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General Aptitude(10)Engineering Mathematics(10)Process Calculations(2)Thermodynamics(5)Fluid Mechanics and Mechanical Operations(7)Heat Transfer(5)Mass Transfer(9)Chemical Reaction Engineering(8)Instrumentation and Process Control(4)Plant Design and Economics(2)Chemical Technology(3)

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '->' denotes increasing order of intensity, then the meaning of the words [simmer $\rightarrow$ seethe $\rightarrow$ smolder] is analogous to [break $\rightarrow$ raze $\rightarrow$ [blank]].

(A)

obfuscate

(B)

obliterate

(C)

fracture

(D)

fissure

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

In a locality, the houses are numbered with consecutive odd/even integers. If the difference of the sum of house-numbers between the two sides is 27, the number of houses on each side is

(A)

27

(B)

52

(C)

54

(D)

26

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

For $p > 0$, $q > 0$ and $p \neq 1$, $q \neq 1$. If $p^{q} = q^{p}$ and $q = p^2$, then the value of $p$ is

(A)

\sqrt{2}

(B)

q^p = p^{2q}

(C)

\sqrt{q} = \sqrt{p}

(D)

\sqrt[p]{q} = \sqrt[q]{p}

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Which one of the given options is a possible value of $x$ in the sequence: 3, 7, 15, $x$, 63, 127, 255?

(A)

35

(B)

40

(C)

45

(D)

31

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

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)

48

(B)

49

(C)

50

(D)

55

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

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

(A)

hold, wait, culminates, pivot

(B)

holds, wait, culminate, pivots

(C)

holds, waits, culminates, pivot

(D)

hold, waits, culminate, pivots

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs such that each person sits next to their twin. Unique arrangements = ?

(A)

12

(B)

14

(C)

10

(D)

28

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

Which one of the given technologies has the highest Capacity Factor based on the chart?

(A)

T3

(B)

T4

(C)

T2

(D)

T1

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

In the 4x4 array shown, maximum number of crosses possible in the empty column is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

During a half-moon phase, Earth-Moon-Sun form a right triangle with angle 89.85°. The ratio of Earth-Sun and Earth-Moon distances is closest to

(A)

328

(B)

382

(C)

238

(D)

283

Explanation

Engineering Mathematics

10 Questions

GATE→2024→Engineering Mathematics→Calculus

Q11

MCQ[1 Mark]

The first non-zero term in the Taylor series expansion of $(1-x)-e^{-x}$ about $x=0$ is

(A)

1

(B)

x^2 / 2

(C)

-x^2 / 2

(D)

-x^2 / 2

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q12

MCQ[1 Mark]

Consider normal probability distribution function $f(x)=\frac{4}{\sqrt{2\pi}}e^{-8(x+3)^{2}}$. Ordered pair $(\mu, \sigma)$ is

(A)

(3, 1/4)

(B)

(-3, 1/4)

(C)

(3, 4)

(D)

(-3, 4)

Explanation

GATE→2024→Engineering Mathematics→Complex Variables

Q13

MCQ[1 Mark]

If $z_{1}=-1+i$ and $z_{2}=2i$, then $\text{Arg}(z_{1}/z_{2})$ is

(A)

3\pi/4

(B)

\pi/4

(C)

\pi/2

(D)

\pi/3

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q14

MSQ[1 Mark]

Consider a linear homogeneous system of equations $Ax = 0$. 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

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q15

NAT[1 Mark]

Consider a matrix $A = \begin{bmatrix} -5 & a \\ -2 & -2 \end{bmatrix}$. If eigenvalues are $-1$ and $-6$, value of $a$ is.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

Area of cardioid $r = a(1 - \cos \theta)$, $0 \le \theta \le 2\pi$ is.

(A)

3\pi a^2 / 2

(B)

2\pi a^2 / 3

(C)

2\pi a^2

(D)

3\pi a^2

Explanation

GATE→2024→Engineering Mathematics→Numerical Methods

Q17

NAT[2 Marks]

Newton-Raphson method for $f(x) = e^x - 5x = 0$ with initial guess $x^{(0)} = 1.0$, value of next iterate $x^{(1)}$ rounded off to 2 decimal places is.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q18

NAT[2 Marks]

Line integral $\int_C F(r) \cdot dr$ for $F(r) = x\hat{i} + y\hat{j} + z\hat{k}$ along path $r(t) = \cos(t)\hat{i} + \sin(t)\hat{j} + t\hat{k}$ ($0 \le t \le \pi$) is.

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q19

NAT[2 Marks]

Consider ODE $x^2 y'' - x y' - 3y = 0$ with $y(1)=2$ and $y(2)=17/2$. Solution $y(x)$ at $x=3/2$ is.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q20

NAT[2 Marks]

Function $f(x,y,z) = x^4 + 2y^3 + z^2$. Directional derivative at point $P(-1,1,-1)$ along $(\hat{i} + \hat{j})$ is.

Explanation

Process Calculations

2 Questions

GATE→2024→Process Calculations→Process Calculations

Q21

NAT[1 Mark]

Consider the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$ with inlet flow rates $100$ mol/s ($N_2$), $300$ mol/s ($H_2$). If $H_2$ conversion is $0.60$, outlet flow rate of $N_2$ is ______ mol s$^{-1}$.

Explanation

GATE→2024→Process Calculations→Process Calculations

Q22

NAT[2 Marks]

Consider manufacturing process for B with feed of 90 mol% A and inert I. Product rate 100 kmol/h, single-pass conversion 50%, recycle-to-purge ratio 10. Flow rate of A in purge stream is kmol h$^{-1}$.

Explanation

Thermodynamics

5 Questions

GATE→2024→Thermodynamics→Thermodynamics

Q23

NAT[1 Mark]

Consider binary mixture. Given $(\partial \overline{V}_A / \partial x_A) = 22$ and $(\partial \overline{V}_B / \partial x_A) = -18$, value of $x_A$ is.

Explanation

GATE→2024→Thermodynamics→Thermodynamics

Q24

NAT[2 Marks]

Methane combustion in insulated furnace... for $r = 1.05 r_s$, exit flue gas temperature is °C.

Explanation

GATE→2024→Thermodynamics→Thermodynamics

Q25

NAT[2 Marks]

Isolated system with compartments A and B separated by movable rigid wall with spring... final equilibrium temperature of gas in A is K.

Explanation

GATE→2024→Thermodynamics→Thermodynamics

Q26

NAT[2 Marks]

Ethylene obeys truncated virial EOS. At 340 K, slope of compressibility factor vs pressure is given. Value of $(\partial G^R / \partial P)_T$ in $\text{cm}^3 \text{mol}^{-1}$ is.

Explanation

GATE→2024→Thermodynamics→Thermodynamics

Q27

NAT[2 Marks]

Heat available at $2 \text{ kW}$ from thermal reservoir at $400$ K. Two-stage process rejects heat at $360$ K and $300$ K. Power delivered at 50% Carnot efficiency is kW.

Explanation

Fluid Mechanics and Mechanical Operations

7 Questions

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q28

MCQ[1 Mark]

An infinitely long cylindrical water filament of radius $R$ surrounded by air... $P_{in} - P_{out}$ is

(A)

2\gamma/R

(B)

0

(C)

\gamma/R

(D)

4\gamma/R

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q29

MCQ[1 Mark]

Velocity field in incompressible flow is given, with $v_y=0$ at $y=0$. The correct expression for $v_y$ is

(A)

-\alpha xy / 2

(B)

-\alpha y^2 / 2

(C)

\alpha y^2 / 2

(D)

\alpha xy / 2

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q30

NAT[1 Mark]

Steady laminar flow through pipe of radius $5.0$ cm. Wall shear stress is $0.1 \text{ N m}^{-2}$. Magnitude of shear stress at radial distance $1.0$ cm from axis is.

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q31

MCQ[2 Marks]

Consider steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid between two plates separated by $2H$ driven by pressure gradient and bottom plate motion. Which option represents the x-component of fluid velocity vector?

(A)

option A

(B)

option B

(C)

option C

(D)

option D

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q32

NAT[2 Marks]

Metallic spherical particle density $7001 \text{ kg m}^{-3}$, diameter $1 \text{ mm}$ settling in gas... drag coefficient $C_D = 0.44$. Terminal settling velocity in $\text{m s}^{-1}$ is.

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q33

NAT[2 Marks]

Water pumped from Reservoir 1 to Reservoir 2 at height $50$ m through pipe of $10$ cm diameter and $100$ m length. Darcy friction factor $f=0.06$. Pump power in kW is.

Explanation

GATE→2024→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q34

NAT[2 Marks]

Venturi meter throat $d=2$ cm, pipe $D=6$ cm. If volumetric flow rate is doubled $Q_2 = 2 Q_1$, ratio of manometer readings $\Delta h_2 / \Delta h_1$ is.

Explanation

Heat Transfer

5 Questions

GATE→2024→Heat Transfer→Heat Transfer

Q35

MSQ[1 Mark]

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

(A)

Momentum diffusivity much larger than thermal diffusivity

(B)

Thickness of momentum boundary layer much smaller than thermal

(C)

Thickness of momentum boundary layer much larger than thermal

(D)

Momentum diffusivity much smaller than thermal diffusivity

Explanation

GATE→2024→Heat Transfer→Heat Transfer

Q36

NAT[1 Mark]

Metal slab of thickness $5$ cm, $k = 400 \text{ W m}^{-1}~^\circ\text{C}^{-1}$, faces at $500^\circ\text{C}$ and $200^\circ\text{C}$, area $0.02 \text{ m}^2$. Heat transfer rate in kW is.

Explanation

GATE→2024→Heat Transfer→Heat Transfer

Q37

MCQ[2 Marks]

Temperatures of two parallel plates are 900 K and 300 K. A radiation shield is placed between them. Steady-state temperature of the shield is K.

(A)

759

(B)

559

(C)

659

(D)

859

Explanation

GATE→2024→Heat Transfer→Heat Transfer

Q38

MCQ[2 Marks]

Hot oil at $110^\circ\text{C}$ heats water from $30^\circ\text{C}$ to $70^\circ\text{C}$ in a counter-current double-pipe heat exchanger... heat transfer area in $\text{m}^2$ is

(A)

5.2

(B)

35.2

(C)

15.2

(D)

25.2

Explanation

GATE→2024→Heat Transfer→Heat Transfer

Q39

MCQ[2 Marks]

Solid slab of thickness $H_1$... time required for temperature at mid-plane to reach 99% of final value is $\tau_1$. If thickness is doubled to $H_2 = 2 H_1$, ratio $\tau_2 / \tau_1$ is

(A)

2

(B)

4

(C)

1/2

(D)

1/4

Explanation

Mass Transfer

9 Questions

GATE→2024→Mass Transfer→Mass Transfer

Q40

MCQ[1 Mark]

For the azeotropic distillation process with heavy entrainer shown in the figure, steady-state degrees of freedom equals

(A)

3

(B)

4

(C)

5

(D)

6

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q41

MCQ[1 Mark]

Consider steady uni-directional diffusion across vertical slab... molar flow rate of A in mol s$^{-1}$ along x direction is

(A)

6 x 10^-4

(B)

6 x 10^-6

(C)

3 x 10^-6

(D)

3 x 10^-4

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q42

MCQ[1 Mark]

Consider a vapour-liquid mixture obeying Raoult's law. Vapour pressure of A is half that of B. Vapour phase concentrations of A and B are 3 and 6 mol m$^{-3}$. Equilibrium ratio of liquid phase concentration of A to B is

(A)

1.0

(B)

0.5

(C)

2.0

(D)

1.5

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q43

MCQ[1 Mark]

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

(A)

tray tower more suitable for foaming than packed

(B)

tray towers preferred for frequent cleaning

(C)

gas flow rate in loading region greater than flooding

(D)

flooding can never occur for counter-current

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q44

MCQ[2 Marks]

Gas stream containing 5 mol% ethanol scrubbed with water... water flow rate is twice the minimum. Mole fraction of ethanol in spent water is

(A)

0.0225

(B)

0.0126

(C)

0.0428

(D)

0.0316

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q45

MCQ[2 Marks]

Sulfur dioxide gas diffuses through stagnant air-film of thickness 2 mm at 1 bar and 30 °C... steady-state flux of $SO_2$ in mol m$^{-2}$ s$^{-1}$ is

(A)

option A

(B)

0.022

(C)

0.085

(D)

0.057

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q46

MCQ[2 Marks]

Simple distillation column separates binary mixture with relative volatility 2. Vapour compositions on 1st, 2nd, 3rd trays are 94, 90, 85 mol%. Reflux-to-distillate ratio is

(A)

1.9

(B)

2.7

(C)

1.2

(D)

1.1

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q47

MCQ[2 Marks]

Alumina particles with initial moisture 5 kg/kg dry solid... total drying time to reduce moisture content to half initial value is h.

(A)

4.13

(B)

2.55

(C)

3.22

(D)

5.13

Explanation

GATE→2024→Mass Transfer→Mass Transfer

Q48

NAT[2 Marks]

Tray-column diameter $120$ cm, downcomer area $575 \text{ cm}^2$ each (two downcomers typically). Percentage column cross-sectional area not available for vapour flow due to downcomers is %.

Explanation

Chemical Reaction Engineering

8 Questions

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q49

MCQ[1 Mark]

Ratio of activation energy to universal gas constant is 1000 K. Temperature dependence follows collision theory. Ratio of rate constant at 600 K to 400 K is

(A)

1.502

(B)

0.500

(C)

2.000

(D)

1.000

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q50

MCQ[1 Mark]

Rate of reaction $A \to B$ is $0.2 \text{ mol m}^{-3}\text{s}^{-1}$ at $C_{A1}$. Rate constant is $0.1 \text{ m}^3\text{mol}^{-1}\text{s}^{-1}$. If concentration is increased to $10 C_{A1}$, the reaction rate is

(A)

20

(B)

10

(C)

100

(D)

50

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q51

MCQ[1 Mark]

Two parallel first-order liquid phase reactions $A \to B$ and $A \to C$ in batch reactor... rate constants $k_1$ and $k_2$ in h$^{-1}$ are

(A)

0.40, 0.20

(B)

0.23, 0.12

(C)

0.50, 0.25

(D)

0.36, 0.18

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q52

MCQ[2 Marks]

First-order heterogeneous reaction $A \to B$ in porous spherical catalyst with intraphase diffusion control... observed reaction rate is

(A)

0.011

(B)

0.033

(C)

0.022

(D)

0.005

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q53

MCQ[2 Marks]

First-order liquid phase reaction $A \to B$ in two PFRs in series... if replaced by two equal-volume CSTRs for same conversion, volume of each CSTR is m$^3$.

(A)

1.54

(B)

3.84

(C)

7.28

(D)

1.98

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q54

MCQ[2 Marks]

RTD curve given for non-ideal reactor. First-order reaction with $k = 0.2 \text{ min}^{-1}$, inlet concentration $2 \text{ mol L}^{-1}$. Reactant concentration in exit stream is mol L$^{-1}$.

(A)

0.905

(B)

0.452

(C)

1.902

(D)

0.225

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q55

NAT[2 Marks]

Chemostat with cell recycle... Monod kinetics parameters given. Glucose concentration in recycle stream $C_{S1}$ is g L$^{-1}$.

Explanation

GATE→2024→Chemical Reaction Engineering→Chemical Reaction Engineering

Q56

NAT[2 Marks]

Process for manufacturing C via $A+B \to C$ in CSTR with recycle. Cost objective minimized to find optimum reactor volume $V$ m$^3$.

Explanation

Instrumentation and Process Control

4 Questions

GATE→2024→Instrumentation and Process Control→Instrumentation and Process Control

Q57

MCQ[1 Mark]

For the feedforward controller block diagram, the ordered pair $(K, \alpha/\beta)$ is

(A)

(0.5, 2)

(B)

(-0.5, 0.5)

(C)

(-2, 2)

(D)

(2, 2)

Explanation

GATE→2024→Instrumentation and Process Control→Instrumentation and Process Control

Q58

MCQ[1 Mark]

The sign of the controller gain for the pressure controller (PC) and composition controller (CC) are, respectively,

(A)

negative, negative

(B)

negative, positive

(C)

positive, positive

(D)

positive, negative

Explanation

GATE→2024→Instrumentation and Process Control→Instrumentation and Process Control

Q59

MCQ[2 Marks]

For the block diagram shown in the figure, correct expression for transfer function $G_d = y_1(s)/d(s)$ is.

(A)

option A

(B)

option B

(C)

option C

(D)

option D

Explanation

GATE→2024→Instrumentation and Process Control→Instrumentation and Process Control

Q60

NAT[2 Marks]

Surge drum hold-up control with P-only controller. Step increase in feed from $1$ to $2 \text{ m}^3\text{h}^{-1}$. Minimum controller gain $K_c^{min}$ ensuring hold-up never exceeds $V_{high}$ is h$^{-1}$.

Explanation

Plant Design and Economics

2 Questions

GATE→2024→Plant Design and Economics→Plant Design and Economics

Q61

NAT[1 Mark]

Distillation column cost 90 lakhs. Depreciated using double-declining balance method over 10 years. Book value after 2 years is ______ lakhs of rupees.

Explanation

GATE→2024→Plant Design and Economics→Plant Design and Economics

Q62

MCQ[2 Marks]

For purchasing a batch reactor, three alternatives P, Q and R. For compound interest rate 10% per annum, arrange alternatives from least to most expensive.

(A)

P, Q, R

(B)

R, P, Q

(C)

R, Q, P

(D)

Q, P, R

Explanation

Chemical Technology

3 Questions

GATE→2024→Chemical Technology→Chemical Technology

Q63

MCQ[1 Mark]

In an ammonia manufacturing facility starting from methane feed, the correct order of units [P: Methanator, Q: CO shift convertor, R: CO2 stripper, S: Reformer, T: Ammonia convertor] 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

Explanation

GATE→2024→Chemical Technology→Chemical Technology

Q64

MSQ[1 Mark]

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

(A)

Membrane cell operates at higher brine concentration than diaphragm cell

(B)

Chlorine gas produced at cathode

(C)

Hydrogen gas produced at cathode

(D)

Membrane cell produces purer caustic soda than diaphragm cell

Explanation

GATE→2024→Chemical Technology→Chemical Technology

Q65

MSQ[1 Mark]

Which of the following statements regarding chemical industry is/are correct?

(A)

statement A

(B)

statement B

(C)

statement C

(D)

statement D

Explanation