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Engineering Mathematics(8)Metallurgical Thermodynamics(9)Transport Phenomena and Rate Processes(6)Mineral Processing and Extractive Metallurgy(8)Physical Metallurgy(9)Mechanical Behaviour of Materials(7)Manufacturing Processes(7)Materials Science and Non-Metallic Materials(1)General Aptitude(10)

Engineering Mathematics

8 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q1

MCQ[1 Mark]

Which one of the following matrices has eigenvalues 1 and 6? (A) $\begin{bmatrix} 5 & -2 \\ -2 & 2 \end{bmatrix}$ (B) $\begin{bmatrix} 3 & -1 \\ -2 & 2 \end{bmatrix}$ (C) $\begin{bmatrix} 3 & -1 \\ -1 & 2 \end{bmatrix}$ (D) $\begin{bmatrix} 2 & -1 \\ -1 & 3 \end{bmatrix}$

(A)

$\begin{bmatrix} 5 & -2 \\ -2 & 2 \end{bmatrix}$

(B)

$\begin{bmatrix} 3 & -1 \\ -2 & 2 \end{bmatrix}$

(C)

$\begin{bmatrix} 3 & -1 \\ -1 & 2 \end{bmatrix}$

(D)

$\begin{bmatrix} 2 & -1 \\ -1 & 3 \end{bmatrix}$

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q2

MSQ[1 Mark]

Which of the following functions is/are expandable using Maclaurin series? (A) $\ln(1+z)$ (B) $\ln z$ (C) $\frac{1}{z^2}$ (D) $\exp(z)$

(A)

\ln(1+z)

(B)

\ln z

(C)

\frac{1}{z^{2}}

(D)

\exp(z)

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q3

NAT[1 Mark]

A linear regression model was fitted to a set of $(x,y)$ data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination ($R^2$) of the fit is ___ (rounded off to one decimal place).

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q4

MCQ[2 Marks]

For two continuous functions $M(x,y)$ and $N(x,y)$, the relation $M\text{ }dx + N\text{ }dy = 0$ describes an exact differential equation if (A) $\frac{\partial M}{\partial x} = \frac{\partial N}{\partial y}$ (B) $\frac{\partial M}{\partial x} = -\frac{\partial N}{\partial y}$ (C) $\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$ (D) $\frac{\partial M}{\partial y} = -\frac{\partial N}{\partial x}$

(A)

\frac{\partial M}{\partial x}=\frac{\partial N}{\partial y}

(B)

\frac{\partial M}{\partial x}=-\frac{\partial N}{\partial y}

(C)

\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}

(D)

\frac{\partial M}{\partial y}=-\frac{\partial N}{\partial x}

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q5

MCQ[2 Marks]

Which one of the following matrices is orthogonal?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2025→Engineering Mathematics→Vector Calculus

Q6

NAT[2 Marks]

For a two-dimensional field described by $T(x,y) = \frac{1}{3}xy(x+y)$, the magnitude of its gradient at the point $(1,1)$ is ___ (rounded off to two decimal places).

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q7

NAT[2 Marks]

The value of $\lim_{x\rightarrow 0}\frac{6(x - \sin x)}{x^3}$ is ___ (in integer).

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q8

NAT[2 Marks]

Two consecutive estimates of the root of a function $f(x)$ obtained using the Newton-Raphson method are $x_i = 8.5$ and $x_{i+1} = 13.5$, and the value of the function at $x_i$ is $15$. The numerical value of first derivative of the function evaluated at $x_i$ is ___ (in integer).

Explanation

Metallurgical Thermodynamics

9 Questions

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q9

MCQ[1 Mark]

For an isobaric process, the heat transferred is equal to the change in _______ of the system. (A) enthalpy (B) entropy (C) Helmholtz free energy (D) Gibbs free energy

(A)

enthalpy

(B)

entropy

(C)

Helmholtz free energy

(D)

Gibbs free energy

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q10

MCQ[1 Mark]

Which one of the following is an intensive property? (A) Chemical potential (B) Volume (C) Mass (D) Entropy

(A)

Chemical potential

(B)

Volume

(C)

Mass

(D)

Entropy

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q11

MCQ[1 Mark]

Consider the following gas-phase reaction: $$2SO_{2}+O_{2}\rightleftharpoons 2SO_{3}$$\nIf the enthalpy of reaction is negative, which one of the following conditions promotes a higher equilibrium concentration of $SO_{3}$? (A) Higher pressure and higher temperature (B) Higher pressure and lower temperature (C) Lower pressure and higher temperature (D) Lower pressure and lower temperature

(A)

Higher pressure and higher temperature

(B)

Higher pressure and lower temperature

(C)

Lower pressure and higher temperature

(D)

Lower pressure and lower temperature

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q12

MSQ[1 Mark]

Standard Gibbs free energies of formation of some solid oxides per mole of $O_2$ at $1000\text{ K}$ are given below: $SiO_2$: $-728\text{ kJ}$, $TiO_2$: $-737\text{ kJ}$, $VO$: $-712\text{ kJ}$, $MnO$: $-624\text{ kJ}$\nRegarding thermodynamic feasibility of oxide reduction, which of the following statements is/are CORRECT under standard conditions at $1000\text{ K}$? (A) Si can reduce $TiO_2$ (B) Mn can reduce VO (C) Ti can reduce MnO (D) V can reduce $SiO_2$

(A)

Si can reduce TiO_{2}

(B)

Mn can reduce VO

(C)

Ti can reduce MnO

(D)

V can reduce SiO_{2}

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q13

NAT[1 Mark]

Consider the gas phase reaction: $$CO + \frac{1}{2}O_2 \rightleftharpoons CO_2$$\nAt equilibrium for a particular temperature, the partial pressures of $CO$, $O_2$, and $CO_2$ are found to be $10^{-6}\text{ atm}$, $10^{-6}\text{ atm}$, and $16\text{ atm}$, respectively. The equilibrium constant for the reaction is ___ $\times 10^{10}$ (rounded off to one decimal place).

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q14

MCQ[2 Marks]

Consider the phase diagram of a one component system given below. $V_{\alpha}$, $V_{\beta}$, and $V_{Liquid}$ are the molar volumes of $\alpha$, $\beta$, and liquid phases, respectively. Which one of the following statements is TRUE?\nGiven: The change in molar enthalpies, $\Delta H^{\alpha\rightarrow\beta}$ and $\Delta H^{\beta\rightarrow Liquid}$, are positive. (A) $V_{\alpha} < V_{\beta}$ and $V_{\beta} < V_{Liquid}$ (B) $V_{\alpha} > V_{\beta}$ and $V_{\beta} < V_{Liquid}$ (C) $V_{\alpha} < V_{\beta}$ and $V_{\beta} > V_{Liquid}$ (D) $V_{\alpha} > V_{\beta}$ and $V_{\beta} > V_{Liquid}$

(A)

V_{\alpha}<V_{\beta} and V_{\beta}<V_{Liquid}

(B)

V_{\alpha}>V_{\beta} and V_{\beta}<V_{Liquid}

(C)

V_{\alpha}<V_{\beta} and V_{\beta}>V_{Liquid}

(D)

V_{\alpha}>V_{\beta} and V_{\beta}>V_{Liquid}

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q15

NAT[2 Marks]

The excess molar Gibbs free energy of a solution of element A and B at $1000\text{ K}$ is given by $G^{XS} = -3000\text{ }X_A X_B\text{ J mol}^{-1}$, where $X_A$ and $X_B$ are mole fractions of A and B, respectively. The activity of B in a solution of A and B containing $40\text{ mol}\%$ of B at $1000\text{ K}$ is ___ (rounded off to two decimal places). (Given: $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$)

Explanation

GATE→2025→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q16

NAT[2 Marks]

Consider the following reactions and their standard Gibbs free energies (in J): $Fe(s) + \frac{1}{2}O_2(g) \rightleftharpoons FeO(s)$, $\Delta G^\circ = -264900 + 65T$ $2H_2(g) + O_2(g) \rightleftharpoons 2H_2O(g)$, $\Delta G^\circ = -492900 + 109T$\nThe value of $\frac{p_{H_2O}}{p_{H_2}}$ required to reduce solid FeO to solid Fe at $1000\text{ K}$ is ___ (rounded off to two decimal places).

Explanation

GATE→2025→Metallurgical Thermodynamics→Electrochemistry

Q17

NAT[2 Marks]

Consider the following cell reaction: $$Mg + Cd^{2+} \rightleftharpoons Mg^{2+} + Cd$$\nThe standard Gibbs free energy change for the reaction is ___ $\text{kJ}$ (rounded off to an integer).\nGiven: Standard oxidation potentials are $Mg \rightleftharpoons Mg^{2+} + 2e^-$, $E^\circ = 2.37\text{ V}$; $Cd \rightleftharpoons Cd^{2+} + 2e^-$, $E^\circ = 0.403\text{ V}$. Faraday's constant $= 96500\text{ C mol}^{-1}$

Explanation

Transport Phenomena and Rate Processes

6 Questions

GATE→2025→Transport Phenomena and Rate Processes→Momentum Transfer

Q18

MCQ[1 Mark]

At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity $\mu$ of a Newtonian liquid with absolute temperature $T$? Given: $A$ and $B$ are positive constants. (A) $\mu = A + BT$ (B) $\mu = A \exp\left(-\frac{B}{T}\right)$ (C) $\mu = A \exp(BT)$ (D) $\mu = A \exp\left(\frac{B}{T}\right)$

(A)

\mu = A + BT

(B)

\mu = A \exp(-B/T)

(C)

\mu = A \exp(BT)

(D)

\mu = A \exp(B/T)

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Momentum Transfer

Q19

MSQ[1 Mark]

Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities?\nGiven: $\Delta P$ is the pressure drop, $\mu$ is dynamic viscosity, and $R$ and $L$ are radius and length of the pipe, respectively. (A) $\Delta P$ (B) $1/R^2$ (C) $1/\mu$ (D) $1/L$

(A)

\Delta P

(B)

1/R^{2}

(C)

1/\mu

(D)

1/L

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Dimensional Analysis

Q20

NAT[1 Mark]

For an application where the Reynolds number is to be kept constant, a liquid with a density of $1\text{ g cm}^{-3}$ and viscosity $0.01\text{ Poise}$ results in a characteristic speed of $1\text{ cm s}^{-1}$. If this liquid is replaced by another with a density of $1.25\text{ g cm}^{-3}$ and viscosity of $0.015\text{ Poise}$, the characteristic velocity will be ___ $\text{cm s}^{-1}$ (rounded off to one decimal place).

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Heat Transfer

Q21

MCQ[2 Marks]

Radiative heat flux $\dot{q}$ at a hot surface at a temperature $T_s$ can be expressed as $\dot{q} = A \cdot f(T_s, T_\infty)(T_s - T_\infty)$ where $A$ is a constant and $T_\infty$ is the temperature of the surroundings. The function $f(T_s, T_\infty)$ is given by (A) $(T_s + T_\infty)^2(T_s - T_\infty)$ (B) $(T_s^2 + T_\infty^2)(T_s + T_\infty)$ (C) $(T_s^2 - T_\infty^2)(T_s + T_\infty)$ (D) $(T_s - T_\infty)^2(T_s + T_\infty)$

(A)

(T_{s}+T_{\infty})^{2}(T_{s}-T_{\infty})

(B)

(T_{s}^{2}+T_{\infty}^{2})(T_{s}+T_{\infty})

(C)

(T_{s}^{2}-T_{\infty}^{2})(T_{s}+T_{\infty})

(D)

(T_{s}-T_{\infty})^{2}(T_{s}+T_{\infty})

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Heat Transfer

Q22

NAT[2 Marks]

Temperatures at two sides of a $0.4\text{ m}$ thick copper plate are $1000^{\circ}\text{C}$ and $500^{\circ}\text{C}$. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is ___ $\times 10^5\text{ W m}^{-2}$ (in integer). (Given: Thermal conductivity of copper is $400\text{ W m}^{-1}\text{K}^{-1}$)

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Basic Laws of Chemical Kinetics

Q23

NAT[2 Marks]

The reaction represented by $A \rightarrow B$ follows first order kinetics. At a given temperature, $20\%$ of the reaction is completed in $223\text{ s}$. The time taken to complete $50\%$ of the reaction at the same temperature is ___ $\text{s}$ (rounded off to the nearest integer).

Explanation

Mineral Processing and Extractive Metallurgy

8 Questions

GATE→2025→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q24

MCQ[1 Mark]

Hot metal from a blast furnace is treated with mill scale prior to oxygen steelmaking for _______. (A) dephosphorization (B) decarburization (C) desulphurization (D) desiliconization

(A)

dephosphorization

(B)

decarburization

(C)

desulphurization

(D)

desiliconization

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q25

MCQ[1 Mark]

Which one of the following slag components is responsible for the oxidizing power of steelmaking slags? (A) $SiO_{2}$ (B) $CaO$ (C) $MgO$ (D) $FeO$

(A)

SiO2

(B)

CaO

(C)

MgO

(D)

FeO

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q26

MCQ[1 Mark]

Match the following elements in Column I with their respective ores in Column II.\nColumn I:\nP. Al\nQ. Fe\nR. Ti\nS. Cu\nColumn II: 1. Rutile 2. Hematite 3. Chalcopyrite 4. Bauxite (A) P-4, Q-2, R-3, S-1 (B) P-2, Q-4, R-1, S-3 (C) P-3, Q-1, R-4, S-2 (D) P-4, Q-2, R-1, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Ironmaking

Q27

MSQ[1 Mark]

Which of the following conditions is/are favorable for producing low-silicon hot metal in blast furnace ironmaking? (A) Reduced raceway adiabatic flame temperature (B) Oxygen-enriched blast (C) Lime injection through tuyeres (D) Increased hearth temperature

(A)

Reduced raceway adiabatic flame temperature

(B)

Oxygen-enriched blast

(C)

Lime injection through tuyeres

(D)

Increased hearth temperature

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q28

MCQ[2 Marks]

Match the steel plant related processes in Column I with the associated information in Column II.\nColumn I:\nP. Corex\nQ. Electric Arc Furnace\nR. Midrex\nS. Continuous Casting\nColumn II: 1. Melter-gasifier 2. Natural gas reformer 3. Electromagnetic stirrer 4. Hot heel (A) P-1, Q-4, R-2, S-3 (B) P-1, Q-4, R-3, S-2 (C) P-2, Q-4, R-1, S-3 (D) P-1, Q-3, R-2, S-4

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q29

NAT[2 Marks]

Molten steel at $1900\text{ K}$ having dissolved hydrogen needs to be vacuum degassed. The equilibrium partial pressure of hydrogen to be maintained to achieve $1\text{ ppm}$ (mass basis) of dissolved hydrogen is ___ Torr (rounded off to two decimal places).\nGiven: For $\frac{1}{2}H_2(g) \rightleftharpoons [H]$, $\log_{10} K_{eq} = -\frac{1900}{T} + 2.4$, $1\text{ atm} = 760\text{ Torr}$

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q30

NAT[2 Marks]

The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter $25\text{ }\mu\text{m}$ (both settling in water) is ___ $\mu\text{m}$ (rounded off to one decimal place). Assume Stokes law of settling to be valid. (Given: Density of galena $= 7400\text{ kg m}^{-3}$, density of quartz $= 2600\text{ kg m}^{-3}$, density of water $= 1000\text{ kg m}^{-3}$)

Explanation

GATE→2025→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q31

NAT[2 Marks]

Copper is being electrodeposited from a $CuSO_4$ bath onto a stainless steel cathode of total surface area of $2\text{ m}^2$ in an electrolytic cell operated at a current density of $200\text{ A m}^{-2}$ with a current efficiency of $90\%$. The mass of copper deposited in $24\text{ h}$ is ___ $\text{kg}$ (rounded off to two decimal places). (Given: Faraday's constant $= 96500\text{ C mol}^{-1}$, atomic mass of copper $= 63.5\text{ g mol}^{-1}$)

Explanation

Physical Metallurgy

9 Questions

GATE→2025→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q32

MCQ[1 Mark]

Match each crystal defect in Column I with the corresponding type in Column II:\nColumn I:\nP. Edge dislocation\nQ. Stacking fault\nR. Frenkel defect\nS. Porosity\nColumn II: 1. Zero-dimensional defect 2. One-dimensional defect 3. Two-dimensional defect 4. Three-dimensional defect (A) P-3, Q-4, R-2, S-1 (B) P-3, Q-4, R-1, S-2 (C) P-2, Q-3, R-1, S-4 (D) P-2, Q-4, R-3, S-1

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q33

MCQ[1 Mark]

In optical microscopy, which one of the following combinations of wavelength ($\lambda$) and numerical aperture (NA) provides the best spatial resolution? (A) $\lambda = 400\text{ nm}$ and $\text{NA} = 1.0$ (B) $\lambda = 600\text{ nm}$ and $\text{NA} = 1.2$ (C) $\lambda = 400\text{ nm}$ and $\text{NA} = 1.2$ (D) $\lambda = 600\text{ nm}$ and $\text{NA} = 1.0$

(A)

\lambda=400 nm and NA=1.0

(B)

\lambda=600 nm and NA=1.2

(C)

\lambda=400 nm and NA=1.2

(D)

\lambda=600 nm and NA=1.0

Explanation

GATE→2025→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q34

MCQ[1 Mark]

The coordination number for an octahedral site in pure copper is _______. (A) 4 (B) 6 (C) 8 (D) 12

(A)

4

(B)

6

(C)

8

(D)

12

Explanation

GATE→2025→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q35

MCQ[1 Mark]

In the Fe-C system, the invariant reaction $\text{Liquid} + \delta \rightleftharpoons \gamma$ takes place at $1493^\circ\text{C}$. This type of reaction is called _______. (A) eutectic (B) eutectoid (C) peritectic (D) monotectic

(A)

eutectic

(B)

eutectoid

(C)

peritectic

(D)

monotectic

Explanation

GATE→2025→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q36

MSQ[1 Mark]

Which of the following statements is/are CORRECT with respect to the initial stage of GP zone formation in a precipitation hardenable Al - 4.5 wt.% Cu alloy? (A) GP zones are Cu-rich clusters. (B) GP zones are CuAl$_2$ precipitates. (C) GP zones are incoherent with the matrix. (D) GP zones are coherent with the matrix.

(A)

GP zones are Cu-rich clusters.

(B)

GP zones are CuAl2 precipitates.

(C)

GP zones are incoherent with the matrix.

(D)

GP zones are coherent with the matrix.

Explanation

GATE→2025→Physical Metallurgy→Diffusion in Solids

Q37

MCQ[2 Marks]

The following are the activation energies for diffusion of carbon and iron at $773\text{ K}$ in polycrystalline BCC iron: $P =$ Activation energy for diffusion of carbon in BCC iron through the lattice $Q =$ Activation energy for diffusion of iron in BCC iron through the lattice $R =$ Activation energy for diffusion of iron in BCC iron along the grain boundary\nWhich one of the following statements is CORRECT? (A) $R < P < Q$ (B) $R < Q < P$ (C) $Q < P < R$ (D) $P < R < Q$

(A)

R < P < Q

(B)

R < Q < P

(C)

Q < P < R

(D)

P < R < Q

Explanation

GATE→2025→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q38

MSQ[2 Marks]

Which of the following statements is/are CORRECT when Ni is added as an alloying element to a low alloy steel? (A) Hardenability is increased AND the $M_s$ temperature is lowered. (B) Hardenability is decreased AND the $M_s$ temperature is lowered. (C) Hardenability is increased AND the $M_s$ temperature is raised. (D) Hardenability is decreased AND the $M_s$ temperature is raised.

(A)

Hardenability is increased AND the Ms temperature is lowered.

(B)

Hardenability is decreased AND the Ms temperature is lowered.

(C)

Hardenability is increased AND the Ms temperature is raised.

(D)

Hardenability is decreased AND the Ms temperature is raised.

Explanation

GATE→2025→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q39

NAT[2 Marks]

X-ray diffraction using a monochromatic radiation of wavelength $0.154\text{ nm}$ is performed on powder samples of metal A (with FCC crystal structure) and metal B (with BCC crystal structure). If the first peak in both the cases occurs at a Bragg angle $\theta = 20^\circ$, then the value of $\frac{\text{lattice parameter of metal A}}{\text{lattice parameter of metal B}}$ is ___ (rounded off to two decimal places).

Explanation

GATE→2025→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q40

NAT[2 Marks]

A single crystal BCC metal with a lattice parameter $a = 0.4\text{ nm}$ is subjected to deformation at a shear strain rate of $0.001\text{ s}^{-1}$. If the average mobile dislocation density in the single crystal is $10^{10}\text{ m}^{-2}$, the average dislocation velocity is ___ $\times 10^{-3}\text{ m s}^{-1}$ (rounded off to two decimal places). Given: Burgers vector $b = \frac{a}{2}\langle 111 \rangle$

Explanation

Mechanical Behaviour of Materials

7 Questions

GATE→2025→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q41

MCQ[1 Mark]

Two randomly oriented polycrystalline copper samples with average grain sizes of $10\text{ }\mu\text{m}$ (Sample A) and $100\text{ }\mu\text{m}$ (Sample B) were tested at room temperature. Given: $E_A, E_B$ are Young's moduli and $YS_A, YS_B$ are yield strengths. Which one of the following statements is CORRECT? (A) $E_A > E_B$ and $YS_A > YS_B$ (B) $E_A = E_B$ and $YS_A < YS_B$ (C) $E_A > E_B$ and $YS_A = YS_B$ (D) $E_A = E_B$ and $YS_A > YS_B$

(A)

$E_{A}>E_{B}$ and $YS_{A}>YS_{B}$

(B)

$E_{A}=E_{B}$ and $YS_{A}<YS_{B}$

(C)

$E_{A}>E_{B}$ and $YS_{A}=YS_{B}$

(D)

$E_{A}=E_{B}$ and $YS_{A}>YS_{B}$

Explanation

GATE→2025→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q42

MSQ[1 Mark]

With reference to edge and screw dislocations, which of the following statements is/are CORRECT? (A) Both edge and screw dislocations can leave the slip plane by climb. (B) Burgers vector of a screw dislocation is parallel to its line vector. (C) Both edge and screw dislocations can leave the slip plane by cross-slip. (D) Strain energy per unit length of an edge dislocation is higher than that of a screw dislocation.

(A)

Both edge and screw dislocations can leave the slip plane by climb.

(B)

Burgers vector of a screw dislocation is parallel to its line vector.

(C)

Both edge and screw dislocations can leave the slip plane by cross-slip.

(D)

Strain energy per unit length of an edge dislocation is higher than that of a screw dislocation.

Explanation

GATE→2025→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q43

NAT[1 Mark]

The hydrostatic stress for the stress tensor provided below is _______ $\text{MPa}$ (in integer). $$\begin{bmatrix} 150 & 0 & 0 \\ 0 & -100 & 100 \\ 0 & 100 & 250 \end{bmatrix}\text{ MPa}$

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q44

MCQ[2 Marks]

Match the phenomena in Column I with the typical observations in Column II.\nColumn I:\nP. Dynamic strain aging\nQ. Recrystallization\nR. Bauschinger effect\nS. Superplasticity\nColumn II: 1. Grain boundary sliding 2. Decrease in yield stress with a reversal of loading direction 3. Decrease in dislocation density 4. Serrations in stress-strain curve (A) P-4, Q-1, R-2, S-3 (B) P-4, Q-3, R-2, S-1 (C) P-3, Q-4, R-2, S-1 (D) P-1, Q-4, R-2, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q45

NAT[2 Marks]

For a component fabricated from an alloy A with plane strain fracture toughness, $K_{IC} = 50\text{ MPa m}^{1/2}$, fracture was observed to take place at a crack length of $0.4\text{ mm}$ at a tensile service stress of $\sigma$. If the same component is instead fabricated from alloy B with $K_{IC} = 75\text{ MPa m}^{1/2}$, the crack length at which a similar crack geometry will result in fracture (under identical tensile service stress of $\sigma$) is ___ $\text{mm}$ (rounded off to one decimal place).

Explanation

GATE→2025→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q46

NAT[2 Marks]

In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate controlling creep mechanism at a certain temperature. At that temperature, if the steady state strain rate is $10^{-8}\text{ s}^{-1}$ at a stress of $10\text{ MPa}$, the steady state strain rate of $10^{-9}\text{ s}^{-1}$ will be obtained at a stress value of ___ $\text{MPa}$ (in integer).

Explanation

GATE→2025→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q47

NAT[2 Marks]

A cylindrical specimen is subjected to plastic deformation in tension up to a uniform elongation of $10\%$. The final cross-sectional area of the gage section is found to be $20\text{ mm}^2$. The initial cross-sectional area of the gage section is ___ $\text{mm}^2$ (rounded off to an integer).

Explanation

Manufacturing Processes

7 Questions

GATE→2025→Manufacturing Processes→Metal Casting

Q48

MCQ[1 Mark]

In metal casting, which one of the following gating ratios (sprue-runner-gate area ratio) represents a non-pressurized gating system? (A) $1:2:3$ (B) $3:2:1$ (C) $4:3:1$ (D) $5:4:1$

(A)

1:2:3

(B)

3:2:1

(C)

4:3:1

(D)

5:4:1

Explanation

GATE→2025→Manufacturing Processes→Non-destructive Testing (NDT)

Q49

MSQ[1 Mark]

Which of the following techniques can be used to detect an internal defect in a metal casting? (A) Ultrasonic inspection (B) Liquid (or dye) penetrant inspection (C) Gamma-ray radiography (D) X-ray radiography

(A)

Ultrasonic inspection

(B)

Liquid (or dye) penetrant inspection

(C)

Gamma-ray radiography

(D)

X-ray radiography

Explanation

GATE→2025→Manufacturing Processes→Metal Casting

Q50

MCQ[2 Marks]

Match the casting defects in Column I with the characteristic features in Column II.\nColumn I:\nP. Misrun\nQ. Expansion scab\nR. Pin holes\nS. Hot tearing\nColumn II: 1. Penetration of liquid metal behind surface layer of sand moulds 2. Metal solidifies prematurely in the mould and some sections of the casting are not filled 3. Cracking because of restraint to contraction in certain areas of the casting during solidification and cooling to room temperature 4. Evolution of gases during solidification resulting in porosity (A) P-2, Q-4, R-3, S-1 (B) P-1, Q-3, R-2, S-4 (C) P-1, Q-2, R-4, S-3 (D) P-2, Q-1, R-4, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2025→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q51

MSQ[2 Marks]

Front tension is applied during cold rolling of a thin metal sheet. Which of the following statements is/are TRUE? (A) The neutral point shifts towards the roll entrance. (B) The rolling load is decreased. (C) The neutral point shifts towards the roll exit. (D) The rolling load is increased.

(A)

The neutral point shifts towards the roll entrance.

(B)

The rolling load is decreased.

(C)

The neutral point shifts towards the roll exit.

(D)

The rolling load is increased.

Explanation

GATE→2025→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q52

MSQ[2 Marks]

Which of the following statements is/are CORRECT with respect to fusion welding and solid-state welding of metals and alloys? (A) Thermomechanically affected zone is found in the fusion welding of pure metals. (B) Partially melted zone is NOT found in the fusion welding of pure metal. (C) Diffusion bonding is one type of solid-state welding process. (D) Partially melted zone is found in the fusion welding of alloys with a large freezing range.

(A)

Thermomechanically affected zone is found in the fusion welding of pure metals.

(B)

Partially melted zone is NOT found in the fusion welding of pure metal.

(C)

Diffusion bonding is one type of solid-state welding process.

(D)

Partially melted zone is found in the fusion welding of alloys with a large freezing range.

Explanation

GATE→2025→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q53

MSQ[2 Marks]

Which of the following welding processes does NOT / do NOT utilize consumable electrode? (A) Plasma arc welding (B) Gas metal arc welding (C) Shielded metal arc welding (D) Electron beam welding

(A)

Plasma arc welding

(B)

Gas metal arc welding

(C)

Shielded metal arc welding

(D)

Electron beam welding

Explanation

GATE→2025→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q54

NAT[2 Marks]

A cylindrical Al alloy billet of $300\text{ mm}$ diameter is hot extruded to produce a cylindrical rod of $75\text{ mm}$ diameter at a constant true strain rate ($\dot{\epsilon}$) of $10\text{ s}^{-1}$. The flow stress ($\sigma$) of the alloy at the extrusion temperature is given by $\sigma = 10(\dot{\epsilon})^{0.3}\text{ MPa}$. Assume the alloy is perfectly plastic and there is no temperature rise during the extrusion process. The ideal plastic work of deformation per unit volume is ___ $\times 10^6\text{ J m}^{-3}$ (rounded off to one decimal place).

Explanation

Materials Science and Non-Metallic Materials

1 Question

GATE→2025→Materials Science and Non-Metallic Materials→Electronic and Magnetic Properties

Q55

NAT[2 Marks]

An intrinsic semiconductor has conductivity of $100\text{ }\Omega^{-1}\text{m}^{-1}$ at $300\text{ K}$ and $300\text{ }\Omega^{-1}\text{m}^{-1}$ at $500\text{ K}$. The band gap of the semiconductor is ___ $\text{eV}$ (rounded off to two decimal places). Given: Boltzmann constant $k_B = 8.6 \times 10^{-5}\text{ eV K}^{-1}$

Explanation

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

Despite his initial hesitation, Rehman's _______ to contribute to the success of the project never wavered. Select the most appropriate option to complete the above sentence. (A) ambivalence (B) satisfaction (C) resolve (D) revolve

(A)

ambivalence

(B)

satisfaction

(C)

resolve

(D)

revolve

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

Bird : Nest :: Bee : _______\nSelect the correct option to complete the analogy. (A) Kennel (B) Hammock (C) Hive (D) Lair

(A)

Kennel

(B)

Hammock

(C)

Hive

(D)

Lair

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

If $Pe^{x} = Qe^{-x}$ for all real values of $x$, which one of the following statements is true? (A) $P = Q = 0$ (B) $P = Q = 1$ (C) $P = 1; Q = -1$ (D) $\frac{P}{Q} = 0$

(A)

$P = Q = 0$

(B)

$P = Q = 1$

(C)

$P = 1; Q = -1$

(D)

$\frac{P}{Q} = 0$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?

(A)

a

(B)

b

(C)

c

(D)

d

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

Let $p_{1}$ and $p_{2}$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_{1}$ and $p_{2}$? (A) $p_{1}+p_{2}$ is not a prime number. (B) $p_{1}p_{2}$ is not a prime number. (C) $p_{1}+p_{2}+1$ is a prime number. (D) $p_{1}p_{2}+1$ is a prime number.

(A)

$p_{1}+p_{2}$ is not a prime number.

(B)

$p_{1}p_{2}$ is not a prime number.

(C)

$p_{1}+p_{2}+1$ is a prime number.

(D)

$p_{1}p_{2}+1$ is a prime number.

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

Based only on the conversation below, identify the logically correct inference: "Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. (A) Ramya knew that Josephine was in the hospital. (B) Ramya did not know that Josephine was in the hospital. (C) Ramya and Josephine were once close friends; but now, they are not. (D) Josephine was in the hospital due to an injury to her leg.

(A)

Ramya knew that Josephine was in the hospital.

(B)

Ramya did not know that Josephine was in the hospital.

(C)

Ramya and Josephine were once close friends; but now, they are not.

(D)

Josephine was in the hospital due to an injury to her leg.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH ? (A) CEADP (B) IDBFC (C) JGIBC (D) IBCEC

(A)

CEADP

(B)

IDBFC

(C)

JGIBC

(D)

IBCEC

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q63

MCQ[2 Marks]

Which one of the following options is correct for the given data in the table? (A) $X(i)=X(i-1)+I(i)$; $Y(i)=Y(i-1)I(i)$; $i>0$ (B) $X(i)=X(i-1)I(i)$; $Y(i)=Y(i-1)+I(i)$; $i>0$ (C) $X(i)=X(i-1)I(i)$; $Y(i)=Y(i-1)I(i)$; $i>0$ (D) $X(i)=X(i-1)+I(i)$; $Y(i)=Y(i-1)I(i-1)$; $i>0$

(A)

$X(i)=X(i-1)+I(i)$; $Y(i)=Y(i-1)I(i)$; $i>0$

(B)

$X(i)=X(i-1)I(i)$; $Y(i)=Y(i-1)+I(i)$; $i>0$

(C)

$X(i)=X(i-1)I(i)$; $Y(i)=Y(i-1)I(i)$; $i>0$

(D)

$X(i)=X(i-1)+I(i)$; $Y(i)=Y(i-1)I(i-1)$; $i>0$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square. What is the area (in cm$^2$) of the rectangle PLMN? (A) $2\sqrt{2}$ (B) 2 (C) 8 (D) 4

(A)

$2\sqrt{2}$

(B)

2

(C)

8

(D)

4

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct? (A) Bridges on P, Q, and T (B) Bridges on P, Q, S, and T (C) Bridges on Q, R, T, and V (D) Bridges on P, Q, S, U, and V

(A)

Bridges on P, Q, and T

(B)

Bridges on P, Q, S, and T

(C)

Bridges on Q, R, T, and V

(D)

Bridges on P, Q, S, U, and V

Explanation