Metallurgical Engineering Gate Yearwise 



Metallurgical Engineering Gate 2025 Questions with Answer

Ques 1 GATE 2025

Which one of the following matrices has eigenvalues 1 and 6?

A

[(5 -2); (-2 2)]

B

[(3 -1); (-2 2)]

C

[(3 -1); (-1 2)]

D

[(2 -1); (-1 3)]


(a) is the correct answer.

Ques 2 GATE 2025

Which of the following functions is/are expandable using Maclaurin series?

A

ln(1+z)

B

ln z

C

1/z2

D

exp(z)


(a) is the correct answer.

Ques 3 GATE 2025

A linear regression model was fitted to a set of (x,y) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively.
The coefficient of determination (R2) of the fit is ______ (rounded off to one decimal place).


(0.9) is the correct answer.

Ques 4 GATE 2025

For two continuous functions M(x,y) and N(x,y), the relation M dx+N dy=0 describes an exact differential equation if

A

&partial;M/&partial;x = &partial;N/&partial;y

B

&partial;M/&partial;x = -&partial;N/&partial;y

C

&partial;M/&partial;y = &partial;N/&partial;x

D

&partial;M/&partial;y = -&partial;N/&partial;x


(c) is the correct answer.

Ques 5 GATE 2025

Which one of the following matrices is orthogonal?

A

[(1/2 -√3/2); (-√3/2 1/2)]

B

[(1/2 -√3/2); (√3/2 1/2)]

C

[(1/√2 -√3/2); (-√3/2 1/2)]

D

[(1/√2 -√3/2); (1√3/2 -1/√2)]


(b) is the correct answer.

Ques 6 GATE 2025

For a two-dimensional field described by T(x,y)=(1/3)xy(x+y), the magnitude of its gradient at the point (1,1) is ______ (rounded off to two decimal places).


(1.63) is the correct answer.

Ques 7 GATE 2025

The value of limx→0(6(x-sin x))/x3 is ______ (in integer).


(1) is the correct answer.

Ques 8 GATE 2025

Two consecutive estimates of the root of a function f(x) obtained using the Newton-Raphson method are xi=8.5 and xi+1=13.5 and the value of the function at xi is 15.
The numerical value of first derivative of the function evaluated at xi is ______ (in integer).


(3) is the correct answer.

Ques 9 GATE 2025

At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity μ of a Newtonian liquid with absolute temperature T?
Given: A and B are positive constants.

A

μ=A+BT

B

μ=A exp(-B/T)

C

μ=A exp(BT)

D

μ=A exp(B/T)


(d) is the correct answer.

Ques 10 GATE 2025

Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities?
Given: ΔP is the difference between the outlet and inlet pressure, μ is the dynamic viscosity of the liquid, and R and L are radius and length of the pipe, respectively.

A

ΔP

B

1/R2

C

1/μ

D

1/L


(a) is the correct answer.

Ques 11 GATE 2025

For an application where the Reynolds number is to be kept constant, a liquid with a density of 1 g cm-3 and viscosity 0.01 Poise results in a characteristic speed of 1 cms-1.
If this liquid is replaced by another with a density of 1.25 g cm-3 and viscosity of 0.015 Poise, the characteristic velocity will be ______ cms-1 (rounded off to one decimal place).
Assume the characteristic length of the flow to be the same in both cases.


(1.2) is the correct answer.

Ques 12 GATE 2025

Despite his initial hesitation, Rehman's ______ to contribute to the success of the project never wavered.
Select the most appropriate option to complete the above sentence.

A

ambivalence

B

satisfaction

C

resolve

D

revolve


(c) is the correct answer.

Ques 13 GATE 2025

Bird: Nest :: Bee: ______
Select the correct option to complete the analogy.

A

Kennel

B

Hammock

C

Hive

D

Lair


(c) is the correct answer.

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