Metallurgical Engineering Gate 2021 Questions with Answer

Ques 1 GATE 2021

At 25^oC iron corrodes in a deaerated acid of pH 3 with a corrosion current density of 4 µA cm^-2. The corrosion potential (V) is: _______ (round off to 2 decimal places).
Given: β_c = 0.1 V per decade of current density Exchange current density of hydrogen on iron surface = 10^-9 A cm^-2 R = 8.314 J mol^-1K^-1 F = 96500 C mol^-1
All potentials are with reference to standard hydrogen electrode.

Ques 2 GATE 2021

For the matrix given below, the eigenvalues are:

Ques 3 GATE 2021

Which one of the following is a homogeneous function of degree three?

Ques 4 GATE 2021

The divergence of a vector field V⃗(x, y, z), where its three components (V_x, V_y, V_z) are functions of x, y, z, is:

Ques 5 GATE 2021

The value of lim_x→0 sin²5x / sin²x is: _______ (round off to nearest integer).

Ques 6 GATE 2021

The grain size (X) of annealed specimens follows a symmetric distribution with a mean (µ) of 5 µm and a standard deviation (σ) of 0.5 µm. The percentage of specimens with grain size in the range 5 to 6 µm is expected to be: _______ (round off to nearest integer). Given: For the symmetric distribution: Probability P(X ≤ µ + 2σ) = 0.98

Ques 7 GATE 2021

The minimum value of y for the equation y = x² - 2x + 4 is

Ques 8 GATE 2021

Consider the function f(x) = x - cos x. Using Newton-Raphson method, the estimated root of f(x) after the first iteration is: _______ (round off to 3 decimal places). Assume: Initial guess of the root = 0.5 radians.

Ques 9 GATE 2021

The work done by a force F⃗ = 2xi + 3yj along a straight line from point (0, 0) to (1, 2) is: _______ (round off to nearest integer).

Ques 10 GATE 2021

A coin is tossed three times. Given that there are more heads than tails, the probability of getting exactly one tail is: _______ (round off to 2 decimal places).

Ques 11 GATE 2021

Which one of the following is a hydrometallurgical operation?

Ques 12 GATE 2021

A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m radius), as shown in figure. The radiation exchange takes place between the outer surface (surface 1) of the small sphere and the inner surface (surface 2) of the bigger sphere. The value of the view factor, F₂₂ is: _______ (round off to 2 decimal places). Given: View factor (F_ij) is the fraction of the radiation leaving surface i that is intercepted by surface j.

Ques 13 GATE 2021

Which one of the following elements oxidizes first in basic oxygen steel making process?