19 The ratio of the activation energy of a chemical reaction to the universal gas constant
is 1000 K. The temperature-dependence of the reaction rate constant follows the
collision theory. The ratio of the rate constant at 600 K to that at 400 K is

(A) 2.818

(B) 4.323

(C) 1.502

(D) 1.000

Page 14 of 38

Q.20 The rate of a reaction 𝐴 → 𝐵 is 0.2 mol m−3 s −1 at a particular concentration 𝐶𝐴1 .
The rate constant of the reaction at a given temperature is 0.1 m3 mol−1 s −1 . If the
reactant concentration is increased to 10 𝐶𝐴1 at the same temperature, the reaction
rate, in mol m−3 s−1 , is

(A) 20

(B) 10

(C) 100

(D) 50

Q.21 𝑘1 𝑘2
Two parallel first-order liquid phase reactions 𝐴 → 𝐵 and 𝐴 → 𝐶 are carried out in a
well-mixed isothermal batch reactor. The initial concentration of 𝐴 in the reactor is
1 kmol m−3 , while that of 𝐵 and 𝐶 is zero. After 2 hours, the concentration of 𝐴
reduces to half its initial value, and the concentration of 𝐵 is twice that of 𝐶. The
rate constants 𝑘1 and 𝑘2 , in h−1 , are, respectively

(A) 0.40, 0.20

(B) 0.23, 0.12

(C) 0.50, 0.25

(D) 0.36, 0.18

Page 15 of 38

Q.22 Consider the block diagram in the figure with control input 𝑢, disturbance 𝑑 and
output 𝑦. For the feedforward controller, the ordered pair (𝐾, 𝛼⁄𝛽 ) is

(A) (0.5, 2)

(B) (−0.5, 0.5)

(C) (−2, 2)

(D) (2, 0.5)

Page 16 of 38

Q.23 Consider the control structure for the overhead section of a distillation column
shown in the figure. The composition controller (CC) controls the heavy key
impurity in the distillate by adjusting the setpoint of the reflux flow controller in a
cascade arrangement. The sign of the controller gain for the pressure controller (PC)
and that for the composition controller (CC) are, respectively,

(A) negative, negative

(B) negative, positive

(C) positive, positive

(D) positive, negative

Page 17 of 38

Q.24 Which one of the given statements is correct with reference to gas-liquid contactors
for mass transfer applications?

(A) A tray tower is more suitable for foaming systems than a packed tower.

(B) Tray towers are preferred over packed towers for systems requiring frequent
cleaning.

(C) For a given liquid flow rate, the gas flow rate in the loading region is greater than
that in the flooding region.

(D) Flooding can never occur for counter-current contact.

Q.25 In an ammonia manufacturing facility, the necessary hydrogen is generated from
methane. The facility consists of the following process units -

P: Methanator, Q: CO shift convertor, R: CO2 stripper, S: Reformer, T: Ammonia
convertor

The correct order of these units, starting from methane feed is

(A) S, Q, R, P, T

(B) P, Q, R, S, T

(C) S, P, Q, R, T

(D) P, S, T, Q, R

Page 18 of 38

Q.26 Consider a linear homogeneous system of equations Ax = 0, where A is an 𝑛 × 𝑛
matrix, x is an 𝑛 × 1 vector and 0 is an 𝑛 × 1 null vector. Let 𝑟 be the rank of A. For
a non-trivial solution to exist, which of the following conditions is/are satisfied?

(A) Determinant of A = 0

(B) 𝑟=𝑛

(C) 𝑟<𝑛

(D) Determinant of A ≠ 0

Q.27 If the Prandtl number Pr = 0.01, which of the following statements is/are correct?

(A) The momentum diffusivity is much larger than the thermal diffusivity.

(B) The thickness of the momentum boundary layer is much smaller than that of the
thermal boundary layer.

(C) The thickness of the momentum boundary layer is much larger than that of the
thermal boundary layer.

(D) The momentum diffusivity is much smaller than the thermal diffusivity.

Page 19 of 38

Q.28 For the electrolytic cell in a chlor-alkali plant, which of the following statements
is/are correct?

(A) A membrane cell operates at a higher brine concentration than a diaphragm cell.

(B) Chlorine gas is produced at the cathode.

(C) Hydrogen gas is produced at the cathode.

(D) The caustic product stream exits the cathode compartment.

Q.29 Which of the following statements with reference to the petroleum/petrochemical
industry is/are correct?

(A) Catalytic hydrocracking converts heavier hydrocarbons to lighter hydrocarbons.

(B) Catalytic reforming converts straight-chain hydrocarbons to aromatics.

(C) Cumene is manufactured by the catalytic alkylation of benzene with propylene.

(D) Vinyl acetate is manufactured by reacting methane with acetic acid over a palladium
catalyst.

Page 20 of 38

Q.30 −5 𝑎
Consider a matrix A = [ ], where 𝑎 is a constant. If the eigenvalues of A are
−2 −2
−1 and −6, then the value of 𝑎, rounded off to the nearest integer, is ____________

Q.31 Consider the reaction 𝑁2 (𝑔) + 3𝐻2 (𝑔) ⇌ 2𝑁𝐻3 (𝑔) in a continuous flow reactor
under steady-state conditions. The component flow rates at the reactor inlet are
0
𝐹𝑁02 = 100 mol s −1 , 𝐹𝐻02 = 300 mol s −1 , 𝐹inert = 1 mol s−1 . If the fractional
conversion of 𝐻2 is 0.60, the outlet flow rate of 𝑁2 , in mol s −1 , rounded off to the
nearest integer, is _________

Q.32 Consider a binary mixture of components 𝐴 and 𝐵 at temperature 𝑇 and pressure 𝑃.
Let 𝑉̅𝐴 and 𝑉̅𝐵 be the partial molar volumes of 𝐴 and 𝐵, respectively. At a certain
mole fraction of 𝐴, 𝑥𝐴

𝜕𝑉̅𝐴 𝜕𝑉̅𝐵
( ) = 22 cm3 mol−1 and ( ) = −18 cm3 mol−1
𝜕𝑥𝐴 𝑇,𝑃 𝜕𝑥𝐴 𝑇,𝑃

The value of 𝑥𝐴 , rounded off to 2 decimal places, is ________

Q.33 Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow
of an incompressible Newtonian fluid through a circular pipe of inner radius 5.0 cm.
The magnitude of shear stress at the inner wall of the pipe is 0.1 N m−2. At a radial
distance of 1.0 cm from the pipe axis, the magnitude of the shear stress, in N m−2 ,
rounded off to 3 decimal places, is ______

Q.34 The opposite faces of a metal slab of thickness 5 cm and thermal conductivity
400 W m−1 ℃−1 are maintained at 500 ℃ and 200 ℃. The area of each face is
0.02 m2 . Assume that the heat transfer is steady and occurs only in the direction
perpendicular to the faces. The magnitude of the heat transfer rate, in kW, rounded
off to the nearest integer, is _______

Page 21 of 38

Q.35 The capital cost of a distillation column is Rs. 90 lakhs. The cost is to be fully
depreciated (salvage value is zero) using the double-declining balance method over
10 years. At the end of two years of continuous operation, the book-value of the
column, in lakhs of rupees, rounded off to 1 decimal place, is _______

Page 22 of 38

Q.36 – Q.65 Carry TWO marks Each

Q.36 Consider a steady, fully-developed, uni-directional laminar flow of an
incompressible Newtonian fluid (viscosity 𝜇) between two infinitely long
horizontal plates separated by a distance 2𝐻 as shown in the figure. The flow is
driven by the combined action of a pressure gradient and the motion of the bottom
∆𝑃 (𝑃 −𝑃 )
plate at 𝑦 = −𝐻 in the negative 𝑥 direction. Given that 𝐿 = 1 𝐿 2 > 0, where 𝑃1
and 𝑃2 are the pressures at two 𝑥 locations separated by a distance 𝐿. The bottom
plate has a velocity of magnitude 𝑉 with respect to the stationary top plate at
𝑦 = 𝐻. Which one of the following represents the 𝑥-component of the fluid velocity
vector?

(A) ∆𝑃 𝐻 2 𝑦2 𝑉 𝑦
(1 − 2 ) + ( − 1)
𝐿 2𝜇 𝐻 2 𝐻

(B) ∆𝑃 𝐻 2 𝑦 2 𝑉 𝑦
( 2 − 1) + ( − 1)
𝐿 2𝜇 𝐻 2 𝐻

(C) ∆𝑃 𝐻 2 𝑦 2 𝑉 𝑦
( 2 − 1) − ( − 1)
𝐿 2𝜇 𝐻 2 𝐻

(D) ∆𝑃 𝐻 2 𝑦2 𝑉 𝑦
(1 − 2 ) − ( − 1)
𝐿 2𝜇 𝐻 2 𝐻

Page 23 of 38

Q.37 The temperatures of two large parallel plates of equal emissivity are 900 K and
300 K. A reflection radiation shield of low emissivity and negligible conductive
resistance is placed parallelly between them. The steady-state temperature of the
shield, in K, is

(A) 759

(B) 559

(C) 659

(D) 859

Q.38 Hot oil at 110 ℃ heats water from 30 ℃ to 70 ℃ in a counter-current double-pipe
heat exchanger. The flow rates of water and oil are 50 kg min−1 and 100 kg min−1,
respectively and their specific heat capacities are 4.2 kJ kg −1 ℃−1 and
2.0 kJ kg −1 ℃−1 , respectively. Assume the heat exchanger is at steady state. If the
overall heat transfer coefficient is 200 W m−2 ℃−1 , the heat transfer area in m2 is

(A) 17.9

(B) 1.1

(C) 5.2

(D) 35.2

Page 24 of 38

Q. 39 A solid slab of thickness 𝐻1 is initially at a uniform temperature 𝑇0 . At time 𝑡 = 0,
the temperature of the top surface at 𝑦 = 𝐻1 is increased to 𝑇1 , while the bottom
surface at 𝑦 = 0 is maintained at 𝑇0 for 𝑡 ≥ 0. Assume heat transfer occurs only in
the 𝑦-direction, and all thermal properties of the slab are constant. The time required
for the temperature at 𝑦 = 𝐻1 /2 to reach 99% of its final steady value is 𝜏1 . If the
thickness of the slab is doubled to 𝐻2 = 2 𝐻1 , and the time required for the
temperature at 𝑦 = 𝐻2 /2 to reach 99% of its final steady value is 𝜏2 , then 𝜏2 ⁄𝜏1 is

(A) 2

(B) 1
4

(C) 4

(D) 1
2

Page 25 of 38

Q.40 A gas stream containing 95 mol% CO2 and 5 mol% ethanol is to be scrubbed with
pure water in a counter-current, isothermal absorption column to remove ethanol.
The desired composition of ethanol in the exit gas stream is 0.5 mol%. The
equilibrium mole fraction of ethanol in the gas phase, 𝑦 ∗ , is related to that in the
liquid phase, 𝑥, as 𝑦 ∗ = 2𝑥. Assume CO2 is insoluble in water and neglect
evaporation of water. If the water flow rate is twice the minimum, the mole fraction
of ethanol in the spent water is

(A) 0.0225

(B) 0.0126

(C) 0.0428

(D) 0.0316

Q.41 Sulfur dioxide (SO2) gas diffuses through a stagnant air-film of thickness 2 mm at
1 bar and 30 ℃. The diffusion coefficient of SO2 in air is 1 × 10−5 m2 s −1 . The SO2
partial pressures at the opposite sides of the film are 0.15 bar and 0.05 bar. The
universal gas constant is 8.314 J mol−1 K −1. Assuming ideal gas behavior, the
steady-state flux of SO2 in mol m−2 s−1 through the air-film is

(A) 0.077

(B) 0.022

(C) 0.085

(D) 0.057

Page 26 of 38

Q.42 A simple distillation column separates a binary mixture of 𝐴 and 𝐵. The relative
volatility of 𝐴 with respect to 𝐵 is 2. The steady-state composition of 𝐴 in the vapour
leaving the 1st, 2nd and 3rd trays in the rectifying section are 94, 90 and 85 mol%,
respectively. For ideal trays and constant molal overflow, the reflux-to-distillate
ratio is

(A) 1.9

(B) 2.7

(C) 1.2

(D) 1.1

Q.43 Alumina particles with an initial moisture content of 5 kg per kg dry solid are dried
in a batch dryer. For the first two hours, the measured drying rate is constant at
2 kg m−2 h−1 . Thereafter, in the falling-rate period, the rate decreases linearly with
the moisture content. The equilibrium moisture content is 0.05 kg per kg dry solid
and the drying area of the particles is 0.5 m2 per kg dry solid. The total drying
time, in h, to reduce the moisture content to half its initial value is

(A) 4.13

(B) 2.55

(C) 3.22

(D) 5.13

Page 27 of 38

Q.44 A first-order heterogenous reaction 𝐴 → 𝐵 is carried out using a porous spherical
catalyst. Assume isothermal conditions, and that intraphase diffusion controls the
reaction rate. At a bulk 𝐴 concentration of 0.3 mol L−1 , the observed reaction rate
in a 3 mm diameter catalyst particle is 0.2 mol s−1 L−1 catalyst volume. At a bulk
𝐴 concentration of 0.1 mol L−1 , the observed reaction rate, in mol s −1 L−1 catalyst
volume, in a 6 mm diameter catalyst particle, is

(A) 0.011

(B) 0.033

(C) 0.022

(D) 0.005

Q.45 A first-order liquid phase reaction 𝐴 → 𝐵 is carried out in two isothermal plug
flow reactors (PFRs) of volume 1 m3 each, connected in series. The feed flow rate
and concentration of 𝐴 to the first reactor are 10 m3 h−1 and 1 kmol m−3 ,
respectively. At steady-state, the concentration of 𝐴 at the exit of the second reactor
is 0.2 kmol m−3 . If the two PFRs are replaced by two equal-volume continuously
stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion,
the volume of each CSTR, in m3 , is

(A) 1.54

(B) 3.84

(C) 7.28

(D) 1.98

Page 28 of 38

Q.46 The residence time distribution, 𝐸, for a non-ideal flow reactor is given in the figure.
A first-order liquid phase reaction with a rate constant 0.2 min−1 is carried out in
the reactor. For an inlet reactant concentration of 2 mol L−1 , the reactant
concentration (in mol L−1) in the exit stream is

(A) 0.905

(B) 0.452

(C) 1.902

(D) 0.502

Page 29 of 38

Q.47 Let 𝑟 and 𝜃 be the polar coordinates defined by 𝑥 = 𝑟 𝑐𝑜𝑠 𝜃 and 𝑦 = 𝑟 𝑠𝑖𝑛 𝜃.
The area of the cardioid 𝑟 = 𝑎 (1 − 𝑐𝑜𝑠 𝜃), 0 ≤ 𝜃 ≤ 2𝜋, is

(A) 3𝜋𝑎2
2

(B) 2𝜋𝑎2
3

(C) 3𝜋𝑎2

(D) 2𝜋𝑎2

Page 30 of 38

Q.48 For the block diagram shown in the figure, the correct expression for the transfer
𝑦1 (𝑠)
function 𝐺𝑑 = 𝑑(𝑠) is

(A) −𝐺𝑝1 𝐺𝑐2
(1 + 𝐺𝑐1 𝐺𝑐2 𝐺𝑝1 )(1 + 𝐺𝑐2 𝐺𝑝2 )

(B) −𝐺𝑝1 𝐺𝑐2
1 + 𝐺𝑐2 𝐺𝑝2 + 𝐺𝑐1 𝐺𝑐2 𝐺𝑝1 𝐺𝑝2

(C) −𝐺𝑝1 𝐺𝑐2
1 + 𝐺𝑐2 𝐺𝑝2 + 𝐺𝑐1 𝐺𝑐2 𝐺𝑝1

(D) 1
1 + 𝐺𝑐2 𝐺𝑝2 + 𝐺𝑐1 𝐺𝑐2 𝐺𝑝1 𝐺𝑝2

Page 31 of 38

Q.49 For purchasing a batch reactor, three alternatives P, Q and R have emerged, as
summarized in the table. For a compound interest rate of 10% per annum, choose
the correct option that arranges the alternatives, in order, from the least expensive
to the most expensive.

P Q R

Installed Cost
15 25 35
(lakh rupees)

Equipment Life
3 5 7
(years)

Maintenance Cost
4 3 2
(lakh rupees per year)

(A) P, Q, R

(B) R, P, Q

(C) R, Q, P

(D) Q, R, P

Q.50 The Newton-Raphson method is used to solve 𝑓(𝑥) = 0, where 𝑓(𝑥) = 𝑒 𝑥 − 5𝑥.

If the initial guess 𝑥 (0) = 1.0, the value of the next iterate, 𝑥 (1) , rounded off to 2
decimal places, is ______

Q.51 ̂ , where 𝒊̂, 𝒋̂ and
Consider the line integral ∫𝐶 𝑭(𝒓) ⋅ 𝑑𝒓 , with 𝑭(𝒓) = 𝑥 𝒊̂ + 𝑦 𝒋̂ + 𝑧 𝒌
̂ are unit vectors in the (𝑥, 𝑦, 𝑧) Cartesian coordinate system. The path C is given
𝒌
by 𝒓(𝑡) = cos(𝑡) 𝒊̂ + sin(𝑡) 𝒋̂ + 𝑡 𝒌̂ , where 0 ≤ 𝑡 ≤ 𝜋. The value of the integral,
rounded off to 2 decimal places, is _________

Page 32 of 38

Q.52 𝑑2 𝑦 𝑑𝑦
Consider the ordinary differential equation 𝑥 2 𝑑𝑥 2 − 𝑥 𝑑𝑥 − 3𝑦 = 0, with the
boundary conditions 𝑦(𝑥 = 1) = 2 and 𝑦(𝑥 = 2) = 17⁄2. The solution 𝑦(𝑥) at
𝑥 = 3⁄2 , rounded off to 2 decimal places, is ___________

Q.53 Consider the function 𝑓(𝑥, 𝑦, 𝑧) = 𝑥 4 + 2 𝑦 3 + 𝑧 2 . The directional derivative of the
function at the point 𝑃 (−1, 1, −1) along (𝒊̂ + 𝒋̂), where 𝒊̂ and 𝒋̂ are unit vectors in
the x and y directions, respectively, rounded off to 2 decimal places, is _______

Q.54 Consider the process in the figure for manufacturing B. The feed to the process is
90 mol% 𝐴 and a close-boiling inert component I. At a particular steady-state:

• 𝐵 product rate is 100 kmol h−1
• Single-pass conversion of A in the reactor is 50%
• Recycle-to-purge stream flow ratio is 10

The flow rate of A in the purge stream in kmol h−1 , rounded off to 1 decimal place,
is _____

Page 33 of 38

Q.55 Methane combusts with air in a furnace as 𝐶𝐻4 + 2𝑂2 → 𝐶𝑂2 + 2𝐻2 𝑂. The heat
of reaction 𝛥𝐻𝑟𝑥𝑛 = −880 kJ per mol 𝐶𝐻4 and is assumed to be constant. The
furnace is well-insulated and no other side reactions occur. All components behave
as ideal gases with a constant molar heat capacity of 44 J mol−1 ℃−1 . Air may be
considered as 20 mol% 𝑂2 and 80 mol% 𝑁2 . The air-fuel mixture enters the furnace
at 50 °C. The methane conversion 𝑋 varies with the air-to-methane mole ratio, 𝑟, as

𝑋 = 1 − 0.1 𝑒 −2(𝑟−𝑟𝑠 ) with 0.9 𝑟𝑠 ≤ 𝑟 ≤ 1.1 𝑟𝑠

where 𝑟𝑠 is the stoichiometric air-to-methane mole ratio. For 𝑟 = 1.05 𝑟𝑠 , the exit
flue gas temperature in ℃, rounded off to 1 decimal place, is ______

Q.56 An isolated system consists of two perfectly sealed cuboidal compartments 𝐴 and
𝐵 separated by a movable rigid wall of cross-sectional area 0.1 m2 as shown in the
figure. Initially, the movable wall is held in place by latches 𝐿1 and 𝐿2 such that the
volume of compartment 𝐴 is 0.1 m3 . Compartment 𝐴 contains a monoatomic ideal
gas at 5 bar and 400 K. Compartment 𝐵 is perfectly evacuated and contains a
massless Hookean spring of force constant 0.3 N m−1 at its equilibrium length
(stored elastic energy is zero). The latches 𝐿1 and 𝐿2 are released, the wall moves
to the right by 0.2 m, where it is held at the new position by latches 𝐿3 and 𝐿4 .
Assume all the walls and latches are massless. The final equilibrium temperature, in
K, of the gas in compartment 𝐴, rounded off to 1 decimal place, is _________

Page 34 of 38

Q.57 Ethylene obeys the truncated virial equation-of-state

𝑃𝑉 𝐵𝑃
=1+
𝑅𝑇 𝑅𝑇

where P is the pressure, V is the molar volume, T is the absolute temperature and B
is the second virial coefficient. The universal gas constant
3 −1 −1
𝑅 = 83.14 bar cm mol K . At 340 K, the slope of the compressibility factor
vs. pressure curve is −3.538 × 10−3 bar −1 . Let 𝐺 𝑅 denote the molar residual Gibbs
𝜕𝐺 𝑅
free energy. At these conditions, the value of ( 𝜕𝑃 ) , in cm3 mol−1 , rounded off
𝑇
to 1 decimal place, is ___________

Q.58 A metallic spherical particle of density 7001 kg m−3 and diameter 1 mm is settling
steadily due to gravity in a stagnant gas of density 1 kg m−3 and viscosity
10−5 kg m−1 s −1. Take 𝑔 = 9.8 m s−2 . Assume that the settling occurs in the
regime where the drag coefficient 𝐶𝐷 is independent of the Reynolds number, and
equals 0.44. The terminal settling velocity of the particle, in m s−1 , rounded off to
2 decimal places, is ____

Page 35 of 38

Q.59 Water of density 1000 kg m−3 is pumped at a volumetric flow rate of
3.14 × 10−2 m3 s −1 , through a pipe of inner diameter 10 cm and length 100 m, from
a large Reservoir 1 to another large Reservoir 2 at a height 50 m above Reservoir 1,
as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy
friction factor 𝑓 = 0.06, and a kinetic energy correction factor 𝛼 = 1. Take 𝑔 =
9.8 m s −2. If all minor losses are negligible, and the pump efficiency is 100%, the
pump power, in kW, rounded off to 2 decimal places, is ______

Q.60 A Venturi meter with a throat diameter 𝑑 = 2 cm measures the flow rate in a pipe of
diameter 𝐷 = 6 cm, as shown in the figure. A U-tube manometer is connected to
measure the pressure drop. Assume the discharge coefficient is independent of the
Reynolds number and geometric ratios. If the volumetric flow rate through the pipe
is doubled 𝑄2 = 2𝑄1 , the corresponding ratio of the manometer readings ∆ℎ2 ⁄∆ℎ1,
rounded off to the nearest integer, is _______

Page 36 of 38

Q.61 Heat is available at a rate of 2 kW from a thermal reservoir at 400 K. A two-stage
process harnesses this heat to produce power. Stages 1 and 2 reject heat at 360 K
and 300 K, respectively. Stage 2 is driven by the heat rejected by Stage 1. If the
overall process efficiency is 50% of the corresponding Carnot efficiency, the power
delivered by the process, in kW, rounded off to 2 decimal places, is ______

Q.62 A chemostat with cell recycle is shown in the figure. The feed flow rate and culture
volume are 𝐹 = 75 L h−1 and 𝑉 = 200 L, respectively. The glucose concentration in
the feed CS0 = 15 g L−1 . Assume Monod kinetics with specific cell growth rate
1 𝑑C 𝜇 C
𝜇𝑔 = C 𝑑𝑡C = 𝐾 𝑚+CS , where 𝜇𝑚 = 0.25 h−1 and 𝐾𝑠 = 1 g L−1. Assume
C 𝑆 S
maintenance and death rates to be zero, input feed to be sterile (CC0 = 0) and steady-
state operation. The glucose concentration in the recycle stream, CS1 , in g L−1 ,
rounded off to 1 decimal place, is _________

Page 37 of 38

Q.63 Consider the surge drum in the figure. Initially the system is at steady-state with a
hold-up 𝑉̅ = 5 m3, which is 50% of full tank capacity, 𝑉𝑓𝑢𝑙𝑙 , and volumetric flow
rates 𝐹̅𝑖𝑛 = 𝐹̅𝑜𝑢𝑡 = 1 m3 h−1. The high hold-up alarm limit 𝑉ℎ𝑖𝑔ℎ = 0.8 𝑉𝑓𝑢𝑙𝑙 while
the low hold-up alarm limit 𝑉𝑙𝑜𝑤 = 0.2 𝑉𝑓𝑢𝑙𝑙 . A proportional (P-only) controller
manipulates the outflow to regulate the hold-up 𝑉 as 𝐹𝑜𝑢𝑡 = 𝐾𝑐 (𝑉 − 𝑉̅ ) + 𝐹̅𝑜𝑢𝑡 . At
𝑡 = 0, 𝐹𝑖𝑛 increases as a step from 1 m3 h−1 to 2 m3 h−1. Assume linear control
valves and instantaneous valve dynamics. Let 𝐾𝑐𝑚𝑖𝑛 be the minimum controller gain
that ensures 𝑉 never exceeds 𝑉ℎ𝑖𝑔ℎ . The value of 𝐾𝑐𝑚𝑖𝑛 , in ℎ−1 , rounded off to 2
decimal places, is _________

Q. 64 A PD controller with transfer function 𝐺𝑐 is used to stabilize an open-loop unstable
process with transfer function 𝐺𝑝 , where

𝜏𝐷 𝑠 + 1 1
𝐺𝑐 = 𝐾𝑐 𝜏 , 𝐺𝑝 =
𝐷
(20 )𝑠 + 1 (𝑠 − 1)(10𝑠 + 1)
and time is in minutes. From the necessary conditions for closed-loop stability, the
maximum feasible value of 𝜏𝐷 , in minutes, rounded off to 1 decimal place, is
____________

Q.65 Consider a tray-column of diameter 120 cm. Each downcomer has a cross-sectional
area of 575 cm2. For a tray, the percentage column cross-sectional area not available
for vapour flow due to the downcomers, rounded off to 1 decimal place, is
_____________

Page 38 of 38

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