Metallurgical Engineering Gate Yearwise 



Metallurgical Engineering Gate 2020 Questions with Answer

Ques 1 GATE 2020

Which one of the following processes is an example of an electrolytic cell?

A

Corrosion of a metal rod in ambient atmosphere

B

Charging of a rechargeable battery

C

Sacrificial cathodic protection system

D

Discharging of a rechargeable battery


(b) is the correct answer.

Ques 2 GATE 2020

A galvanic cell is formed by connecting Zn (EoZn2+/Zn = -0.76 V) and Fe (EoFe2+/Fe = -0.44 V) wires immersed in their respective ion solutions. The cell discharges spontaneously with a voltage of 0.5 V. The ratio of the concentration of [Fe2+] to [Zn2+] ions in the cell is of the order of:
Given, R = 8.314 J⋅mol-1⋅K-1, F = 96500 C⋅mol-1, T = 298 K

A

10-6

B

10-5

C

106

D

107


(c) is the correct answer.

Ques 3 GATE 2020

Iron is corroding in fresh water which has dissolved oxygen concentration of 15 mM. The anodic current density at an overpotential of 120 mV is _______ A⋅cm-2 (round off to three decimal places).
Given:
1. Anodic Tafel slope is 0.06 V.
2. Diffusion coefficient of oxygen is 2.42 × 10-5 cm2⋅s-1.
3. Diffusion layer thickness is 0.06 cm.


(0.214) is the correct answer.

Ques 4 GATE 2020

The general solution to the following homogeneous ODE, d2y / dt2 + 4dy / dt + 3y = 0,
is
y(t) = C1eλ1t + C2eλ2t.
The values of λ1 and λ2 are:

A

-1 and -3

B

-3 and -3

C

1 and -3

D

1 and 3


(a) is the correct answer.

Ques 5 GATE 2020

Given the three vectors X = -i - j + k, Y = -i + 2j + k and Z = i + k, which one of the following statements is TRUE?

A

X, Y and Z are mutually perpendicular.

B

X, Y and Z are coplanar.

C

X makes an angle of 30o with the normal to the plane containing Y and Z.

D

Z makes an angle of 60o with the normal to the plane containing X and Y.


(a) is the correct answer.

Ques 6 GATE 2020

For the function y = ax, the derivative dy / dx at x = 1 is:

A

1

B

a

C

a2

D

a ln a


(d) is the correct answer.

Ques 7 GATE 2020

The functions y = ex and y = e-x intersect at the point:

A

(1, 3)

B

(-2, 2)

C

(0, 1)

D

(-1, -1)


(c) is the correct answer.

Ques 8 GATE 2020

For the function f(x) given in the figure, the value of ∫01(1 - f(x))dx is _______ (round off to one decimal place).


(0.5) is the correct answer.

Ques 9 GATE 2020

The divergence of the vector field (x3 + y3)i + 3xy2j + 3zy2k is:

A

3y2 + 6xy + 6x2

B

3x2 + 6y2 + 9xy + 6yz

C

12xyz

D

3(x + y)2


(d) is the correct answer.

Ques 10 GATE 2020

f(x) = x ln(x) + (1 - x)ln(1 - x) + 3 x(1 - x) has _______ at x = 0.5.

A

a local minimum

B

a local maximum

C

a point of inflection

D

a non-zero slope


(b) is the correct answer.

Ques 11 GATE 2020

The production process of cylindrical pipes results in a statistical scatter in their diameter which is modelled by a normal distribution with a mean value of 10 mm. If the area under the normal curve between 9 mm and 10 mm is 0.35, then the probability of producing pipes of diameter greater than 11 mm is _______ (round off to two decimal places).


(0.15) is the correct answer.

Ques 12 GATE 2020

The solution (using trapezoidal rule) of the integral
∫01exdx
by dividing the range 0 to 1 into two equal intervals is _______ (round off to two decimal places).


(1.75) is the correct answer.

Ques 13 GATE 2020

M and N are 3 × 3 matrices. If the det(M) is -9 and the det(N) is -14, then the det(NM) is _______ (round off to the nearest integer).


(126) is the correct answer.

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