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General Aptitude(10)Engineering Mathematics(8)Thermodynamics(8)Fluid Mechanics and Mechanical Operations(5)Heat Transfer(6)Mass Transfer(9)Chemical Reaction Engineering(8)Instrumentation and Process Control(6)Plant Design and Economics(2)Chemical Technology(3)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Is there any good show [blank] television tonight? Select the most appropriate option to complete the above sentence.

(A)

in

(B)

at

(C)

within

(D)

on

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

As the police officer was found guilty of embezzlement, he was [blank] dismissed from the service in accordance with the Service Rules.

(A)

sumptuously

(B)

brazenly

(C)

unintentionally

(D)

summarily

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The sum of the following infinite series is: $\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots$

(A)

1 + e

(B)

e - 1

(C)

e

(D)

e

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?

(A)

3

(B)

4

(C)

8

(D)

12

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

The figures I, II and III are parts of a sequence. Which one of the following options comes next in the sequence at IV?

(A)

(B)

(C)

(D)

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Based only on the information provided in the passage by Hilaire Belloc's 'The Crooked Streets', which one of the following statements is true?

(A)

The author of the passage takes delight in wondering.

(B)

The wealthier nations are pulling down the crooked streets in their capitals.

(C)

In the past, crooked streets were only built on islands.

(D)

Great broad ways are needed to protect commerce and history.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?

(A)

64 6/11

(B)

66 5/13

(C)

65 5/11

(D)

66 6/13

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays the color codes that are consistent with the color model?

(A)

(B)

(C)

(D)

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

A circle with center at $(x,y)=(0.5,0)$ and radius $=0.5$ intersects with another circle with center at $(x,y)=(1,1)$ and radius $=1$ at two points. One of the points of intersection $(x, y)$ is:

(A)

(0,0)

(B)

(0.2, 0.4)

(C)

(0.5, 0.5)

(D)

(1,2)

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

An object is said to have an $n$-fold rotational symmetry if the object, rotated by an angle of $\frac{2\pi}{n}$ is identical to the original. Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen?

(A)

(B)

(C)

(D)

Explanation

Engineering Mathematics

8 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors $\hat{i}$, $\hat{j}$ and $\hat{k}$. Let vector $a=\sqrt{2}\hat{i}+\frac{1}{\sqrt{2}}\hat{j}+\hat{k}$, and vector $b=\frac{1}{\sqrt{2}}\hat{i}+\sqrt{2}\hat{j}-\hat{k}$. The inner product of these vectors $(a\cdot b)$ is

(A)

0

(B)

1

(C)

-1

(D)

2

Explanation

GATE→2025→Engineering Mathematics→Complex Variables

Q12

MCQ[1 Mark]

Consider two complex numbers $z_{1}=1-i$ and $z_{2}=i$. The argument of $z_{1}z_{2}$ is

(A)

0

(B)

\pi/4

(C)

\pi/2

(D)

\pi

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q13

MCQ[1 Mark]

A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is

(A)

(3P1 * 7P1) / 10P2

(B)

(10P3 * 10P7) / 10P2

(C)

(10C3 * 10C7) / 10C2

(D)

(3C1 * 7C1) / 10C2

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q14

MCQ[2 Marks]

Consider a Cartesian coordinate system... Choose the condition for which the divergence of the vector field $v = ax\hat{i} - by\hat{j}$ is zero.

(A)

a - b = 0

(B)

a < b

(C)

a > b

(D)

a + b = 0

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q15

MCQ[2 Marks]

A probability distribution function is given as $p(x) = 1/a$ for $x \in (0, a)$. For a function $f(x) = x^2$, the expectation of $f(x)$ is

(A)

a^2 / 3

(B)

a^3 / 3

(C)

2a^2 / 3

(D)

2a^3 / 3

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q16

MSQ[2 Marks]

Consider the differential equation $\frac{dy}{dx} + \frac{y}{x} = 0$. Choose the CORRECT option(s) for the solution $y$.

(A)

$y = x + c$

(B)

$y = c/x$

(C)

$y = -x + c$

(D)

$y = 0$

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q17

NAT[2 Marks]

Consider the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$. The eigenvalues of the matrix are $0.27$ and ______ (rounded off to 2 decimal places).

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q18

NAT[2 Marks]

The Newton-Raphson method is used to find the root of $f(x) \equiv x^2 - x - 1 = 0$. Starting with initial guess $x_{(0)} = 1$, the second iterate $x_{(2)}$ is ______ (rounded off to 2 decimal places).

Explanation

Thermodynamics

8 Questions

GATE→2025→Thermodynamics→Thermodynamics

Q19

MCQ[1 Mark]

The number of independent intensive variables that need to be specified to determine the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q20

MCQ[1 Mark]

The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed

(A)

Isolated

(B)

Open

(C)

Adiabatic

(D)

Closed

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q21

NAT[1 Mark]

The following data is given for a ternary ABC gas mixture at 12 MPa and 308 K... The fugacity of the gas mixture is ______ MPa (rounded off to 3 decimal places).

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q22

NAT[1 Mark]

Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber... The change in total entropy for the process is ______ J/K (rounded off to 1 decimal place).

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q23

NAT[2 Marks]

An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring... final equilibrium temperature of the gas is ______ K (rounded off to the nearest integer).

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q24

NAT[2 Marks]

An adiabatic pump of efficiency 40% is used to increase water pressure from 200 kPa to 600 kPa... maximum temperature rise of water across the pump is ______ °C (rounded off to 3 decimal places).

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q25

NAT[2 Marks]

A and B form an azeotrope. The saturation vapour pressures of A and B are 87 kPa and 72.7 kPa... The azeotrope composition is ______ mol% A (rounded off to nearest integer).

Explanation

GATE→2025→Thermodynamics→Thermodynamics

Q26

NAT[2 Marks]

Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide... equilibrium constant is 1.68 at reaction conditions. Mole fraction of $H_2$ in product is 0.4. Mole fraction of methanol is ______ (rounded off to 2 decimal places).

Explanation

Fluid Mechanics and Mechanical Operations

5 Questions

GATE→2025→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q27

MCQ[1 Mark]

The sum of the components of the force due to pressure and shear at the solid-fluid boundary of a solid body in the direction normal to the flow is

(A)

Friction

(B)

Buoyancy

(C)

Lift

(D)

Drag

Explanation

GATE→2025→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q28

MCQ[1 Mark]

Choose the CORRECT option for pathlines, streaklines and streamlines for a STEADY flow field.

(A)

All three lines are identical

(B)

Only pathlines and streaklines are identical

(C)

Only pathlines and streamlines are identical

(D)

Only streamlines and streaklines are identical

Explanation

GATE→2025→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q29

MCQ[2 Marks]

A catalyst particle is modeled as a symmetrical double cone solid as shown in the figure. The sphericity of the particle is given by

(A)

option A

(B)

option B

(C)

option C

(D)

option D

Explanation

GATE→2025→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q30

MSQ[2 Marks]

For a steady state, fully developed laminar flow of a Newtonian fluid through a cylindrical pipe at a constant volumetric flow rate, which of the following statements regarding pressure drop ($\Delta P$) is/are TRUE?

(A)

$\Delta P$ increases with fluid viscosity

(B)

$\Delta P$ increases with pipe length

(C)

$\Delta P$ increases with pipe diameter

(D)

$\Delta P$ remains unchanged with fluid viscosity

Explanation

GATE→2025→Fluid Mechanics and Mechanical Operations→Fluid Mechanics and Mechanical Operations

Q31

NAT[2 Marks]

A leaf filter is operated at 1 atm (gauge)... The volumetric flow rate of the filtrate at 1 hour is ______ $\times 10^{-3}\text{ m}^3\text{/s}$ (rounded off to 2 decimal places).

Explanation

Heat Transfer

6 Questions

GATE→2025→Heat Transfer→Heat Transfer

Q32

MCQ[1 Mark]

In industrial heat exchanger design, the overall heat transfer coefficient U is estimated from the equation $\frac{1}{U}=\frac{1}{h_{i}}+\frac{1}{h_{o}}$. This is valid for (i) tube of (ii) thermal conductivity.

(A)

(i) thick-walled, (ii) high

(B)

(i) thin-walled, (ii) high

(C)

(i) thin-walled, (ii) low

(D)

(i) thick-walled, (ii) low

Explanation

GATE→2025→Heat Transfer→Heat Transfer

Q33

MSQ[1 Mark]

Which of the following statements regarding multiple effect evaporators is/are TRUE?

(A)

Pressure of effect with fresh steam is lowest...

(B)

Backward feed is preferred over forward feed for cold feed.

(C)

Backward feed is preferred for highly viscous concentrated product.

(D)

Temperature is lowest...

Explanation

GATE→2025→Heat Transfer→Heat Transfer

Q34

MCQ[2 Marks]

A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. Which one of the following is an appropriate boundary condition at the surface S?

(A)

Temperature at S is same for both the plates

(B)

Gradient of temperature at S is same for both the plates

(C)

Gradient of temperature vanishes at S

(D)

Temperature at S is the average of Th and Tc

Explanation

GATE→2025→Heat Transfer→Heat Transfer

Q35

NAT[2 Marks]

Water flowing at $70\text{ kg/min}$ is heated from $25^{\circ}\text{C}$ to $65^{\circ}\text{C}$ in a counter-flow double pipe heat exchanger using hot oil... the heat exchanger area is ______ $\text{m}^2$ (rounded off to 1 decimal place).

Explanation

GATE→2025→Heat Transfer→Heat Transfer

Q36

NAT[2 Marks]

Consider laminar flow of water over a wide flat plate maintained at uniform temperature... distance $x$ from leading edge at which thermal boundary layer thickness $\delta_T = 0.01$ m is ______ m (rounded off to 1 decimal place).

Explanation

GATE→2025→Heat Transfer→Heat Transfer

Q37

NAT[2 Marks]

An electrical wire... insulated with a plastic layer... steady state temperature at the wire-insulation interface is ______ °C (rounded off to 1 decimal place).

Explanation

Mass Transfer

9 Questions

GATE→2025→Mass Transfer→Mass Transfer

Q38

MCQ[1 Mark]

Schmidt number is defined as

(A)

Mass Diffusivity / Thermal Diffusivity

(B)

Momentum Diffusivity / Mass Diffusivity

(C)

Momentum Diffusivity / Thermal Diffusivity

(D)

Thermal Diffusivity / Mass Diffusivity

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q39

MCQ[1 Mark]

If $k$ is the mass transfer coefficient and $D_{v}$ is the molecular diffusivity, which one of the following statements is NOT CORRECT with respect to mass transfer theories?

(A)

For Film theory, k proportional to Dv

(B)

For Penetration theory, k proportional to Dv^(1/3)

(C)

For Surface Renewal theory, k proportional to Dv^(1/2)

(D)

For Boundary Layer theory, k proportional to Dv^(2/3)

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q40

NAT[1 Mark]

Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using hexane as a solvent... The percentage oil recovery in hexane is ______ % (rounded off to the nearest integer).

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q41

MCQ[2 Marks]

500 mg of a dry adsorbent is added to a beaker containing 100 mL solution of concentration 100 mg phenol/(L solution)... the amount of phenol adsorbed (in mg per gram of dry adsorbent) is

(A)

7

(B)

14

(C)

28

(D)

18

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q42

NAT[2 Marks]

Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure. The vapour pressure equation is given. The dew temperature of the moist air is ______ °C (rounded off to the nearest integer).

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q43

NAT[2 Marks]

A binary AB liquid mixture containing 30 mol% A is subjected to differential (Rayleigh) distillation... average composition of the collected distillate is ______ mol% A (rounded off to nearest integer).

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q44

NAT[2 Marks]

Gas containing 0.8 mol% component A is to be scrubbed with pure water... number of transfer units, based on the gas side, $N_{OG}$ is ______ (rounded off to 1 decimal place).

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q45

NAT[2 Marks]

Solute A is absorbed from a gas into water... interfacial mole fraction $y_i$ equals ______ (rounded off to 3 decimal places).

Explanation

GATE→2025→Mass Transfer→Mass Transfer

Q46

NAT[2 Marks]

A wet solid of 100 kg containing 30 wt% moisture is to be dried to 2 wt% moisture in a tray dryer... time required for drying is ______ h (rounded off to 1 decimal place).

Explanation

Chemical Reaction Engineering

8 Questions

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q47

MCQ[1 Mark]

Choose the CORRECT ordering of the diameter $d$ of the different types of pores in a solid catalyst.

(A)

d_Micro-pore < d_Macro-pore < d_Meso-pore

(B)

d_Macro-pore < d_Meso-pore < d_Micro-pore

(C)

d_Meso-pore < d_Micro-pore < d_Macro-pore

(D)

d_Micro-pore < d_Meso-pore < d_Macro-pore

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q48

MCQ[1 Mark]

Choose the CORRECT statement that describes the dependence of the variance ($\sigma_{\Theta}^{2}$) of the residence time distribution (RTD) with respect to the number of tanks ($n$) in the Tanks-in-Series model of non-ideal reactors.

(A)

sigma^2 monotonically increases

(B)

first increases then decreases

(C)

first decreases then increases

(D)

sigma^2 monotonically decreases with n

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q49

MCQ[1 Mark]

Choose the option that correctly matches the items in Group 1 with those in Group 2.

(A)

(P)-(III), (Q)-(I), (R)-(II)

(B)

(P)-(II), (Q)-(III), (R)-(I)

(C)

(P)-(II), (Q)-(I), (R)-(III)

(D)

(P)-(I), (Q)-(III), (R)-(II)

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q50

MSQ[1 Mark]

Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let $K_{M}$, $S$, and $V_{max}$ denote constants. Which of the following statements is/are TRUE?

(A)

For S << K_M reaction is apparent first-order in S.

(B)

For S >> K_M reaction rate is nearly independent of S.

(C)

For S = K_M rate equals V_max.

(D)

K_M is independent of total enzyme concentration.

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q51

MCQ[2 Marks]

A zero-order gas phase reaction $A \to B$ carried out in MFR... outlet flow is stopped... rate of consumption of A, $-dC_A/dt$, at $t=1$ min is

(A)

63.2

(B)

36.8

(C)

90.6

(D)

99.0

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q52

NAT[2 Marks]

The reaction $A \to \text{products}$ with rate $(-r_A) = kC_A^3$, occurs in an isothermal PFR... The value of $l_1/l_2$ is ______ (rounded off to 2 decimal places).

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q53

NAT[2 Marks]

The catalytic gas phase reaction $A \to \text{products}$ is carried out in an isothermal batch reactor with catalyst decay... The reactant conversion after 1 day of operation is ______ (rounded off to 2 decimal places).

Explanation

GATE→2025→Chemical Reaction Engineering→Chemical Reaction Engineering

Q54

NAT[2 Marks]

Consider the flowsheet for manufacturing C via $A+B \to C$ in an isothermal CSTR... optimum value of reactor volume $V$ is ______ $\text{m}^3$ (rounded off to the nearest integer).

Explanation

Instrumentation and Process Control

6 Questions

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q55

MCQ[1 Mark]

The vortex shedding meter is primarily used for measuring

(A)

Fluid Flow Rate

(B)

Liquid Level

(C)

Temperature

(D)

Fluid Pressure

Explanation

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q56

MCQ[1 Mark]

Choose the transfer function that best fits the output response to a unit step input change shown in the figure

(A)

transfer function A

(B)

transfer function B

(C)

transfer function C

(D)

transfer function D

Explanation

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q57

NAT[1 Mark]

The residence-time distribution (RTD) function of a reactor (in min$^{-1}$) is given. The mean residence time of the reactor is ______ min (rounded off to 2 decimal places).

Explanation

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q58

MCQ[2 Marks]

The first-order irreversible liquid phase reaction $A \to B$ occurs inside a constant volume ($V$) isothermal CSTR... The gain, in $\frac{\text{kmol/m}^3}{\text{m}^3\text{/h}}$, of the transfer function is

(A)

1.2

(B)

0.4

(C)

0.6

(D)

0.8

Explanation

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q59

NAT[2 Marks]

Consider a process with transfer function $G_p = \frac{2e^{-s}}{(5s+1)^2}$. A FOPDT model is to be fitted using maximum slope method. The value of $\frac{\tau_m}{\theta_m}$ is ______ (rounded off to 2 decimal places).

Explanation

GATE→2025→Instrumentation and Process Control→Instrumentation and Process Control

Q60

NAT[2 Marks]

The block diagram of a series cascade control system is shown. For $\tau_I = 8$ min and $K_c^s = 1$, the maximum value of $K_c^m$ below which stability is maintained is ______ (rounded off to the nearest integer).

Explanation

Plant Design and Economics

2 Questions

GATE→2025→Plant Design and Economics→Plant Design and Economics

Q61

MCQ[1 Mark]

The capital cost ($CC$) of an industrial equipment varies with its capacity ($S$) as $CC \propto S^{\beta}$. The rule-of-thumb value of the exponent $\beta$ is

(A)

0.4

(B)

0.6

(C)

0.8

(D)

1.0

Explanation

GATE→2025→Plant Design and Economics→Plant Design and Economics

Q62

NAT[2 Marks]

It is proposed to install thermal insulation... yearly saving 20 thousand rupees, installation cost 150 thousand rupees, life 12 years, 9% interest rate. Minimum salvage value is ______ thousand rupees (rounded off to nearest integer).

Explanation

Chemical Technology

3 Questions

GATE→2025→Chemical Technology→Chemical Technology

Q63

MCQ[1 Mark]

To manufacture paper from (i), the (ii) must be freed from the binding matrix of (iii) in the pulping step. Which one of the following is the CORRECT option to fill in the gaps (i), (ii) and (iii)?

(A)

(i) wood, (ii) cellulose fibers, (iii) lignin

(B)

(i) lignin, (ii) cellulose fibers, (iii) wood

(C)

(i) lignin, (ii) wood, (iii) cellulose fibers

(D)

(i) wood, (ii) lignin, (iii) cellulose fibers

Explanation

GATE→2025→Chemical Technology→Chemical Technology

Q64

MCQ[1 Mark]

In the production of polyvinyl chloride (PVC) from ethylene and chlorine, the sequential order of reactions is

(A)

Chlorination followed by Dehydrochlorination

(B)

Dehydrochlorination followed by Chlorination

(C)

Hydrogenation followed by Chlorination

(D)

Dehydrochlorination followed by Hydrogenation

Explanation

GATE→2025→Chemical Technology→Chemical Technology

Q65

MCQ[1 Mark]

In the CONTACT PROCESS for manufacturing sulphuric acid, the reaction converting $\text{SO}_2$ to $\text{SO}_3$ is

(A)

Exothermic and reversible

(B)

Endothermic and reversible

(C)

Exothermic and irreversible

(D)

Endothermic and irreversible

Explanation