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)]



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)



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).



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



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)]



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).



Ques 7 GATE 2025

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



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).



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)



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



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.



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



Ques 13 GATE 2025

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

A

Kennel

B

Hammock

C

Hive

D

Lair



Unique Visitor Count

Total Unique Visitors

Loading......

Question Options

Contributed by: