Metallurgical Engineering Gate Yearwise 



Metallurgical Engineering Gate 2022 Questions with Answer

Ques 40 GATE 2022

The equilibrium microstructure of an alloy A-B consists of two phases α and β in the molar proportion 2:1. If the overall composition of the alloy is 70 mol% B and the composition of β is 90 mol% B, the composition of α is _______ (in mol% B) (round off to the nearest integer).


(60) is the correct answer.

Ques 41 GATE 2022

The Taylor series expansion around x=0 of the function f(x)=(x+1)/(ex+1) truncated to first two terms is

A

1/2+1/4x

B

1/2+1/2x

C

1/2+x

D

1/2+2x


(a) is the correct answer.

Ques 42 GATE 2022

Given that V is a closed volume in space bounded by the surface S with unit normal n⃗. If f⃗ is any non-zero vector and ∇⃗ is the gradient operator, then the volume integral ∫V(∇⃗⋅f⃗)dV is equal to the surface integral ∫S(n⃗⋅f⃗)dS by virtue of _______.

A

Stokes Curl theorem

B

Reynolds transport theorem

C

Buckingham Pi theorem

D

Gauss divergence theorem


(d) is the correct answer.

Ques 43 GATE 2022

A set of observations with normal distribution of error as ±1.96σ (where σ is standard deviation) is equivalent to the confidence interval of _______ % (round off to the nearest integer).


(95) is the correct answer.

Ques 44 GATE 2022

The general solution to the following differential equation is _______, where A and B are constants.
d2y/dt2-4dy/dt+4y=0

A

y=A sin(2t)+B

B

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

C

y=Ae2t+Be-2t

D

y=Ae2t+Bte2t


(d) is the correct answer.

Ques 45 GATE 2022

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

ex-3x2=0

C

x-ln(3x)=0

D

tan(x)-x=0


(a) is the correct answer.

Ques 46 GATE 2022

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


(c) is the correct answer.

Ques 47 GATE 2022

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


(d) is the correct answer.

Ques 48 GATE 2022

A cylindrical specimen of an Al alloy with diameter of 30 mm is cold extruded to a diameter of 20 mm. If the flow behavior of the alloy is expressed by the equation, σ=350ε0.3 MPa, the ideal plastic work of deformation per unit volume is _______ x106 J (answer rounded off to the nearest integer).


(210) is the correct answer.

Ques 49 GATE 2022

Given the stress tensor

the maximum shear stress is _______ MPa (round off to the nearest integer).


(70) is the correct answer.

Ques 50 GATE 2022

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


(d) is the correct answer.

Ques 51 GATE 2022

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 cm. QR=4 cm, RS=6 cm and SP=3 cm.
What is the shortest distance between PQ and SR (in cm)?

A

1.80

B

2.40

C

4.20

D

5.76


(b) is the correct answer.

Ques 52 GATE 2022

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 4x4 grid using the unit squares as building blocks?

A

15

B

20

C

21

D

26


(b) is the correct answer.

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