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Type:ALLMCQNATMSQ

Engineering Mathematics(8)Metallurgical Thermodynamics(5)Transport Phenomena and Rate Processes(7)Mineral Processing and Extractive Metallurgy(9)Physical Metallurgy(8)Mechanical Behaviour of Materials(8)Manufacturing Processes(8)Materials Science and Non-Metallic Materials(2)General Aptitude(10)

Engineering Mathematics

8 Questions

GATE→2022→Engineering Mathematics→Calculus

Q1

MCQ[1 Mark]

The Taylor series expansion around $x=0$ of the function $f(x)=\frac{x+1}{e^{x}+1}$ truncated to first two terms is (A) $\frac{1}{2}+\frac{1}{4}x$ (B) $\frac{1}{2}+\frac{1}{2}x$ (C) $\frac{1}{2}+x$ (D) $\frac{1}{2}+2x$

(A)

\frac{1}{2}+\frac{1}{4}x

(B)

\frac{1}{2}+\frac{1}{2}x

(C)

\frac{1}{2}+x

(D)

\frac{1}{2}+2x

Explanation

GATE→2022→Engineering Mathematics→Vector Calculus

Q2

MCQ[1 Mark]

Given that $V$ is a closed volume in space bounded by the surface $S$ with unit normal $\vec{n}$. If $\vec{f}$ is any non-zero vector and $\vec{\nabla}$ is the gradient/divergence operator, then the volume integral $\int_{V}(\vec{\nabla}\cdot\vec{f})\text{ }dV$ is equal to the surface integral $\int_{S}(\n\cdot\vec{f})\text{ }dS$ by virtue of (A) Stokes Curl theorem (B) Reynolds transport theorem (C) Buckingham Pi theorem (D) Gauss divergence theorem

(A)

Stokes Curl theorem

(B)

Reynolds transport theorem

(C)

Buckingham Pi theorem

(D)

Gauss divergence theorem

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q3

NAT[1 Mark]

A set of observations with normal distribution of error as $\pm 1.96\sigma$ (where $\sigma$ is standard deviation) is equivalent to the confidence interval of ___ $\%$ (round off to the nearest integer).

Explanation

GATE→2022→Engineering Mathematics→Differential Equations

Q4

MCQ[2 Marks]

The general solution to the following differential equation where A and B are constants is $$\frac{d^{2}y}{dt^{2}} - 4\frac{dy}{dt} + 4y = 0$$ (A) $y = A \sin(2t) + B$ (B) $y = A \sin(2t) + B \cos(2t)$ (C) $y = A e^{2t} + B e^{-2t}$ (D) $y = A e^{2t} + B t e^{2t}$

(A)

y=A \sin(2t)+B

(B)

y=A \sin(2t)+B \cos(2t)

(C)

y=A e^{2t}+B e^{-2t}

(D)

y=A e^{2t}+B t e^{2t}

Explanation

GATE→2022→Engineering Mathematics→Numerical Methods

Q5

MCQ[2 Marks]

Which one of the following equations will fail to converge to a root with an initial guess value of $x = 0.5$, using the Newton-Raphson method? (A) $x(1-x) = 0$ (B) $e^{x} - 3x^2 = 0$ (C) $x - \ln(3x) = 0$ (D) $\tan(x) - x = 0$

(A)

x(1-x)=0

(B)

e^{x}-3x^{2}=0

(C)

x-\ln(3x)=0

(D)

\tan(x)-x=0

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q6

MCQ[2 Marks]

For a 3x3 matrix, the value of the determinant is $-48$ and the trace is $8$. If one of the eigenvalues is $4$, the other two are (A) $2, -3$ (B) $1, -3$ (C) $6, -2$ (D) $-4, 0$

(A)

2,-3

(B)

1,-3

(C)

6,-2

(D)

-4,0

Explanation

GATE→2022→Engineering Mathematics→Numerical Methods

Q7

NAT[2 Marks]

The integral of the function $f(x) = 0.2 + 10x^2$ estimated by the trapezoidal rule with a single segment from $x = 0$ to $x = 1$ is ___ (round off to 1 decimal place).

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q8

NAT[2 Marks]

A set of 11 $(x, y)$ data points is least-squares fitted to a quadratic polynomial. If the sum of squares of error is $2.4$, the variance of error is ___ (round off to 1 decimal place).

Explanation

Metallurgical Thermodynamics

5 Questions

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q9

NAT[2 Marks]

What is the equilibrium $\frac{p_{CO}}{p_{CO_{2}}}$ ratio for the given reaction at $1873\text{ K}$? (round off to 2 decimal places) $$Mo(s) + O_{2}(g) \leftrightarrow MoO_{2}(s)$$\nGiven: $\Delta_{f}G^{\circ}_{1873} = -262300\text{ J}$; $a_{MoO_{2}(s)} = 0.5$ and $\Delta_{r}G^{\circ}_{1873} = -120860\text{ J}$ for the reaction $CO(g) + 0.5O_{2}(g) \leftrightarrow CO_{2}(g)$; $R = 8.314\text{ J K}^{-1}\text{mol}^{-1}$.

Explanation

GATE→2022→Metallurgical Thermodynamics→Electrochemistry

Q10

NAT[2 Marks]

The emf of the cell $$\text{Au-Pb(liquid) } | \text{ PbCl}_2\text{-KCl(liquid) } | \text{ Cl}_2\text{(gas, } 0.5\text{ atm), C(graphite)}$$\nis $1.2327\text{ V}$ at $873\text{ K}$. Activity of Pb in the Au-Pb alloy is $0.72$ and the activity of $\text{PbCl}_2$ in the electrolyte is $0.18$. The standard Gibbs energy of formation of $\text{PbCl}_2\text{(liquid)}$ at $873\text{ K}$ is ___ $\text{kJ}\cdot\text{mol}^{-1}$ (round off to 1 decimal place).\nGiven: $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$ and $F = 96500\text{ C}\cdot\text{mol}^{-1}$.

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q11

NAT[2 Marks]

The partial molar enthalpy of Au in Ag-Au melt containing $25\text{ mol}\%$ Au at $1400\text{ K}$ is $-8300\text{ J}\cdot\text{mol}^{-1}$. Assuming regular solution behavior, the activity of Au in the melt is ___ (round off to 3 decimal places).\nGiven: $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q12

NAT[2 Marks]

Assuming that Dulong-Petit law is valid for a monoatomic solid, the ratio of heat capacities $\frac{C_p}{C_v}$ at $500\text{ K}$ is ___ (round off to 3 decimals).\nGiven: molar volume $= 7 \times 10^{-6}\text{ m}^3\cdot\text{mol}^{-1}$, isothermal compressibility $\beta = 8 \times 10^{-12}\text{ Pa}^{-1}$, isobaric expansivity $\alpha = 6 \times 10^{-5}\text{ K}^{-1}$, and $R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}$.

Explanation

GATE→2022→Metallurgical Thermodynamics→Laws of Thermodynamics and Solutions

Q13

NAT[2 Marks]

The equilibrium microstructure of an alloy A-B consists of two phases $\alpha$ and $\beta$ in the molar proportion $2:1$. If the overall composition of the alloy is $70\text{ mol}\%$ B and the composition of $\beta$ is $90\text{ mol}\%$ B, the composition of $\alpha$ is ___ (in mol% B) (round off to the nearest integer).

Explanation

Transport Phenomena and Rate Processes

7 Questions

GATE→2022→Transport Phenomena and Rate Processes→Dimensional Analysis

Q14

MCQ[1 Mark]

In fluid flow, the dimensionless number that describes the transition from laminar to turbulent flow is (A) Reynolds number (B) Schmidt number (C) Biot number (D) Prandtl number

(A)

Reynolds number

(B)

Schmidt number

(C)

Biot number

(D)

Prandtl number

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q15

NAT[1 Mark]

A Newtonian incompressible liquid is contained between two parallel metal plates separated by $10^{-3}\text{ m}$. A stress of $5\text{ Pa}$ is required to maintain the upper plate in motion with a constant speed of $2\text{ m s}^{-1}$ in the horizontal direction relative to the bottom plate. The viscosity of liquid contained between the plates is ___ $\times 10^{-3}\text{ Pa-s}$ (answer rounded off to 1 decimal place).

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q16

MSQ[2 Marks]

Which of the following statement(s) is (are) TRUE about black body radiation? (A) Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum (B) The total emissive power of an ideal black body is proportional to the square of its absolute temperature (C) The emissive power of an ideal black body peaks at a wavelength $\lambda$ which is inversely proportional to its absolute temperature (D) The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above $0\text{ K}$

(A)

Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum

(B)

The total emissive power of an ideal black body is proportional to the square of its absolute temperature

(C)

The emissive power of an ideal black body peaks at a wavelength \lambda which is inversely proportional to its absolute temperature

(D)

The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above 0 K

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q17

MSQ[2 Marks]

A non-rotating smooth solid spherical object is fixed in the stream of an inviscid incompressible fluid of density $\rho$. The flow is horizontal, slow, steady, and fully developed far from the object as shown by the streamline arrows near point O. Which of the following statement(s) is (are) TRUE? (A) The velocity of the fluid at the point A is zero (B) The fluid pressure at the point A exceeds that at point O by the amount $\frac{\rho v^2}{2}$, where $v$ is the fluid velocity at point O (C) Fluid moving precisely along OA will turn perpendicular to OA to circumvent the object (D) On each side of the central streamline OA, the flow will be deflected round the object

(A)

The velocity of the fluid at the point A is zero

(B)

The fluid pressure at the point A exceeds that at point O by the amount \frac{\rho v^2}{2}, where v is the fluid velocity at point O

(C)

Fluid moving precisely along OA will turn perpendicular to OA to circumvent the object

(D)

On each side of the central streamline OA, the flow will be deflected round the object

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q18

NAT[2 Marks]

A spherical gas bubble of radius $0.01\text{ mm}$ is entrapped in molten steel held at $1773\text{ K}$. If the pressure outside the bubble is $1.5\text{ bar}$, the pressure inside the bubble is ___ $\text{bar}$ (round off to 1 decimal place).\nGiven: $1\text{ bar} = 10^5\text{ Pa}$ and the surface tension of the steel at $1773\text{ K}$ is $1.4\text{ N m}^{-1}$.

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q19

NAT[2 Marks]

A rectangular block made of Material I and Material II of identical cross sections has a temperature ($T$) of $435\text{ K}$ and $400\text{ K}$ at the bottom and top surfaces, respectively. Assuming purely steady state conductive heat transfer, the temperature at the interface is ___ $\text{K}$ (round off to nearest integer). (Given: The two parts of the block made of Material I and Material II have equal thickness of $25\text{ mm}$ each. The thermal conductivities of Material I and Material II are $50\text{ W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}$ and $200\text{ W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}$ respectively.)

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q20

NAT[2 Marks]

Air at $300\text{ K}$ is passed at a mass flow rate of $1.5\text{ kg}\cdot\text{s}^{-1}$ through a metallic tube of inner diameter $0.08\text{ m}$. Inner wall temperature of the tube is maintained at $700\text{ K}$. Temperature of the air leaving the tube is $600\text{ K}$. Assuming that heat transfer occurs entirely by steady state convection, length of the tube is ___ $\text{m}$ (round off to 2 decimal places).\nGiven: convective heat transfer coefficient $h = 500\text{ W}\cdot\text{m}^{-2}\cdot\text{K}^{-1}$, specific heat $C_p = 1080\text{ J}\cdot\text{kg}^{-1}\cdot\text{K}^{-1}$, $\pi = 3.14$.

Explanation

Mineral Processing and Extractive Metallurgy

9 Questions

GATE→2022→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q21

MCQ[1 Mark]

According to Sieverts' law, the equilibrium solubility of $N_{2}$ (gas) in molten steel is proportional to\nGiven: Equilibrium partial pressure of $N_{2}$ (gas) is $p_{N_{2}}$ (A) $p_{N_{2}}$ (B) $\sqrt{p_{N_{2}}}$ (C) $\frac{1}{p_{N_{2}}}$ (D) $p_{N_{2}}^{2}$

(A)

p_{N_{2}}

(B)

\sqrt{p_{N_{2}}}

(C)

\frac{1}{p_{N_{2}}}

(D)

p_{N_{2}}^{2}

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q22

MCQ[1 Mark]

Titanium is produced commercially by (A) smelting reduction of $TiO_{2}$ (B) thermal dissociation of $TiH_{2}$ (C) reduction of $TiCl_{4}$ by Mg (D) reduction of $TiO_{2}$ by $H_{2}$

(A)

smelting reduction of TiO_{2}

(B)

thermal dissociation of TiH_{2}

(C)

reduction of TiCl4 by Mg

(D)

reduction of TiO_{2} by H_{2}

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Ironmaking

Q23

MCQ[1 Mark]

Magnesium treatment is carried out to produce _______ cast iron. (A) white (B) gray (C) spheroidal graphite (D) malleable

(A)

white

(B)

gray

(C)

spheroidal graphite

(D)

malleable

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q24

MCQ[1 Mark]

Which one of the following elements has the slowest removal rate from hot metal in basic oxygen furnace (BOF) steelmaking? (A) Carbon (B) Sulfur (C) Silicon (D) Phosphorus

(A)

Carbon

(B)

Sulfur

(C)

Silicon

(D)

Phosphorus

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Ironmaking

Q25

MCQ[1 Mark]

Which one of the following modern practices is used for retarding the solution loss reaction in blast furnace ironmaking? (A) High top pressure (B) Bell-less top (C) Pulverized coal injection (D) Rotating chute for burden distribution

(A)

High top pressure

(B)

Bell-less top

(C)

Pulverized coal injection

(D)

Rotating chute for burden distribution

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q26

MSQ[1 Mark]

In continuous casting of steel, mould flux is used for (A) lubrication (B) reducing heat loss (C) inclusion control (D) reducing solidification shrinkage

(A)

lubrication

(B)

reducing heat loss

(C)

inclusion control

(D)

reducing solidification shrinkage

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q27

MCQ[2 Marks]

Match the following mineral processing operations (Column I) with the corresponding physical principles (Column II)\nColumn I: (P) Flotation (Q) Jigging (R) Tabling (S) Comminution\nColumn II: (1) Difference in speed of lateral movements (2) Hydrophobicity (3) Difference in size reduction (4) Difference in initial acceleration (A) P-2, Q-4, R-1, S-3 (B) P-2, Q-3, R-1, S-4 (C) P-3, Q-1, R-4, S-2 (D) P-1, Q-4, R-2, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Primary and Secondary Steelmaking

Q28

NAT[2 Marks]

Molten steel at $1873\text{ K}$ weighing $100\text{ metric tons}$ is desulfurized using $1250\text{ kg}$ of synthetic slag by equilibration. If the sulfur content in the steel is reduced from $0.015\text{ mass}\%$ to $0.0025\text{ mass}\%$, the desulfurizing index is ___ (round off to the nearest integer).

Explanation

GATE→2022→Mineral Processing and Extractive Metallurgy→Mineral Beneficiation and Extraction Principles

Q29

NAT[2 Marks]

A sieve made of steel wire of diameter $53\text{ }\mu\text{m}$ has an aperture size of $74\text{ }\mu\text{m}$. Its mesh number is ___ (round off to the nearest integer).

Explanation

Physical Metallurgy

8 Questions

GATE→2022→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q30

MCQ[1 Mark]

The sequence of peaks corresponding to the planes (in the order of increasing $2\theta$) observed in the X-ray diffractogram of a pure copper powder sample is (A) 111, 200, 220, 311 (B) 110, 200, 211, 220 (C) 110, 200, 211, 311 (D) 111, 200, 311, 220

(A)

111, 200, 220, 311

(B)

110, 200, 211, 220

(C)

110, 200, 211, 311

(D)

111, 200, 311, 220

Explanation

GATE→2022→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q31

MCQ[1 Mark]

The CCT diagram of a eutectoid steel with a superimposed cooling curve is shown in the figure. The microstructure at room temperature (RT) after this heat treatment is (A) pearlite only (B) pearlite + retained austenite (C) martensite only (D) pearlite + martensite

(A)

pearlite only

(B)

pearlite + retained austenite

(C)

martensite only

(D)

pearlite + martensite

Explanation

GATE→2022→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q32

MCQ[1 Mark]

With increase in carbon content (up to 2 mass%) in Fe-C alloy, which one of the following statements is correct with respect to the lattice parameters ($c$ and $a$) of BCT martensite? (A) Both $c$ and $a$ increase (B) $c$ increases but $a$ decreases (C) $c$ decreases but $a$ increases (D) Both $c$ and $a$ decrease

(A)

Both c and a increase

(B)

c increases but a decreases

(C)

c decreases but a increases

(D)

Both c and a decrease

Explanation

GATE→2022→Physical Metallurgy→Principles of Heat Treatment and Corrosion

Q33

MSQ[1 Mark]

Identify the correct statement(s) with respect to the role of nickel as an alloying element in steels. (A) It increases the $M_s$ temperature (B) It is an austenite stabiliser (C) It decreases the $M_s$ temperature (D) It is a carbide former

(A)

It increases the M_{s} temperature

(B)

It is an austenite stabiliser

(C)

It decreases the M_{s} temperature

(D)

It is a carbide former

Explanation

GATE→2022→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q34

MCQ[2 Marks]

Find the correct match between dislocation reactions (Column A) to the descriptions (Column B)\nColumn A: (P) $\frac{a_{o}}{2}[\bar{1}\bar{1}1]+\frac{a_{o}}{2}[111]=a_{o}[001]$ (Q) $\frac{a_{o}}{6}[\bar{1}2\bar{1}]+\frac{a_{o}}{6}[1\bar{1}2]=\frac{a_{o}}{6}[011]$ (R) $\frac{a_{o}}{6}[1\bar{2}1]+\frac{a_{o}}{6}[\bar{1}\bar{1}2]=\frac{a_{o}}{2}[0\bar{1}1]$\nColumn B: (1) Leading partials merging to form a Lomer-Cottrell lock in an FCC metal (2) Energetically unfavorable dislocation reaction in an FCC metal (3) Typical dislocation reaction in a BCC metal (A) P-3, Q-2, R-1 (B) P-3, Q-1, R-2 (C) P-2, Q-3, R-1 (D) P-2, Q-1, R-3

(A)

P-3 Q-2 R-1

(B)

P-3 Q-1 R-2

(C)

P-2 Q-3 R-1

(D)

P-2 Q-1 R-3

Explanation

GATE→2022→Physical Metallurgy→Materials Characterisation and Crystal Imperfections

Q35

NAT[2 Marks]

Consider a tilt boundary of misorientation of $2^{\circ}$ in an aluminium grain. The lattice parameter of aluminium is $0.143\text{ nm}$. The spacing between the dislocations that form the tilt boundary is ___ $\text{nm}$ (round off to 2 decimal places).

Explanation

GATE→2022→Physical Metallurgy→Phase Transformation and Solid-state Transformations

Q36

NAT[2 Marks]

During solidification of a pure metal, the radius of critical nucleus at an undercooling of $10\text{ K}$ is ___ $\times 10^{-9}\text{ m}$ (answer rounded off to 1 decimal place).\nGiven: solid/liquid interface energy $= 0.177\text{ J}\cdot\text{m}^{-2}$, melting point of the metal $= 1356\text{ K}$, and latent heat of fusion $= 1.88\text{ }\times 10^{9}\text{ J}\cdot\text{m}^{-3}$.

Explanation

GATE→2022→Physical Metallurgy→Diffusion in Solids

Q37

NAT[2 Marks]

The concentration $C$ of a solute (in units of atoms-mm$^{-3}$) in a solid along $x$ direction (for $x>0$) follows the expression $$C = a_1 x^2 + a_2 x$$\nwhere $x$ is in $\text{mm}$, $a_1$ and $a_2$ are in units of atoms-mm$^{-4}$ and atoms-mm$^{-3}$, respectively. Assuming $a_1 = a_2 = 1$, the magnitude of flux at $x = 2\text{ mm}$ is ___ $\times 10^{-3}\text{ atoms-mm}^{-2}\cdot\text{s}^{-1}$ (answer rounded off to the nearest integer).\nGiven: diffusion coefficient of the solute in the solid is $3 \times 10^{-3}\text{ mm}^2\cdot\text{s}^{-1}$.

Explanation

Mechanical Behaviour of Materials

8 Questions

GATE→2022→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q38

MCQ[1 Mark]

For a material that undergoes strain hardening, necking instability occurs during tensile testing when\nGiven: $\sigma = \text{true stress}$ and $\epsilon = \text{true strain}$. (A) $\frac{d\sigma}{d\epsilon} = 0$ (B) $\frac{d\sigma}{d\epsilon} = \epsilon$ (C) $\frac{d\sigma}{d\epsilon} = \sigma$ (D) $\frac{d\sigma}{d\epsilon} = \infty$

(A)

\frac{d\sigma}{d\epsilon}=0

(B)

\frac{d\sigma}{d\epsilon}=\epsilon

(C)

\frac{d\sigma}{d\epsilon}=\sigma

(D)

\frac{d\sigma}{d\epsilon}=\infty

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q39

MCQ[1 Mark]

With reference to the stress intensity factor, find the correct match of nomenclature (Column A) with the mode of deformation applied to the crack (Column B).\nColumn A: (P) Mode I (Q) Mode II (R) Mode III\nColumn B: (X) Forward shear mode (Y) Parallel shear mode (Z) Crack opening mode (A) P-Z, Q-Y, R-X (B) P-Z, Q-X, R-Y (C) P-Y, Q-X, R-Z (D) P-Y, Q-Z, R-X

(A)

P-Z, Q-Y, R-X

(B)

P-Z, Q-X, R-Y

(C)

P-Y, Q-X, R-Z

(D)

P-Y, Q-Z, R-X

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q40

MSQ[1 Mark]

While designing a material for high temperature application, which of the following characteristic(s)/attribute(s) is (are) desirable for achieving better creep resistance? (A) Fine grain size (B) FCC crystal structure (C) High melting point (D) Cold worked microstructure

(A)

Fine grain size

(B)

FCC crystal structure

(C)

High melting point

(D)

Cold worked microstructure

Explanation

GATE→2022→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q41

MSQ[1 Mark]

Given the strain rate ($\dot{\epsilon}$), dislocation density ($\rho$), dislocation velocity ($v$), which of the following relationship(s) is (are) correct? Assume that Orowan equation for plastic flow due to the dislocation movement is obeyed. (A) $\dot{\epsilon} \propto v^2$ (B) $\dot{\epsilon} \propto v$ (C) $\dot{\epsilon} \propto \rho^2$ (D) $\dot{\epsilon} \propto \rho$

(A)

\dot{\epsilon}\propto v^{2}

(B)

\dot{\epsilon}\propto v

(C)

\dot{\epsilon}\propto \rho^{2}

(D)

\dot{\epsilon}\propto \rho

Explanation

GATE→2022→Mechanical Behaviour of Materials→Dislocation Theory and Strengthening Mechanisms

Q42

MCQ[2 Marks]

Match the phenomena (Column I) with the descriptions (Column II)\nColumn I: (P) Cottrell atmosphere (Q) Suzuki interaction (R) Bauschinger effect (S) Nabarro-Herring creep\nColumn II: (1) Decrease in yield stress when loading direction is reversed (2) Stress assisted diffusion of vacancies resulting in plastic deformation in a polycrystalline material (3) Lüders bands (4) Segregation of solutes to the stacking fault (A) P-1, Q-2, R-3, S-4 (B) P-1, Q-2, R-4, S-3 (C) P-3, Q-4, R-1, S-2 (D) P-3, Q-1, R-4, S-2

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q43

NAT[2 Marks]

From high temperature tensile testing, the flow stress (measured at the same value of strain) of an alloy was found to be $50\text{ MPa}$ at a strain rate of $0.1\text{ s}^{-1}$ and $70\text{ MPa}$ at a strain rate of $10\text{ s}^{-1}$. The strain rate sensitivity parameter is ___ (round off to 3 decimal places).

Explanation

GATE→2022→Mechanical Behaviour of Materials→Fracture, Fatigue, and High Temperature Deformation

Q44

NAT[2 Marks]

High cycle fatigue data for an alloy at various alternating stresses, $\sigma_a$, is given below: $500\text{ MPa} \rightarrow 1000\text{ cycles}$ $400\text{ MPa} \rightarrow 10000\text{ cycles}$ $300\text{ MPa} \rightarrow 100000\text{ cycles}$ $200\text{ MPa} \rightarrow 1000000\text{ cycles}$\nA specimen is subjected to: (i) $5000\text{ cycles}$ at $400\text{ MPa}$, (ii) $25000\text{ cycles}$ at $300\text{ MPa}$, and finally (iii) at $500\text{ MPa}$. Assuming Miner's law is obeyed, the number of cycles to failure at $500\text{ MPa}$ is ___.

Explanation

GATE→2022→Mechanical Behaviour of Materials→Elasticity, Plasticity, and Yield Criteria

Q45

NAT[2 Marks]

Given the stress tensor $$\begin{bmatrix} 130 & 30 & 0 \\ 30 & 50 & 0 \\ 0 & 0 & 0 \end{bmatrix}\text{ MPa}$$\nthe maximum shear stress is ___ $\text{MPa}$ (round off to the nearest integer).

Explanation

Manufacturing Processes

8 Questions

GATE→2022→Manufacturing Processes→Non-destructive Testing (NDT)

Q46

MCQ[1 Mark]

Which one of the following Non Destructive Testing (NDT) techniques CANNOT be used to identify volume defects in the interior of a casting? (A) Ultrasonic testing (B) X-ray computed tomography (C) Dye-penetrant testing (D) Gamma ray radiography

(A)

Ultrasonic testing

(B)

X-ray computed tomography

(C)

Dye-penetrant testing

(D)

Gamma ray radiography

Explanation

GATE→2022→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q47

MCQ[1 Mark]

Neutral point in rolling is defined as the point along the surface of contact between the roll and the sheet, where the surface velocity of the roll is (A) zero (B) half the velocity of the sheet (C) twice the velocity of the sheet (D) equal to the velocity of the sheet

(A)

zero

(B)

half the velocity of the sheet

(C)

twice the velocity of the sheet

(D)

equal to the velocity of the sheet

Explanation

GATE→2022→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q48

MCQ[1 Mark]

Which one of the following figures illustrates a lap joint with fillet weld?

(A)

I

(B)

II

(C)

III

(D)

IV

Explanation

GATE→2022→Manufacturing Processes→Metal Casting

Q49

MCQ[1 Mark]

In green sand moulding, the casting defect resulting from the displacement of mould cavity by an oversized core is known as (A) crush (B) hot tear (C) blow (D) fin

(A)

crush

(B)

hot tear

(C)

blow

(D)

fin

Explanation

GATE→2022→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q50

MCQ[1 Mark]

Match the processes (Column I) with the corresponding defects (Column II).\nColumn I: (P) Extrusion (Q) Deep drawing (R) Forging (S) Rolling\nColumn II: (1) Earing (2) Cold shut (3) Edge cracking (4) Fir-tree cracking (A) P-1, Q-4, R-2, S-3 (B) P-2, Q-1, R-4, S-3 (C) P-4, Q-1, R-3, S-2 (D) P-4, Q-1, R-2, S-3

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2022→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q51

MSQ[2 Marks]

Which of the following parameter(s) influence(s) the melting rate of the consumable wire in a gas metal arc welding process? (A) Stick-out length (B) Welding speed (C) Welding current (D) Diameter of the consumable wire

(A)

Stick-out length

(B)

Welding speed

(C)

Welding current

(D)

Diameter of the consumable wire

Explanation

GATE→2022→Manufacturing Processes→Metal Joining and Powder Metallurgy

Q52

NAT[2 Marks]

Steel plates are welded autogenously using Gas Tungsten Arc welding with an arc heat transfer efficiency of $0.65$. The first weld is made using a welding current of $200\text{ A}$ at an arc voltage of $18\text{ V}$ with a welding speed of $0.002\text{ m}\cdot\text{s}^{-1}$. The second weld is made at a welding speed of $0.0022\text{ m}\cdot\text{s}^{-1}$ with the same arc voltage. If both the welds have identical heat input, the welding current of the second weld is ___ $\text{A}$ (round off to the nearest integer).

Explanation

GATE→2022→Manufacturing Processes→Metal Working (Hot, Warm, Cold)

Q53

NAT[2 Marks]

A cylindrical specimen of an Al alloy with diameter of $30\text{ mm}$ is cold extruded to a diameter of $20\text{ mm}$. If the flow behavior of the alloy is expressed by the equation, $\sigma = 350\text{ }\epsilon^{0.3}\text{ MPa}$, the ideal plastic work of deformation per unit volume is ___ $\times 10^6\text{ J}$ (answer rounded off to the nearest integer).

Explanation

Materials Science and Non-Metallic Materials

2 Questions

GATE→2022→Materials Science and Non-Metallic Materials→Classification, Chemical Bonding, and Crystal Structures

Q54

MCQ[1 Mark]

Match the nature of bonding (Column I) with material (Column II)\nColumn I:\nP. Ionic\nQ. Covalent\nR. Metallic\nS. Secondary\nColumn II: 1. Diamond 2. Silver 3. NaCl 4. Solid argon (A) P-4, Q-3, R-2, S-1 (B) P-2, Q-1, R-3, S-4 (C) P-3, Q-1, R-4, S-2 (D) P-3, Q-1, R-2, S-4

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2022→Materials Science and Non-Metallic Materials→Electronic and Magnetic Properties

Q55

MCQ[2 Marks]

Figures P, Q, R and S schematically show the atomic dipole moments in the absence of external magnetic field. Which one of the following is the correct mapping of nature of magnetism to atomic dipole moments? (A) P - Diamagnetism, Q - Antiferromagnetism, R - Paramagnetism, S - Ferromagnetism (B) P - Ferromagnetism, Q - Antiferromagnetism, R - Diamagnetism, S - Paramagnetism (C) P - Paramagnetism, Q - Ferromagnetism, R - Diamagnetism, S - Antiferromagnetism (D) P - Ferromagnetism, Q - Diamagnetism, R - Antiferromagnetism, S - Paramagnetism

(A)

P - Diamagnetism, Q- Antiferromagnetism, R - Paramagnetism, S- Ferromagnetism

(B)

P-Ferromagnetism, Q - Antiferromagnetism, R - Diamagnetism, S-Paramagnetism

(C)

P- Paramagnetism, Q- Ferromagnetism, R - Diamagnetism, S-Antiferromagnetism

(D)

P-Ferromagnetism, Q - Diamagnetism, R - Antiferromagnetism, S-Paramagnetism

Explanation

General Aptitude

10 Questions

GATE→2022→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

Mr. X speaks _______ Japanese _______ Chinese. (A) neither/or (B) either/nor (C) neither / nor (D) also / but

(A)

neither/or

(B)

either/nor

(C)

neither / nor

(D)

also / but

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

A sum of money is to be distributed among P, Q, R, and S in the proportion $5:2:4:3$, respectively. If R gets 1000 more than S, what is the share of Q (in ?)? (A) 500 (B) 1000 (C) 1500 (D) 2000

(A)

500

(B)

1000

(C)

1500

(D)

2000

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, $PQ=11\text{ cm}$, $QR=4\text{ cm}$, $RS=6\text{ cm}$ and $SP=3\text{ cm}$. What is the shortest distance between PQ and SR (in cm)? (A) 1.80 (B) 2.40 (C) 4.20 (D) 5.76

(A)

1.80

(B)

2.40

(C)

4.20

(D)

5.76

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a "hole in the interior" that can be formed within the $4\times4$ grid using the unit squares as building blocks? (A) 15 (B) 20 (C) 21 (D) 26

(A)

15

(B)

20

(C)

21

(D)

26

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

An art gallery engages a security guard... boundary walls are opaque... Which one of the following correctly represents the set of ALL possible locations among P, Q, R and S where the security guard can be posted to watch over the entire inner space? (A) P and Q (B) Q (C) Q and S (D) R and S

(A)

P and Q

(B)

Q

(C)

Q and S

(D)

R and S

Explanation

GATE→2022→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.\nWhich one of the following is the correct logical inference based on the information in the above passage? (A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous (B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects (C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous (D) Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence

(A)

Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous

(B)

Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects

(C)

Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous

(D)

Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Consider the following inequalities. (i) $2x - 1 > 7$ (ii) $2x - 9 < 1$\nWhich one of the following expressions below satisfies the above two inequalities? (A) $x \le -4$ (B) $-4 < x \le 4$ (C) $4 < x < 5$ (D) $x \ge 5$

(A)

x\le-4

(B)

-4<x\le4

(C)

4<x<5

(D)

x\ge5

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

Four points $P(0,1)$, $Q(0,-3)$, $R(-2,-1)$, and $S(2,-1)$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? (A) 4 (B) $4\sqrt{2}$ (C) 8 (D) $8\sqrt{2}$

(A)

4

(B)

4\sqrt{2}

(C)

8

(D)

8\sqrt{2}

Explanation

GATE→2022→General Aptitude→Verbal Ability

Q64

MCQ[2 Marks]

In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.\nStatement of P: R has copied in the exam.\nStatement of Q: S has copied in the exam.\nStatement of R: P did not copy in the exam.\nStatement of S: Only one of us is telling the truth.\nStatement of T: R is telling the truth.\nThe investigating team had authentic information that S never lies.\nBased on the information given above, the person who has copied in the exam is (A) R (B) P (C) Q (D) T

(A)

R

(B)

P

(C)

Q

(D)

T

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively. Operations X, Y, Z defined... sequences (1) XYZZ, (2) XY, (3) ZZZZ. Which statement is correct? (A) The sequence of operations (1) and (2) are equivalent (B) The sequence of operations (1) and (3) are equivalent (C) The sequence of operations (2) and (3) are equivalent (D) The sequence of operations (1), (2) and (3) are equivalent

(A)

The sequence of operations (1) and (2) are equivalent

(B)

The sequence of operations (1) and (3) are equivalent

(C)

The sequence of operations (2) and (3) are equivalent

(D)

The sequence of operations (1), (2) and (3) are equivalent

Explanation