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Type:ALLMCQNATMSQ

Engineering Mathematics(9)Metallurgical Thermodynamics(9)Transport Phenomena and Rate Processes(6)Mineral Processing and Extractive Metallurgy(6)Physical Metallurgy(13)Mechanical Behaviour of Materials(5)Manufacturing Processes(5)Materials Science and Non-Metallic Materials(2)General Aptitude(10)

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Differential Equations

Q1

MCQ[1 Mark]

Given a function $f(t) = e^{-at}$, where $a$ is a constant. The Laplace transform of the function is $\mathcal{L}[f(t)] = F(s)$. Which one of the following options is correct? (A) $F(s) = \frac{1}{s-a}$ (B) $F(s) = \frac{s}{s^2-a^2}$ (C) $F(s) = \frac{a}{s^2-a^2}$ (D) $F(s) = \frac{1}{s+a}$

(A)

$F(s)=\frac{1}{(s-a)}$

(B)

$F(s)=\frac{s}{(s^{2}-a^{2})}$

(C)

$F(s)=\frac{a}{s^{2}-a^{2}}$

(D)

$F(s)=\frac{1}{(s+a)}$

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q2

MCQ[1 Mark]

Select the correct pair of eigenvectors for the following symmetric matrix: $$\begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix}$$ (A) $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} -2 \\ 1 \end{bmatrix}$ (B) $\begin{bmatrix} 1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} 2 \\ 1 \end{bmatrix}$ (C) $\begin{bmatrix} -1 \\ -2 \end{bmatrix}$ and $\begin{bmatrix} 2 \\ 1 \end{bmatrix}$ (D) $\begin{bmatrix} -1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} 2 \\ -1 \end{bmatrix}$

(A)

$\begin{bmatrix} 1 \\ 2 \end{bmatrix} \text{and} \begin{bmatrix} -2 \\ 1 \end{bmatrix}$

(B)

$\begin{bmatrix} 1 \\ 2 \end{bmatrix} \text{and} \begin{bmatrix} 2 \\ 1 \end{bmatrix}$

(C)

$\begin{bmatrix} -1 \\ -2 \end{bmatrix} \text{and} \begin{bmatrix} 2 \\ 1 \end{bmatrix}$

(D)

$\begin{bmatrix} -1 \\ 2 \end{bmatrix} \text{and} \begin{bmatrix} 2 \\ -1 \end{bmatrix}$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q3

MCQ[1 Mark]

Choose one correct option. Given $w = f(ax + by)$ where $a$ and $b$ are constants. The value of $\left(b\frac{\partial w}{\partial x} - a\frac{\partial w}{\partial y}\right)$ is: (A) $-a$ (B) $b$ (C) $b-a$ (D) $0$

(A)

-a

(B)

b

(C)

b-a

(D)

0

Explanation

GATE→2026→Engineering Mathematics→Vector Calculus

Q4

NAT[1 Mark]

Value of scalar triple product $\vec{a}\cdot(\vec{b}\times\vec{c})$ is (answer in integer) $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ $\vec{b} = \hat{i} + 2\hat{j} - 3\hat{k}$ $\vec{c} = 3\hat{i} + 4\hat{j} - \hat{k}$

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q5

NAT[1 Mark]

A box contains 20 thermometers, 3 of which are defective. One person randomly draws 2 thermometers from the box, one-by-one, without replacement. The probability in percent (rounded-off to two decimal places) that none of these TWO thermometers is defective, is ___ %.

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q6

NAT[2 Marks]

Consider a distribution with the following probability density function: $$f(x) = \begin{cases} 0.5, & 0 < x < 2 \\ 0.0, & \text{Otherwise} \end{cases}$$\nGiven that the mean of the above probability distribution is 1, the variance (rounded off to two decimal places) is ___.

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q7

NAT[2 Marks]

Taking number of intervals $n = 3$, the value of the integral $\int_{0}^{0.3} e^{-x^2} dx$ using Trapezoidal method is (rounded off to two decimal places).

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q8

NAT[2 Marks]

Solution of the differential equation $10x^2 \frac{d^2y}{dx^2} - 20x \frac{dy}{dx} + 22.4y = 0$ is $y = c_1 x^{m_1} + c_2 x^{m_2}$ where $m_1 \neq m_2$. The value of $m_1 + m_2$ (answer in integer) is

Explanation

GATE→2026→Engineering Mathematics→Vector Calculus

Q9

NAT[2 Marks]

Magnitude of the vector in the direction of the most rapid increase of $\phi(x,y,z) = x^2 - yz$ at point $P(3, 4, 1)$ is ___.

Explanation

Metallurgical Thermodynamics

9 Questions

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q10

MCQ[1 Mark]

Which one of the following is NOT a state function? (A) Enthalpy (B) Entropy (C) Work (D) Internal Energy

(A)

Enthalpy

(B)

Entropy

(C)

Work

(D)

Internal Energy

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q11

MCQ[1 Mark]

For a regular solution, which one of the following statements is correct? ($\Delta H_{mix}$ is the enthalpy of mixing and $\Delta S_{mix}$ is the entropy of mixing) (A) Both $\Delta H_{mix}$ and $\Delta S_{mix}$ are finite (B) $\Delta H_{mix}$ is zero and $\Delta S_{mix}$ is finite (C) $\Delta H_{mix}$ is finite and $\Delta S_{mix}$ is zero (D) Both $\Delta H_{mix}$ and $\Delta S_{mix}$ are zero

(A)

Both \Delta H_{mix} and \Delta S_{mix} are finite

(B)

\Delta H_{mix} is zero and \Delta S_{mix} is finite

(C)

\Delta H_{mix} is finite and \Delta S_{mix} is zero

(D)

Both \Delta H_{mix} and \Delta S_{mix} are zero

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q12

MSQ[1 Mark]

Choose the correct option(s). Here $A$ is the Helmholtz free energy and $G$ is the Gibbs free energy. (A) $A$ provides a criterion for equilibrium in a system with constant temperature and constant pressure (B) $G$ provides a criterion for equilibrium in a system with constant temperature and constant pressure (C) $A$ provides a criterion for equilibrium in a system with constant temperature and constant volume (D) $G$ provides a criterion for equilibrium in a system with constant temperature and constant volume

(A)

'A' provides a criterion for equilibrium in a system with constant temperature and constant pressure

(B)

'G' provides a criterion for equilibrium in a system with constant temperature and constant pressure

(C)

'A' provides a criterion for equilibrium in a system with constant temperature and constant volume

(D)

'G' provides a criterion for equilibrium in a system with constant temperature and constant volume

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q13

NAT[1 Mark]

For an equilibrium phase diagram of a binary A-B alloy at a constant pressure as shown in the figure, the degree of freedom at 'X' is (answer in integer)

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q14

NAT[2 Marks]

$20\text{ g}$ of Au and $20\text{ g}$ of Ag form an ideal solid solution. Total entropy of mixing is ___ $\text{J/K}$.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q15

NAT[2 Marks]

$2$ moles of an ideal gas are reversibly expanded from $10\text{ L}$ to $20\text{ L}$ isothermally at $27^\circ\text{C}$. Magnitude of work done is ___ Joules.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q16

NAT[2 Marks]

For $2$ moles of metal with $C_p = 20 + 5 \times 10^{-3}T$, change in enthalpy upon heating from $300\text{ K}$ to $600\text{ K}$ is ___ Joules.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q17

NAT[2 Marks]

Given Ellingham oxidation equations for solid and liquid metal M, the melting point of metal M is ___ Kelvin.

Explanation

GATE→2026→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q18

NAT[2 Marks]

For the combustion of methane with stoichiometric air, estimated adiabatic flame temperature is ___ Kelvin.

Explanation

Transport Phenomena and Rate Processes

6 Questions

GATE→2026→Transport Phenomena and Rate Processes→Mass Transfer and Dimensional Analysis

Q19

MCQ[1 Mark]

Which one of the following options is correct? In convective heat transfer for laminar flow over a flat plate, Nusselt number is a function of Reynolds and Prandtl numbers. Similarly, in convective mass transfer, Sherwood number is a function of: (A) Schmidt number and Reynolds number (B) Weber number and Reynolds number (C) Schmidt number and Weber number (D) Weber number and Prandtl number

(A)

Schmidt number and Reynolds number

(B)

Weber number and Reynolds number

(C)

Schmidt number and Weber number

(D)

Weber number and Prandtl number

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Heat Transfer

Q20

MCQ[1 Mark]

Which one of the following options is correct? For a solid immersed in a fluid, the convective heat transfer coefficient across the solid-fluid interface is NOT dependent on: (A) Solid-fluid interfacial area (B) Thermal conductivity of solid (C) Roughness of solid surface (D) Viscosity of fluid

(A)

Solid-fluid interfacial area

(B)

Thermal conductivity of solid

(C)

Roughness of solid surface

(D)

Viscosity of fluid

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q21

NAT[1 Mark]

Two parallel plates, with Newtonian incompressible liquid in between, are 2 mm apart. The upper plate is stationary and the lower plate moves with a velocity of $4\text{ m/s}$. A force per unit area of $5\text{ N/m}^2$ is applied parallel to the lower plate to maintain its motion. The viscosity of the liquid (rounded off to two decimal places) is ___ $\times 10^{-3}\text{ N}\cdot\text{s/m}^2$.

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q22

MCQ[2 Marks]

The equation below represents steady-state laminar flow of a fluid through a horizontal tube: $$\eta \frac{1}{r} \frac{d}{dr}\left(r \frac{dv_z}{dr}\right) - \frac{dP}{dz} = 0$$\nWhich one of the following statements related to the above case is NOT correct? (A) The fluid is Newtonian (B) Shear stress is maximum at the center ($r=0$) (C) Radial velocity is zero (D) There is no variation of $v_z$ in $z$-direction

(A)

The fluid is Newtonian

(B)

Shear stress is maximum at the center (r=0)

(C)

Radial velocity is zero

(D)

There is no variation of v_{z} in z-direction

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q23

MSQ[2 Marks]

Choose the correct option(s). Permeability of a porous bed made of spherical particles is/are: (A) Independent of particle size (B) Increases with increase in particle size (C) Decreases with increase in particle size (D) Affected by particle size distribution

(A)

Independent of particle size

(B)

Increases with increase in particle size

(C)

Decreases with increase in particle size

(D)

Affected by particle size distribution

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Heat Transfer

Q24

NAT[2 Marks]

For a cylindrical furnace with $0.1\text{ m}$ diameter and $0.2\text{ m}$ height operating at $1873\text{ K}$, power needed is ___ W.

Explanation

Mineral Processing and Extractive Metallurgy

6 Questions

GATE→2026→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q25

MCQ[1 Mark]

Which one of the following options is correct? Red mud is generated in the production of: (A) Aluminium (B) Iron (C) Titanium (D) Copper

(A)

Aluminium

(B)

Iron

(C)

Titanium

(D)

Copper

Explanation

GATE→2026→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q26

MCQ[1 Mark]

Ergun equation is NOT applied in which one of the following unit operations to analyze gas flow behavior: (A) Blast Furnace (B) Sintering (C) Roasting (D) LD Converter

(A)

Blast Furnace

(B)

Sintering

(C)

Roasting

(D)

LD Converter

Explanation

GATE→2026→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q27

MCQ[2 Marks]

Match the unit operation in Column I with the resulting product in Column II:\nColumn I: (P) COREX Process (Q) Bayer Process (R) Matte Smelting (S) MIDREX Process\nColumn II: (1) Direct Reduced Iron (2) Pig Iron (3) Alumina (4) Copper (A) P-4, Q-3, R-2, S-1 (B) P-2, Q-3, R-4, S-1 (C) P-1, Q-3, R-4, S-2 (D) P-2, Q-4, R-3, S-1

(A)

P-4, Q-3, R-2, S-1

(B)

P-2, Q-3, R-4, S-1

(C)

P-1, Q-3, R-4, S-2

(D)

P-2, Q-4, R-3, S-1

Explanation

GATE→2026→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q28

NAT[2 Marks]

An ore containing $30\text{ wt.}\%$ chalcopyrite has ___ $\text{wt.}\%$ copper.

Explanation

GATE→2026→Mineral Processing and Extractive Metallurgy→Ironmaking

Q29

NAT[2 Marks]

Amount of ore required to produce $1000\text{ kg}$ of hot metal with given blast furnace parameters is ___ $\text{kg}$[cite: 66, 70].

Explanation

GATE→2026→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q30

NAT[2 Marks]

Decrease in decomposition potential when replacing inert anode with carbon anode at $1300\text{ K}$ is ___ Volts.

Explanation

Physical Metallurgy

13 Questions

GATE→2026→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q31

MCQ[1 Mark]

During metallography, Nital is the most commonly used etchant for (A) Bronze (B) Brass (C) Mild Steel (D) Aluminium

(A)

Bronze

(B)

Brass

(C)

Mild Steel

(D)

Aluminium

Explanation

GATE→2026→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q32

MCQ[1 Mark]

Which one of the following options is correct? In a face-centered cubic metal, a Shockley partial is: (A) Perfect and mobile dislocation (B) Perfect and immobile dislocation (C) Imperfect and immobile dislocation (D) Imperfect and mobile dislocation

(A)

Perfect and mobile dislocation

(B)

Perfect and immobile dislocation

(C)

Imperfect and immobile dislocation

(D)

Imperfect and mobile dislocation

Explanation

GATE→2026→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q33

MCQ[1 Mark]

Which one of the following options is correct? For Al - 4% Ag alloy (composition in atom %), the correct sequence of operations involved in precipitation hardening is: (A) Quenching $\rightarrow$ Aging $\rightarrow$ Solution treatment (B) Solution treatment $\rightarrow$ Aging $\rightarrow$ Quenching (C) Aging $\rightarrow$ Solution treatment $\rightarrow$ Quenching (D) Solution treatment $\rightarrow$ Quenching $\rightarrow$ Aging

(A)

Quenching \rightarrow Aging \rightarrow Solution treatment

(B)

Solution treatment \rightarrow Aging \rightarrow Quenching

(C)

Aging \rightarrow Solution treatment \rightarrow Quenching

(D)

Solution treatment \rightarrow Quenching \rightarrow Aging

Explanation

GATE→2026→Physical Metallurgy→Diffusion in Solids

Q34

MCQ[1 Mark]

Which one of the following options is correct? In a binary alloy system, during spinodal decomposition, uphill diffusion occurs: (A) From higher to lower concentration and from higher to lower chemical potential (B) From higher to lower concentration and from lower to higher chemical potential (C) From lower to higher concentration and from lower to higher chemical potential (D) From lower to higher concentration and from higher to lower chemical potential

(A)

From higher to lower concentration and from higher to lower chemical potential

(B)

From higher to lower concentration and from lower to higher chemical potential

(C)

From lower to higher concentration and from lower to higher chemical potential

(D)

From lower to higher concentration and from higher to lower chemical potential

Explanation

GATE→2026→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q35

MCQ[1 Mark]

Which one of the following options is correct? In Al - 4 wt.% Cu alloy during isothermal aging, the correct precipitation sequence is: (A) $\theta'' \rightarrow \theta' \rightarrow \theta \rightarrow \text{GP zone}$ (B) $\text{GP zone} \rightarrow \theta \rightarrow \theta' \rightarrow \theta''$ (C) $\theta \theta' \theta'' \rightarrow \text{GP zone}$ (D) $\text{GP zone} \rightarrow \theta'' \rightarrow \theta' \rightarrow \theta$

(A)

\Theta^{\prime\prime}\rightarrow\theta^{\prime}\rightarrow\theta\rightarrow GP zone

(B)

GP zone \rightarrow\theta\rightarrow\theta^{\prime}\rightarrow\theta^{\prime\prime}

(C)

00'0" \rightarrow GP zone

(D)

GP zone \rightarrow\theta^{\prime\prime}\rightarrow\theta^{\prime}\rightarrow\theta

Explanation

GATE→2026→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q36

MCQ[1 Mark]

Which one of the following options is correct? After cold-working of a metallic specimen, during the recovery stage, its electrical conductivity: (A) Always increases (B) Always decreases (C) Can increase or decrease (D) Remains unaffected

(A)

Always increases

(B)

Always decreases

(C)

Can increase or decrease

(D)

Remains unaffected

Explanation

GATE→2026→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q37

MCQ[1 Mark]

Residual stress present in a material can be determined by which one of the following techniques: (A) X-ray Diffraction (XRD) (B) Tensile Testing (C) Thermo-Gravimetric Analysis (TGA) (D) Optical Microscopy

(A)

X-ray Diffraction (XRD)

(B)

Tensile Testing

(C)

Thermo-Gravimetric Analysis (TGA)

(D)

Optical Microscopy

Explanation

GATE→2026→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q38

MSQ[1 Mark]

Which of the following elements, when present in iron, enhance(s) its corrosion resistance? (A) H (B) Cr (C) S (D) C

(A)

H

(B)

Cr

(C)

S

(D)

C

Explanation

GATE→2026→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q39

NAT[2 Marks]

An alloy having composition W-20 wt.% Ni is prepared by mixing elemental powders. The resulting powder mixture is liquid phase sintered at $1550^\circ\text{C}$ for 1 hour. The tungsten grain size is $70\text{ }\mu\text{m}$ and neck diameter is $35\text{ }\mu\text{m}$. If W-Ni interfacial energy is $0.30\text{ J/m}^2$, W-W interfacial energy is ___ $\text{J/m}^2$.

Explanation

GATE→2026→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q40

NAT[2 Marks]

A metal having body-centered cubic structure is analyzed through X-ray diffraction using monochromatic X-ray of wavelength $0.154\text{ nm}$. The diffraction angle ($2\theta$) corresponding to $\{200\}$ plane is $60^\circ$. The atomic radius is ___ $\text{nm}$.

Explanation

GATE→2026→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q41

NAT[2 Marks]

The lattice parameter of Ni is $0.35\text{ nm}$ and shear modulus is $76\text{ GPa}$. Strain energy per unit length of screw dislocation is ___ $\times 10^{-9}\text{ J/m}$.

Explanation

GATE→2026→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q42

NAT[2 Marks]

For homogeneous nucleation with $\Delta G_v = -0.5 \times 10^8\text{ J/m}^3$ and $\gamma = 0.1\text{ J/m}^2$, the critical nucleus size is ___ $\text{nm}$.

Explanation

GATE→2026→Physical Metallurgy→Diffusion in Solids

Q43

NAT[2 Marks]

During carburizing of steel at $950^\circ\text{C}$, the time required to reach $0.8859\text{ wt.}\%$ C at $0.2\text{ mm}$ depth is ___ seconds.

Explanation

Mechanical Behaviour of Materials

5 Questions

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q44

MCQ[1 Mark]

Deformation mechanism map of a given material is used for determining which one of the following properties? (A) Fatigue strength (B) Creep rate (C) Tensile strength (D) Impact toughness

(A)

Fatigue strength

(B)

Creep rate

(C)

Tensile strength

(D)

Impact toughness

Explanation

GATE→2026→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q45

MCQ[1 Mark]

Which one of the following dislocation dissociation reactions is feasible in face-centered cubic metals? (A) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{2}1] + \frac{a}{6}[\bar{1}\bar{1}2]$ (B) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1 1 2] + \frac{a}{6}[2 1 \bar{1}]$ (C) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{1}2] + \frac{a}{6}[\bar{1}\bar{2}\bar{1}]$ (D) $\frac{a}{2}[0\bar{1}1] \rightarrow \frac{a}{6}[1\bar{2}1] + \frac{a}{6}[2\bar{1}\bar{1}]$

(A)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{2}1]+a/6[\bar{1}\bar{1}2]

(B)

a/2[0\bar{1}1]\rightarrow a/6[1 1 2]+a/6[2 1 \bar{1}]

(C)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{1}2]+a/6[\bar{1}\bar{2}\bar{1}]

(D)

a/2[0\bar{1}1]\rightarrow a/6[1\bar{2}1]+a/6[2\bar{1}\bar{1}]

Explanation

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q46

MCQ[2 Marks]

Match the concepts listed in Column I with the associated terms listed in Column II:\nColumn I: (P) Paris Law (Q) Schmid Factor (R) Larson - Miller Parameter (S) Portevin - Le Chatelier Effect\nColumn II: (1) Creep (2) Fatigue (3) Dynamic Strain Aging (4) Critical Resolved Shear Stress (A) P-3, Q-1, R-2, S-4 (B) P-2, Q-4, R-1, S-3 (C) P-2, Q-4, R-3, S-1 (D) P-1, Q-3, R-2, S-4

(A)

P-3, Q-1, R-2, S-4

(B)

P-2, Q-4, R-1, S-3

(C)

P-2, Q-4, R-3, S-1

(D)

P-1, Q-3, R-2, S-4

Explanation

GATE→2026→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q47

NAT[2 Marks]

A cylindrical single crystal of copper having $10\text{ mm}$ diameter is deformed under uniaxial tensile load of $2200\text{ N}$. If $\alpha = \beta$, the critical resolved shear stress (CRSS) is ___ $\text{MPa}$.

Explanation

GATE→2026→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q48

NAT[2 Marks]

For plane strain fracture toughness ($K_{Ic}$) testing of Maraging steel, minimum thickness to achieve valid $K_{Ic}$ is ___ (Given: $K_{Ic} = 90\text{ MPa}\sqrt{\text{m}}$, yield stress $= 900\text{ MPa}$)

Explanation

Manufacturing Processes

5 Questions

GATE→2026→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q49

MCQ[1 Mark]

Which one of the following fusion welding techniques results in least Heat-Affected Zone (HAZ)? (A) Submerged Arc Welding (SAW) (B) Tungsten Inert Gas Welding (TIG) (C) Electron Beam Welding (EBW) (D) Oxy-Acetylene Welding (OAW)

(A)

Submerged Arc Welding (SAW)

(B)

Tungsten Inert Gas Welding (TIG)

(C)

Electron Beam Welding (EBW)

(D)

Oxy-Acetylene Welding (OAW)

Explanation

GATE→2026→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q50

MCQ[2 Marks]

Match the type of defects in Column I with the corresponding metal manufacturing processes listed in Column II:\nColumn I: (P) Edge Cracking (Q) Flashline Cracking (R) Chevron Cracking (S) Cracked Core\nColumn II: (1) Casting (2) Forging (3) Rolling (4) Extrusion (A) P-3, Q-4, R-2, S-1 (B) P-4, Q-3, R-1, S-2 (C) P-4, Q-2, R-3, S-1 (D) P-3, Q-2, R-4, S-1

(A)

P-3, Q-4, R-2, S-1

(B)

P-4, Q-3, R-1, S-2

(C)

P-4, Q-2, R-3, S-1

(D)

P-3, Q-2, R-4, S-1

Explanation

GATE→2026→Manufacturing Processes→Non-destructive Testing (NDT)

Q51

MCQ[2 Marks]

Match the descriptions listed in Column I with the corresponding non-destructive testing methods listed in Column II:\nColumn I: (P) Internal flaws in railroad wheel (Q) In-service monitoring of crack (R) Inclusion in mild steel (S) Surface crack in Al-based alloy\nColumn II: (1) Ultrasonic (2) Radiography (3) Dye Penetrant (4) Acoustic Emission (A) P-1, Q-4, R-2, S-3 (B) P-3, Q-2, R-4, S-1 (C) P-3, Q-2, R-1, S-4 (D) P-1, Q-3, R-4, S-2

(A)

P-1, Q-4, R-2, S-3

(B)

P-3, Q-2, R-4, S-1

(C)

P-3, Q-2, R-1, S-4

(D)

P-1, Q-3, R-4, S-2

Explanation

GATE→2026→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q52

NAT[2 Marks]

Iron powder is compacted at room temperature to 75% of its theoretical density. The as-pressed iron compact is sintered in inert-gas atmosphere at $1200^\circ\text{C}$ to 90% of its theoretical density. Assuming isotropic shrinkage, the linear shrinkage (in percent) undergone by the iron compact during sintering (rounded off to one decimal place) is ___ %.

Explanation

GATE→2026→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q53

NAT[2 Marks]

For cold-rolling an aluminium plate from $50\text{ mm}$ to $25\text{ mm}$ with roll diameter $1250\text{ mm}$, the minimum required coefficient of friction is ___.

Explanation

Materials Science and Non-Metallic Materials

2 Questions

GATE→2026→Materials Science and Non-Metallic Materials→Classification, Chemical Bonding, and Crystal Structures

Q54

MCQ[2 Marks]

Match the crystal systems in Column I with the corresponding axial lengths ($a, b, c$) and interaxial angles ($\alpha, \beta, \gamma$) provided in Column II:\nColumn I: (P) Tetragonal (Q) Rhombohedral (R) Orthorhombic (S) Monoclinic\nColumn II: (1) $a \neq b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (2) $a = b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (3) $a \neq b \neq c$, $\alpha = \gamma = 90^\circ \neq \beta$ (4) $a = b = c$, $\alpha = \beta = \gamma \neq 90^\circ$ (A) P-3, Q-1, R-2, S-4 (B) P-2, Q-3, R-4, S-1 (C) P-4, Q-3, R-2, S-1 (D) P-2, Q-4, R-1, S-3

(A)

P-3, Q-1, R-2, S-4

(B)

P-2, Q-3, R-4, S-1

(C)

P-4, Q-3, R-2, S-1

(D)

P-2, Q-4, R-1, S-3

Explanation

GATE→2026→Materials Science and Non-Metallic Materials→Electronic and Magnetic Properties

Q55

MCQ[2 Marks]

Match the terms in Column I with the corresponding attributes in Column II:\nColumn I: (P) Wiedemann-Franz law (Q) Neel temperature (R) Hall voltage (S) Curie law\nColumn II: (1) Charge carrier concentration (2) Paramagnetism (3) Ratio between thermal conductivity and electrical conductivity of metals (4) Diamagnetism (5) Anti-ferromagnetism (A) P-4, Q-3, R-2, S-1 (B) P-2, Q-5, R-1, S-3 (C) P-3, Q-5, R-1, S-2 (D) P-3, Q-4, R-5, S-2

(A)

P-4, Q-3, R-2, S-1

(B)

P-2, Q-5, R-1, S-3

(C)

P-3, Q-5, R-1, S-2

(D)

P-3, Q-4, R-5, S-2

Explanation

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

'The team _______ more than 300 runs in 20 overs _______ rains. However, some players needed to improve their batting skills.' Choose the option with the correct sequence of words to fill the blanks. (A) score; despite (B) scoring; instead of (C) scored; despite (D) scoring; in spite of

(A)

score; despite

(B)

scoring; instead of

(C)

scored; despite

(D)

scoring; in spite of

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

If a positive real $x$ satisfies the following equation $\log_{2}x + \log_{\sqrt{2}}x = 48$, then the value of $x$ is (A) $2^{16}$ (B) $4^{16}$ (C) $2^{14}$ (D) $4^{14}$

(A)

$2^{16}$

(B)

$4^{16}$

(C)

$2^{14}$

(D)

$4^{14}$

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

The next figure (indicated by '?') in the sequence is...

(A)

a

(B)

b

(C)

c

(D)

d

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q59

MCQ[1 Mark]

'All the mangoes in the basket are good.' If the above statement is false, then which one of the following statements is necessarily true? (A) All the mangoes in the basket are not good. (B) No mango in the basket is good. (C) In the basket, some of the mangoes are good and some are not good. (D) There exists at least one mango in the basket that is not good.

(A)

All the mangoes in the basket are not good.

(B)

No mango in the basket is good.

(C)

In the basket, some of the mangoes are good and some are not good.

(D)

There exists at least one mango in the basket that is not good.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20\nChoose the option that is necessarily correct. (A) (S1) and (S2) together imply (S3) (B) (S2) and (S3) together imply (S1) (C) (S1) and (S3) together imply (S2) (D) (S1) implies (S3)

(A)

(S1) and (S2) together imply (S3)

(B)

(S2) and (S3) together imply (S1)

(C)

(S1) and (S3) together imply (S2)

(D)

(S1) implies (S3)

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

'People are crowding around [blank 1] pit into which [blank 2] elephant has fallen. I have never seen an elephant looking more bewildered [blank 3] miserable. Here it is in a most undignified position, thrust into a pit and made to look up [blank 4] a vast, curiosity-stricken crowd.' Choose the option with the correct sequence of words to fill the blanks. (A) an; a; at; and (B) a; an; and; at (C) and; a; an; at (D) at; a; an; and

(A)

an; a; at; and

(B)

a; an; and; at

(C)

and; a; an; at

(D)

at; a; an; and

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q62

MCQ[2 Marks]

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The observations are: - Q of S = $2 \times$ Q of T - Q of R = $3 \times$ Q of T - Q of Q = $4 \times$ Q of T\nPrices: P = 50, Q = 100, R = 60, S = 60, T = 40.\nWhat is the quantity of product P sold on that day? (A) 40 (B) 50 (C) 60 (D) 70

(A)

40

(B)

50

(C)

60

(D)

70

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

Consider a string P of length $l$ laid out as a straight-line segment. String K is a semicircular arc with P as diameter. Both strings are shortened by length $x$, such that shortened K forms a full circle with shortened P as its diameter. The value of $x/l$ is (A) $\pi$ (B) $\frac{\pi-1}{2\pi}$ (C) $\frac{\pi}{2(\pi-1)}$ (D) $\frac{\pi}{\pi-1}$

(A)

\pi

(B)

\frac{\pi-1}{2\pi}

(C)

\frac{\pi}{2(\pi-1)}

(D)

\frac{\pi}{\pi-1}

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels, seated in a 2x2 grid. Conditions given: (i) Daughter and brother in same column. (ii) Son is seated diagonally across the sibling of the worst orator. (iii) Best and worst orators in the same row. Who is the best orator? (A) Meritorius (B) Meritorius' brother (C) Meritorius' son (D) Meritorius' daughter

(A)

Meritorius

(B)

Meritorius' brother

(C)

Meritorius' son

(D)

Meritorius' daughter

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

Which one of the patterns labelled P, Q, R, and S is used to generate the given figure? (A) P (B) Q (C) R (D) S

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation