Quiz

April 04, 2025

TestUrSelf

GATE 2025 Metallurgical Engineering

Practice with authentic GATE questions and boost your preparation

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General Aptitude (Q1-Q5)

Q1.

1 Mark

Despite his initial hesitation, Rehman's ______ to contribute to the success of the project never wavered.

A) ambivalence B) satisfaction C) resolve D) revolve

<button class="testurself-action" onclick="checkAnswer('q1', 'C', 'The correct answer is C) resolve. "Resolve" means firm determination, which fits the context of the sentence.', 1)"> TestUrSelf </button>

Q2.

2 Marks

Bird : Nest :: Bee : ______

A) Kennel B) Hammock C) Hive D) Lair

Q3.

1 Mark

If $x + \frac{1}{x} = 5$, then the value of $x^2 + \frac{1}{x^2}$ is:

A) 23 B) 25 C) 27 D) 29

Q4.

1 Mark

The sum of the first 20 terms of the arithmetic series 3, 7, 11, 15,... is:

A) 820 B) 840 C) 860 D) 880

Q5.

2 Marks

The probability that a randomly chosen positive divisor of $10^8$ is also a multiple of $10^4$ is:

A) $\frac{1}{625}$ B) $\frac{12}{625}$ C) $\frac{16}{625}$ D) $\frac{20}{625}$

Engineering Mathematics (Q6-Q10)

Q6.

1 Mark

The value of the integral $\int_0^\pi x \sin x \, dx$ is:

A) $\pi$ B) $\frac{\pi}{2}$ C) $2\pi$ D) $\frac{3\pi}{2}$

Q7.

2 Marks

The solution to the differential equation $\frac{dy}{dx} + y = e^{-x}$ with $y(0) = 1$ is:

A) $y = (x + 1)e^{-x}$ B) $y = (x - 1)e^{-x}$ C) $y = (x + 1)e^{x}$ D) $y = (x - 1)e^{x}$

Q8.

1 Mark

The eigenvalues of the matrix $\begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix}$ are:

A) 1 and 2 B) 1 and 3 C) 2 and 3 D) 3 and 4

Q9.

2 Marks

The Laplace transform of $t^2 e^{3t}$ is:

A) $\frac{2}{(s-3)^3}$ B) $\frac{2}{(s+3)^3}$ C) $\frac{6}{(s-3)^4}$ D) $\frac{6}{(s+3)^4}$

Q10.

1 Mark

The directional derivative of $f(x,y) = x^2 y$ at the point (1,2) in the direction of the vector $\vec{v} = 3\hat{i} + 4\hat{j}$ is:

A) $\frac{38}{5}$ B) $\frac{28}{5}$ C) $\frac{18}{5}$ D) $\frac{8}{5}$

Metallurgical Engineering (Q11-Q35)

Q11.

2 Marks MSQ

Which of the following matrices have eigenvalues 1 and 6? (Select all that apply)

A)

5	-2
-2	2

B)

3	-1
-2	2

C)

3	-1
-1	2

D)

2	-1
-1	3

Q12.

1 Mark NAT

The hydrostatic stress for the given stress tensor is ______ MPa (enter integer value):

150	0	0
0	-100	100
0	100	250

Q13.

1 Mark

The Hall-Petch equation relates yield strength ($\sigma_y$) to grain size ($d$) as: $$\sigma_y = \sigma_0 + \frac{k}{\sqrt{d}}$$ Where $\sigma_0$ and $k$ are material constants. If the yield strength increases from 200 MPa to 250 MPa when grain size decreases from 100 μm to 25 μm, the value of $k$ (in MPa·μm^1/2) is:

A) 25 B) 50 C) 75 D) 100

Q14.

2 Marks

In the Ellingham diagram for oxides, the Gibbs free energy change ($\Delta G^\circ$) is given by: $$\Delta G^\circ = A + BT$$ Where $A$ and $B$ are constants. For the reaction $2M + O_2 \rightarrow 2MO$, if $\Delta G^\circ = -400,000 + 120T$ J/mol, the temperature (in K) at which the oxide becomes unstable is:

A) 2500 B) 3000 C) 3333 D) 3500

Q15.

1 Mark

The diffusion coefficient $D$ follows the Arrhenius relationship: $$D = D_0 \exp\left(-\frac{Q}{RT}\right)$$ Where $Q$ is activation energy (150 kJ/mol), $R$ is gas constant (8.314 J/mol·K), and $D_0$ is pre-exponential factor (2×10^-5 m²/s). The value of $D$ at 1000 K (in m²/s) is approximately:

A) 1.5 × 10^-12 B) 2.7 × 10^-12 C) 4.8 × 10^-12 D) 6.3 × 10^-12

Q16.

2 Marks

The lever rule in phase diagrams is used to determine:

A) The composition of phases in a two-phase region B) The relative amounts of phases in a two-phase region C) The temperature of phase transformations D) The free energy of phase formation

Q17.

1 Mark

The Burgers vector for a dislocation in an FCC crystal with lattice parameter $a$ is:

A) $\frac{a}{2}\langle 100 \rangle$ B) $\frac{a}{2}\langle 110 \rangle$ C) $\frac{a}{2}\langle 111 \rangle$ D) $\frac{a}{2}\langle 112 \rangle$

Q18.

2 Marks

The Jominy end-quench test is used to determine:

A) Hardness of a material B) Hardenability of a steel C) Toughness of a material D) Fatigue strength of a material

Q19.

1 Mark

The eutectic reaction in the Fe-C system occurs at:

A) 0.77 wt% C and 727°C B) 2.11 wt% C and 1147°C C) 4.3 wt% C and 1147°C D) 4.3 wt% C and 727°C

Q20.

2 Marks

The TTT diagram for eutectoid steel shows the transformation of austenite to different phases. The "nose" of the curve represents:

A) The fastest transformation rate B) The slowest transformation rate C) The highest temperature for martensite formation D) The lowest temperature for pearlite formation

<button class="testurself-action" onclick="checkAnswer('q20', 'A', 'The correct answer is A) The fastest transformation rate. The "nose" of the TTT curve represents the temperature where the transformation from austenite to pearlite occurs most rapidly.', 2)"> TestUrSelf </button>

Q21.

1 Mark

The Hall-Héroult process for aluminum production uses cryolite (Na₃AlF₆) primarily to:

A) Reduce the melting point of alumina B) Increase the conductivity of the electrolyte C) Prevent oxidation of aluminum D) All of the above

Q22.

2 Marks

The Kroll process for titanium extraction involves:

A) Reduction of TiO₂ with carbon B) Reduction of TiCl₄ with magnesium C) Electrolysis of TiCl₄ D) Reduction of TiO₂ with hydrogen

Q23.

1 Mark

The main purpose of adding limestone (CaCO₃) in the blast furnace is to:

A) Act as a flux to remove impurities B) Provide additional heat C) Reduce iron oxide D) Increase furnace temperature

Q24.

2 Marks

The Bessemer process is used for:

A) Steel making by oxidizing impurities B) Aluminum production C) Copper refining D) Titanium extraction

Q25.

1 Mark

The main advantage of the basic oxygen furnace (BOF) over the Bessemer process is:

A) Better control of composition B) Lower capital cost C) Ability to process high-phosphorus iron D) All of the above