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Type:ALLMCQNATMSQ

Engineering Mathematics(9)Metallurgical Thermodynamics(5)Transport Phenomena and Rate Processes(5)Mineral Processing and Extractive Metallurgy(8)Physical Metallurgy(10)Mechanical Behaviour of Materials(8)Manufacturing Processes(8)Materials Science and Non-Metallic Materials(2)General Aptitude(10)

Engineering Mathematics

9 Questions

GATE→2024→Engineering Mathematics→Probability and Statistics

Q1

MCQ[1 Mark]

If $X_{1}$ and $X_{2}$ are independent normally distributed random variables with means $\mu_{1}$ and $\mu_{2}$, and variances $\rho_{1}$ and $\rho_{2}$ (or standard deviations/variances), respectively, then the combination $X = X_{1} + X_{2}$ has mean $\mu$ and variance $\rho$ such that (A) $\mu = \mu_{1} + \mu_{2}$ and $\rho = \rho_{1} + \rho_{2}$ (B) $\mu^{2} = \mu_{1}^{2} + \mu_{2}^{2}$ and $\rho = \rho_{1} + \rho_{2}$ (C) $\mu = \mu_{1} + \mu_{2}$ and $\rho^{2} = \rho_{1}^{2} + \rho_{2}^{2}$ (D) $\mu^{2} = \mu_{1}^{2} + \mu_{2}^{2}$ and $\rho^{2} = \rho_{1}^{2} + \rho_{2}^{2}$

(A)

\mu = \mu_{1} + \mu_{2} and \rho = \rho_{1} + \rho_{2}

(B)

\mu^{2} = \mu_{1}^{2} + \mu_{2}^{2} and \rho = \rho_{1} + \rho_{2}

(C)

\mu = \mu_{1} + \mu_{2} and \rho^{2} = \rho_{1}^{2} + \rho_{2}^{2}

(D)

\mu^{2} = \mu_{1}^{2} + \mu_{2}^{2} and \rho^{2} = \rho_{1}^{2} + \rho_{2}^{2}

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q2

MCQ[1 Mark]

Which one of the expansions of $\ln\left(\frac{1+x}{1-x}\right)$ about the origin for $|x|<1$ is correct? (A) $x - \frac{x^2}{2} + \frac{x^3}{3}$ (B) $2\left(x - \frac{x^2}{2} + \frac{x^3}{3} - \dots\right)$ (C) $x + \frac{x^3}{3} + \frac{x^5}{5} + \dots$ (D) $2\left(x + \frac{x^3}{3} + \frac{x^5}{5} + \dots\right)$

(A)

x-\frac{x^{2}}{2}+\frac{x^{3}}{3}

(B)

2(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\cdot\cdot\cdot)

(C)

x+\frac{x^{3}}{3}+\frac{x^{5}}{5}+\cdot\cdot\cdot

(D)

2(x+\frac{x^{3}}{3}+\frac{x^{5}}{5}+\cdot\cdot\cdot)

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q3

MCQ[1 Mark]

Consider the normal (Gaussian) distributions $a$, $b$, $c$ shown in the figure. $\sigma_p$ and $\mu_p$ are standard deviation and mean of distribution $p$, respectively, and means are positive. Which one of the following deductions is correct? (A) $\sigma_a < \sigma_b < \sigma_c$ (B) $\sigma_a > \sigma_b > \sigma_c$ (C) $\mu_a = \mu_b = \mu_c$ (D) $\mu_a > \mu_b > \mu_c$

(A)

\sigma_{a}<\sigma_{b}<\sigma_{c}

(B)

\sigma_{a}>\sigma_{b}>\sigma_{c}

(C)

\mu_{a}=\mu_{b}=\mu_{c}

(D)

\mu_{a}>\mu_{b}>\mu_{c}

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q4

MSQ[1 Mark]

Which of the following statements is/are correct for a square matrix $A$ with real number entries? $A^T$ denotes the transpose of $A$ and $A^{-1}$ denotes the inverse of $A$. (A) $A$ is symmetric if $A^T = -A$ (B) $A$ is skew-symmetric if $A^T = -A$ (C) If $A$ is orthogonal, then $A^T = A^{-1}$ (D) If $A$ is orthogonal, then its determinant is zero.

(A)

A is symmetric if A^{T} = -A

(B)

A is skew-symmetric if A^{T} = -A

(C)

If A is orthogonal, then A^{T} = A^{-1}

(D)

If A is orthogonal, then its determinant is zero.

Explanation

GATE→2024→Engineering Mathematics→Vector Calculus

Q5

NAT[1 Mark]

The divergence of the vector field $$\vec{V} = x^{2}y\hat{i} + y^{3}z\hat{j} + z^{4}\hat{k}$|\nat the point $(1,1,1)$ is ___ (Round off to the nearest integer).

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q6

MCQ[2 Marks]

If $\begin{bmatrix} 1 & 2 \\ 8 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \lambda \begin{bmatrix} x \\ y \end{bmatrix}$ where $x, y$ are not identically zero, then the values of $\lambda$ are (A) $5, -3$ (B) $4, -4$ (C) $3, -5$ (D) $5, -4$

(A)

5,-3

(B)

4,-4

(C)

3,-5

(D)

5,-4

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q7

MCQ[2 Marks]

If $\frac{dy}{dx} = 4xy$, $y(0) = 1$, then (A) $y = 2x^2 + 1$ (B) $y = 2e^{2x^2} - 1$ (C) $y = 2e^{x^2} - 1$ (D) $y = e^{2x^2}$

(A)

y = 2x^{2} + 1

(B)

y = 2e^{2x^{2}} - 1

(C)

y = 2e^{x^{2}} - 1

(D)

y = e^{2x^{2}}

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q8

NAT[2 Marks]

The following data is obtained from an experiment: $x$: 1, 2, 3 $y$: 8, 15, 19\nIf the data is fit using the straight line $y = mx + c$ using the least-squares method, then the value of $m$ is ___ (Round off to one decimal place).

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q9

NAT[2 Marks]

The integral $\int_{0}^{1} x e^{-x} dx$ evaluates to ___ (Round off to two decimal places).

Explanation

Metallurgical Thermodynamics

5 Questions

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q10

MCQ[1 Mark]

If in an A-B solid solution, the activity and mole fraction of A are given by $a_{A}$ and $X_{A}$ respectively, then the activity coefficient of A is given by (A) $\frac{a_{A}}{X_{A}}$ (B) $\frac{X_{A}}{a_{A}}$ (C) $a_{A}$ (D) $a_{A}X_{A}^{2}$

(A)

\frac{a_{A}}{X_{A}}

(B)

\frac{X_{A}}{a_{A}}

(C)

a_{A}

(D)

a_{A}{X_{A}}^{2}

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q11

MSQ[1 Mark]

Which of the following is/are criterion/criteria for equilibrium of an isolated system? (A) Maximum entropy (B) Minimum internal energy (C) Minimum Helmholtz free energy (D) Minimization of Gibbs free energy

(A)

Maximum entropy

(B)

Minimum internal energy

(C)

Minimum Helmholtz free energy

(D)

Minimization of Gibbs free energy

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q12

NAT[2 Marks]

An ideal solution is formed by mixing $10\text{ grams}$ of A and $50\text{ grams}$ of B at $673\text{ K}$. The molar free energy of mixing is ___ $\text{J mol}^{-1}$ (Round off to one decimal place).\nGiven: Universal gas constant $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$, atomic weight of $\text{A} = 40\text{ g mol}^{-1}$, atomic weight of $\text{B} = 60\text{ g mol}^{-1}$

Explanation

GATE→2024→Metallurgical Thermodynamics→Electrochemistry

Q13

NAT[2 Marks]

The cupric ion ($Cu^{2+}$) concentration in the electrolyte (at $298\text{ K}$) required to make the potential of pure copper equal to $0.17\text{ V}$ is ___ $\times 10^{-6}\text{ gram-mol (litre)}^{-1}$ (Round off to two decimal places). (Given: $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$, $F = 96500\text{ C mol}^{-1}$, standard reduction potential $E^\circ = 0.34\text{ V}$)

Explanation

GATE→2024→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q14

NAT[2 Marks]

800 grams of A-B alloy containing $20\text{ wt.}\%$ B is held at temperature $T_1$. The weight of B dissolved in $\alpha$ at that temperature is ___ grams (Round off to the nearest integer).

Explanation

Transport Phenomena and Rate Processes

5 Questions

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q15

MCQ[1 Mark]

As shown in the figure, two rods of different metals of equal lengths $L/2$, diameter $d$, and constant thermal conductivities $k_1$ and $k_2$ (with $k_1 > k_2$) are connected perfectly. Which one of the graphs represents the steady-state temperature distribution?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Mass Transfer and Dimensional Analysis

Q16

MCQ[1 Mark]

Match the laws listed in Column I with the corresponding material properties listed in Column II:\nColumn I:\nP. Hooke's law\nQ. Fick's law\nR. Fourier's law\nS. Darcy's law\nColumn II: 1. Thermal conductivity 2. Young's modulus 3. Permeability 4. Diffusivity (A) P-2, Q-1, R-4, S-3 (B) P-4, Q-3, R-1, S-2 (C) P-2, Q-4, R-1, S-3 (D) P-4, Q-3, R-2, S-1

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q17

MCQ[2 Marks]

As shown in the figure, the right end of a slender, long solid cylindrical metal rod of thermal conductivity $k$, length $L$ and diameter $d$ is in contact with an infinite liquid heat sink at $T_0$. At steady-state, temperatures are $T_2$ at the right end and $T_0$ at the heat sink, with convection coefficient $h$. The temperature of the left end $T_1$ at steady-state is determined by fin/rod heat transfer balances.

(A)

T_{1}=T_{2}+(T_{2}-T_{0})\frac{hL}{k}

(B)

T_{1}=T_{2}-(T_{2}-T_{0})\frac{hL}{k}

(C)

T_{1}=T_{2}-(T_{2}-T_{0})\frac{k}{hL}

(D)

T_{1}=T_{2}+(T_{2}-T_{0})\frac{k}{hL}

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Dimensional Analysis

Q18

MCQ[2 Marks]

Match the dimensionless numbers listed in Column I with their applications to transport phenomena listed in Column II.\nColumn I:\nP. Reynolds number\nQ. Schmidt number\nR. Prandtl number\nS. Biot number\nColumn II: 1. Momentum and mass transfer 2. Momentum and heat transfer 3. Convective and conductive heat transfer 4. Laminar to turbulent flow (A) P-4, Q-1, R-3, S-2 (B) P-3, Q-2, R-4, S-1 (C) P-4, Q-1, R-2, S-3 (D) P-2, Q-3, R-1, S-4

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q19

NAT[2 Marks]

A long metallic cylindrical rod of radius $r$, length $L$ and electrical resistivity $\rho_e$ is kept in vacuum and is carrying an electric current of $I$. The only way it loses heat to the ambient is via radiation. If the ambient temperature is $T_0$, then the steady-state temperature of the rod is ___ $\text{K}$ (Round off to the nearest integer).\nGiven: Stefan-Boltzmann constant $= 5.667 \times 10^{-8}\text{ W m}^{-2}\text{K}^{-4}$, $r = 0.1\text{ mm} = 10^{-4}\text{ m}$, $I = 0.3\text{ A}$, $L = 1\text{ m}$, $\rho_e = 10^{-8}\text{ }\Omega\text{m}$, $T_0 = 300\text{ K}$.

Explanation

Mineral Processing and Extractive Metallurgy

8 Questions

GATE→2024→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q20

MCQ[1 Mark]

Wet high intensity magnetic separators (WHIMS) are used to concentrate (A) fine ($<75\text{ }\mu\text{m}$) paramagnetic minerals. (B) coarse ($>75\text{ }\mu\text{m}$) ferromagnetic minerals. (C) coarse ($>75\text{ }\mu\text{m}$) paramagnetic minerals. (D) fine ($<75\text{ }\mu\text{m}$) ferromagnetic minerals.

(A)

fine (<75 \mu m) paramagnetic minerals.

(B)

coarse (>75 \mu m) ferromagnetic minerals.

(C)

coarse (>75 \mu m) paramagnetic minerals.

(D)

fine (<75 \mu m) ferromagnetic minerals.

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q21

MCQ[1 Mark]

Which one of the following reagents is NOT used in froth flotation process? (A) Lixiviants (B) Collectors (C) Activators (D) Depressants

(A)

Lixiviants

(B)

Collectors

(C)

Activators

(D)

Depressants

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Ironmaking

Q22

MCQ[1 Mark]

Which one of the following reactions is the Boudouard's reaction? (A) $C(s) + H_2O(l) \rightarrow H_2(g) + CO(g)$ (B) $C(s) + O_2(g) \rightarrow CO_2(g)$ (C) $C(s) + CO_2(g) \rightarrow 2CO(g)$ (D) $2C(s) + O_2(g) \rightarrow 2CO(g)$

(A)

C(s)+H_{2}O(l)\rightarrow H_{2}(g)+CO(g)

(B)

C(s)+O_{2}(g)\rightarrow CO_{2}(g)

(C)

C(s)+CO_{2}(g)\rightarrow2CO(g)

(D)

2C(s)+O_{2}(g)\rightarrow2CO(g)

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q23

MCQ[1 Mark]

Which one of the following processes is NOT related to the extraction and refining of titanium from ilmenite ore? (A) Pidgeon's process (B) Sorel process (C) Van Arkel process (D) Kroll's process

(A)

Pidgeon's process

(B)

Sorel process

(C)

Van Arkel process

(D)

Kroll's process

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q24

MCQ[1 Mark]

Which one of the following is the correct statement about the industrial production of aluminium from pure dry alumina by Hall-Héroult electrolytic reduction? (A) Cell is operated at a high voltage (220 to 240 V) with a very low current density. (B) Cell is operated at a low voltage (5 to 7 V) with a very low current density. (C) Cell is operated at a high voltage (220 to 240 V) with a very high current density. (D) Cell is operated at a low voltage (5 to 7 V) with a very high current density.

(A)

Cell is operated at a high voltage (220 to 240 V) with a very low current density.

(B)

Cell is operated at a low voltage (5 to 7 V) with a very low current density.

(C)

Cell is operated at a high voltage (220 to 240 V) with a very high current density.

(D)

Cell is operated at a low voltage (5 to 7 V) with a very high current density.

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Ironmaking

Q25

MSQ[2 Marks]

Which of the following statements is/are correct? (A) Ultimate analysis of coal involves determination of moisture, volatile matter, fixed carbon and ash. (B) Reduction of wustite in blast furnace occurs at the lower part of the stack. (C) Roasting involves reduction of sulfide ores to pure metals. (D) White metal (impure $Cu_2S$) is produced by oxidizing Fe and S during smelting of Cu-Fe matte.

(A)

Ultimate analysis of coal involves determination of moisture, volatile matter, fixed carbon and ash.

(B)

Reduction of wustite in blast furnace occurs at the lower part of the stack.

(C)

Roasting involves reduction of sulfide ores to pure metals.

(D)

White metal (impure Cu_{2}S) is produced by oxidizing Fe and S during smelting of Cu-Fe matte.

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Ironmaking

Q26

NAT[2 Marks]

A non-porous spherical $Fe_2O_3$ particle of initial radius of $5 \times 10^{-2}\text{ m}$ is topo-chemically reduced by $H_2$, where the reactant-product interface is sharp and spherical, and reaction rate is proportional to the interfacial area. The radius of the unreacted $Fe_2O_3$ particle after $600\text{ s}$ will be ___ $\times 10^{-2}\text{ m}$ (Round off to the nearest integer).\nGiven: Rate constant $k = 5 \times 10^{-5}\text{ m s}^{-1}$

Explanation

GATE→2024→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q27

NAT[2 Marks]

1000 kg of sphalerite concentrate containing $60\%\text{ ZnS}$ is COMPLETELY roasted with stoichiometric amount of pure oxygen. The amount of oxygen required is ___ $\text{kg}$ (Round off to one decimal place).\nAtomic weights: $\text{Zn} = 65$, $\text{S} = 32$, $\text{O} = 16$.

Explanation

Physical Metallurgy

10 Questions

GATE→2024→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q28

MCQ[1 Mark]

Which one of the following schematics represents the variation of the rate of nucleation of solid from a pure liquid metal as a function of undercooling ($\Delta T = T_m - T$)?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q29

MCQ[1 Mark]

Which one of the following crystal structure changes occurs during the transformation of mild steel from austenite to martensite? (A) Face centered cubic to body centered cubic (B) Face centered cubic to body centered tetragonal (C) Body centered cubic to body centered tetragonal (D) Body centered tetragonal to face centered cubic

(A)

Face centered cubic to body centered cubic

(B)

Face centered cubic to body centered tetragonal

(C)

Body centered cubic to body centered tetragonal

(D)

Body centered tetragonal to face centered cubic

Explanation

GATE→2024→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q30

MSQ[1 Mark]

Which of the following $(h\text{ }k\text{ }l)$ reflections is/are allowed in an X-ray diffraction pattern of a crystal with face centered cubic lattice? (A) $(0\text{ }0\text{ }1)$ (B) $(0\text{ }1\text{ }1)$ (C) $(1\text{ }1\text{ }1)$ (D) $(0\text{ }0\text{ }2)$

(A)

(0 0 1)

(B)

(0 1 1)

(C)

(1 1 1)

(D)

(0 0 2)

Explanation

GATE→2024→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q31

NAT[1 Mark]

For a solid embryo in contact with a perfectly flat mould wall as shown in the schematic, the wetting angle $\theta$ is ___ degrees (Round off to one decimal place).\nGiven: Surface tension between liquid and mould wall $= 0.35\text{ J m}^{-2}$, surface tension between solid and mould wall $= 0.02\text{ J m}^{-2}$, surface tension between liquid and solid $= 0.30\text{ J m}^{-2}$

Explanation

GATE→2024→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q32

MCQ[2 Marks]

The constitutional undercooling condition for a hypothetical binary alloy of A with solute B during solidification is shown in the figure along with its binary phase diagram. Based on these two schematics, one can conclude that the solute concentration in region X will be _______ the average composition of the initial liquid phase. (A) less than (B) greater than (C) same as (D) independent of

(A)

less than

(B)

greater than

(C)

same as

(D)

independent of

Explanation

GATE→2024→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q33

MCQ[2 Marks]

The microstructures of a quenched steel tempered at three temperatures $T_1 < T_2 < T_3$ for a fixed time are schematically illustrated with average radii $\bar{r}_1 < \bar{r}_2 < \bar{r}_3$ and volume fractions $V_1 < V_2 = V_3$. If cementite is more noble than ferrite, which microstructure has the highest corrosion rate in 3.5 wt.% NaCl? (A) Microstructure at $T_1$ (B) Microstructure at $T_3$ (C) Microstructure at $T_2$ (D) All have equal corrosion rate

(A)

Microstructure at T_{1}

(B)

Microstructure at T_{3}

(C)

Microstructure at T_{2}

(D)

All have equal corrosion rate

Explanation

GATE→2024→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q34

MCQ[2 Marks]

Match the entries in Column I with the stacking sequences of the close-packed planes listed in Column II.\nColumn I:\nP. Face centered cubic (FCC) structure\nQ. Intrinsic stacking fault in FCC\nR. Across an annealing twin boundary in FCC\nS. Hexagonal close-packed structure\nColumn II: 1. ABCABABC 2. ABABABAB 3. ABCABCABC 4. ABACABA (A) P-1, Q-3, R-4, S-2 (B) P-2, Q-3, R-1, S-4 (C) P-3, Q-1, R-4, S-2 (D) P-3, Q-2, R-1, S-4

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q35

NAT[2 Marks]

If for element A, the formation enthalpy and formation entropy per vacancy created are $0.5\text{ eV}$ and $3k_B$, respectively, then the equilibrium vacancy concentration (in mole fraction) at $500\text{ K}$ is ___ $\times 10^{-4}$ (Round off to two decimal places).\nGiven: Boltzmann constant $k_B = 8.62 \times 10^{-5}\text{ eV atom}^{-1}\text{K}^{-1}$

Explanation

GATE→2024→Physical Metallurgy→Diffusion in Solids

Q36

NAT[2 Marks]

During carburization of a steel at $950^\circ\text{C}$, carbon concentration is measured as $0.8\text{ wt.}\%$ at a depth of $0.3\text{ mm}$ after one hour. The time required to get the same carbon concentration at a depth of $0.6\text{ mm}$ at the same carburization temperature is ___ hours (Round off to the nearest integer).

Explanation

GATE→2024→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q37

NAT[2 Marks]

A mild steel pipeline is connected to zinc for cathodic protection at a current density of $10\text{ mA m}^{-2}$. The quantity of zinc required per square meter of the pipeline per year is ___ grams (Round off to the nearest integer).\nGiven: Atomic weight of Zn is $65\text{ g mol}^{-1}$, Faraday's constant $F = 96500\text{ C mol}^{-1}$.

Explanation

Mechanical Behaviour of Materials

8 Questions

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q38

MCQ[1 Mark]

The figure shows a dislocation loop, whose Burgers vector is $\mathbf{b}$ (horizontal arrow). Identify the nature of the dislocation segment at locations p, q, and r. (A) p: pure edge, q: mixed, r: pure screw (B) p: pure edge, q: pure screw, r: pure edge (C) p: pure screw, q: mixed, r: pure screw (D) p: pure screw, q: pure edge, r: pure screw

(A)

p: pure edge, q: mixed, r: pure screw

(B)

p: pure edge, q: pure screw, r: pure edge

(C)

p: pure screw, q: mixed, r: pure screw

(D)

p: pure screw, q: pure edge, r: pure screw

Explanation

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q39

MCQ[1 Mark]

Match the concepts listed in Column I with the phenomena listed in Column II.\nColumn I:\nP. Peierls-Nabarro stress\nQ. Cottrell's atmosphere\nR. Paris law\nS. Considère's criterion\nColumn II: 1. Yield point phenomenon 2. Fatigue 3. Dislocation glide 4. Onset of necking (A) P-1, Q-2, R-3, S-4 (B) P-4, Q-1, R-2, S-3 (C) P-3, Q-1, R-2, S-4 (D) P-3, Q-4, R-2, S-1

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q40

NAT[1 Mark]

A single crystal is oriented such that the normal to the slip plane makes an angle of $60^\circ$ with the tensile axis. If the slip direction makes an angle of $45^\circ$ with respect to the tensile axis and the critical resolved shear stress for slip is $2\text{ MPa}$, then the tensile stress at which plastic deformation commences is ___ $\text{MPa}$ (Round off to one decimal place).

Explanation

GATE→2024→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q41

MCQ[2 Marks]

An isotropic metallic cuboid block has coefficient of linear thermal expansion $\alpha$, Young's modulus $E$, and Poisson's ratio $\nu$. Dimensions are $a, b, c$ in $X, Y, Z$ directions. It is rigidly constrained against expansion in the $X$ direction, but free in $Y$ and $Z$. Heated by $\Delta T$. What would be the CHANGE in dimension in the $Y$ direction? (A) $b(1-\nu)\alpha \Delta T$ (B) $b(1+\nu)\alpha \Delta T$ (C) $b\alpha \Delta T$ (D) $b(1+\alpha)\Delta T$

(A)

b(1-\nu)\alpha\Delta T

(B)

b(1+\nu)\alpha\Delta T

(C)

ba\Delta T

(D)

b(1+\alpha)\Delta T

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q42

MCQ[2 Marks]

Which one of the following graphs represents Griffith's criterion for the growth of a crack in a brittle isotropic infinitely large plate with a center crack? In the graph, $\Delta SE$ is the magnitude of total strain energy released (solid curve) and $\Gamma_s$ is total surface energy (dashed line), and $a_c$ is critical crack length (downward arrow).

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q43

MSQ[2 Marks]

A creep test of a pure polycrystalline metal is performed in tension and the creep strain rate is observed to decrease during the primary stage. The creep mechanism is later determined to be dislocation-climb-controlled. The observed decrease in creep strain rate is/are due to (A) an increase in dislocation density. (B) grain growth. (C) a decrease in the dislocation density. (D) an increase in the cross-sectional area of the sample.

(A)

an increase in dislocation density.

(B)

grain growth.

(C)

a decrease in the dislocation density.

(D)

an increase in the cross-sectional area of the sample.

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q44

NAT[2 Marks]

A steel bar is subjected to fatigue loading with a tensile mean stress. Given that the ultimate tensile strength is $1000\text{ MPa}$ and the fatigue limit under fully reversed loading is $250\text{ MPa}$, the fatigue limit for a mean stress of $100\text{ MPa}$, considering Goodman relationship is ___ $\text{MPa}$ (Round off to the nearest integer).

Explanation

GATE→2024→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q45

NAT[2 Marks]

A large rectangular component is undergoing fully-reversed cyclic loading, and the component is known to grow the dominant fatigue crack from the outer surface. If the stress amplitude ($\sigma_A$) is $100\text{ MPa}$ and the critical stress intensity factor $K_{IC}$ of the material is $50\text{ MPa m}^{1/2}$, then the crack length at which the component will fail catastrophically is ___ $\text{mm}$ (Round off to one decimal place).\nGiven: The geometric factor $Y$ (or $\alpha$) for this loading condition is $1.12$.

Explanation

Manufacturing Processes

8 Questions

GATE→2024→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q46

MCQ[1 Mark]

Match the defects listed in Column I with the associated manufacturing processes listed in Column II.\nColumn I:\nP. Misrun\nQ. Earing\nR. Alligatoring\ns. Chevron cracking\nColumn II: 1. Extrusion 2. Rolling 3. Casting 4. Deep drawing (A) P-3, Q-1, R-2, S-4 (B) P-3, Q-4, R-2, S-1 (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-3, Q-4, R-2, S-1

(C)

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

(D)

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

Explanation

GATE→2024→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q47

MCQ[1 Mark]

Which one of the following is NOT involved in the sintering of a green compact of ceramic powders? Assume that sintering is performed without external pressure. (A) Surface diffusion (B) Dynamic recrystallization (C) Lattice diffusion (D) Grain boundary diffusion

(A)

Surface diffusion

(B)

Dynamic recrystallization

(C)

Lattice diffusion

(D)

Grain boundary diffusion

Explanation

GATE→2024→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q48

NAT[1 Mark]

The extrusion force required to extrude an aluminum rod of cross-sectional area of $150\text{ mm}^2$ to cross-sectional area of $50\text{ mm}^2$ is ___ $\text{N}$ (Round off to the nearest integer). Assume that the extrusion constant, which accounts for flow stress, strain hardening, friction and inhomogeneous deformation, is equal to $2\text{ MPa}$ ($2\text{ N/mm}^2$).

Explanation

GATE→2024→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q49

MCQ[2 Marks]

For rolling of slabs, determine the correctness or otherwise of the following Assertion [a] and Reason [r].\nAssertion [a]: Grooves are made on the surface of the rolls parallel to their roll axes to achieve large thickness reduction in a short time.\nReason [r]: Given $\mu$ is the coefficient of friction between the rolls and the slab, and $\alpha$ is the angle of bite between the entrance plane and the centerline of the rolls, unaided entry of slab in the rolls can take place only if $\mu < \tan\alpha$. (A) Both [a] and [r] are true, and [r] is the correct reason of [a]. (B) Both [a] and [r] are true, but [r] is not the correct reason of [a]. (C) Both [a] and [r] are false. (D) [a] is true, but [r] is false.

(A)

Both [a] and [r] are true, and [r] is the correct reason of [a].

(B)

Both [a] and [r] are true, but [r] is the not the correct reason of [a].

(C)

Both [a] and [r] are false.

(D)

[a] is true, but [r] is false.

Explanation

GATE→2024→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q50

MSQ[2 Marks]

Which of the following statements is/are correct for welding processes? (A) In TIG welding, the filler material (if used) generally has a melting point comparable to or higher than/suitable for the base metal, or tungsten is non-consumable. (B) In TIG welding, tungsten is the filler material. (C) Friction welding is a solid-state joining process. (D) The reaction $C_2H_2 + 5/2 O_2 \rightarrow 2CO_2 + H_2O + Heat$ is associated with thermit welding.

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Manufacturing Processes→Non-destructive Testing (NDT)

Q51

MSQ[2 Marks]

Which of the following statements is/are correct for non-destructive testing? (A) Liquid dye penetration technique can be utilized for detecting surface cracks. (B) In radiographic examination, internal cracks cannot be detected. (C) Eddy current-based techniques can be used for detecting sub-surface defects in pure alumina at room temperature. (D) Ultrasonic inspection is unsuitable for inspecting sub-surface defects in high damping capacity material (e.g., cast iron).

(A)

Liquid dye penetration technique can be utilized for detecting surface cracks.

(B)

In radiographic examination, internal cracks cannot be detected.

(C)

Eddy current-based techniques can be used for detecting sub-surface defects in pure alumina at room temperature.

(D)

Ultrasonic inspection is unsuitable for inspecting sub-surface defects in high damping capacity material (e.g., cast iron).

Explanation

GATE→2024→Manufacturing Processes→Metal Casting

Q52

NAT[2 Marks]

In casting, for a simple vertical gating system with a gate of cross-sectional area $2\text{ cm}^2$ and sprue height of $10\text{ cm}$, the filling time for a mould of dimensions $40\text{ cm} \times 20\text{ cm} \times 10\text{ cm}$, is ___ $\text{s}$ (Round off to one decimal place).\nGiven: Acceleration due to gravity $g = 980\text{ cm s}^{-2}$.

Explanation

GATE→2024→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q53

NAT[2 Marks]

During arc welding, the actual heat input is $200\text{ J mm}^{-3}$ and the current and voltage are $200\text{ A}$ and $20\text{ V}$, respectively. For a weld cross-sectional area of $2\text{ mm}^2$ and heat transfer efficiency of $0.9$, the velocity of welding is ___ $\text{mm s}^{-1}$ (Round off to the nearest integer).

Explanation

Materials Science and Non-Metallic Materials

2 Questions

GATE→2024→Materials Science and Non-Metallic Materials→Classification, Chemical Bonding, and Crystal Structures

Q54

NAT[1 Mark]

The pair-interaction energy between two atoms is given by the following expression: $$U = -\frac{1.6}{r^6} + \frac{51.2}{r^{12}}$$\nwhere $U$ is the interaction energy in $\text{eV}$ and $r$ is the interatomic distance in $\text{}\text{\AA}$. The equilibrium bond-length between the atoms is ___ $\text{}\text{\AA}$ (Round off to the nearest integer).

Explanation

GATE→2024→Materials Science and Non-Metallic Materials→Classification, Chemical Bonding, and Crystal Structures

Q55

MCQ[2 Marks]

In a cubic lattice, what is the ratio of interplanar spacings of the (100), (110) and (111) planes? (Round off to two decimal places) (A) $1 : 0.32 : 0.71$ (B) $1 : 0.71 : 0.58$ (C) $1 : 0.58 : 0.71$ (D) $1 : 0.58 : 0.32$

(A)

1:0.32:0.71

(B)

1:0.71:0.58

(C)

1:0.58:0.71

(D)

1:0.58:0.32

Explanation

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

If '$\rightarrow$' denotes increasing order of intensity, then the meaning of the words [dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\rightarrow$ fast $\rightarrow$ \_]. Which one of the given options is appropriate to fill the blank? (A) starve (B) reject (C) feast (D) deny

(A)

starve

(B)

reject

(C)

feast

(D)

deny

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\frac{x+y}{x-y}$ or related ratio... [Note: options evaluate constant ratio properties]

(A)

depends on xy

(B)

depends only on x and not on y

(C)

depends only on y and not on x

(D)

is a constant

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

Consider the following sample of numbers: $9, 18, 11, 14, 15, 17, 10, 69, 11, 13$\nThe median of the sample is (A) 13.5 (B) 14 (C) 11 (D) 18.7

(A)

13.5

(B)

14

(C)

11

(D)

18.7

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

The number of coins of ₹1, 25 paise, and 10 paise denominations that a person has are in the ratio $5:3:13$. Of the total amount, the percentage of money in 25 paise coins is (A) $21\%$ (B) $14\frac{2}{7}\%$ (C) $10\%$ (D) $30\%$

(A)

21%

(B)

14\frac{2}{7}%

(C)

10%

(D)

30%

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

For positive non-zero real variables $p$ and $q$, if $\log(p^2 + q^2) = \log p + \log q + 2\log 3$, then the value of $\frac{p^4 + q^4}{p^2 q^2}$ is (A) 79 (B) 81 (C) 9 (D) 83

(A)

79

(B)

81

(C)

9

(D)

83

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

In the given text, fill in the blanks with the correct prepositions/words: Steve was advised to keep his head (i) his shoulders... [Options match (C)]

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

A rectangular paper sheet of dimensions $54\text{ cm} \times 4\text{ cm}$ is taken. The two longer edges are joined to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is (A) $1/\pi$ (B) $2/\pi$ (C) $3/\pi$ (D) $4/\pi$

(A)

1/\pi

(B)

2/\pi

(C)

3/\pi

(D)

4/\pi

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q63

MCQ[2 Marks]

The pie chart presents the percentage contribution of different macronutrients to a typical $2,000\text{ kcal}$ diet (Carbohydrates 35%, Proteins 20%, Unsaturated fat 20%, Saturated fat 20%, Trans fat 5%). Energy densities: Carb 4, Protein 4, Fat 9 kcal/g. Total fat consumed in grams is (A) 44.4 (B) 77.8 (C) 100 (D) 3,600

(A)

44.4

(B)

77.8

(C)

100

(D)

3,600

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

A rectangular paper of $20\text{ cm} \times 8\text{ cm}$ is folded 3 times along lines of symmetry perpendicular to the long edge. The perimeter of the final folded sheet (in cm) is (A) 18 (B) 24 (C) 20 (D) 21

(A)

18

(B)

24

(C)

20

(D)

21

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

The least number of squares to be added in the figure to make AB a line of symmetry is...

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation