Electrical Engineering Gate Yearwise 




Electrical Engineering Gate 2025 Questions with Answer

Ques 27 GATE 2025

Assuming ideal op-amps, the circuit represents a

A

summing amplifier.

B

difference amplifier.

C

logarithmic amplifier.

D

buffer.


(b) is the correct answer.

Ques 28 GATE 2025

In the circuit, IDC is an ideal current source. The transistors M1 and M2 are assumed to be biased in saturation, wherein Vin is the input signal and VDC is fixed DC voltage. Both transistors have a small signal resistance of rds and trans-conductance of gm. The small signal output impedance of this circuit is

A

2rds

B

1/gm+rds

C

gmrds2+2rds

D

infinity


(a) is the correct answer.

Ques 29 GATE 2025

In the circuit, shown below, if the values of R and C are very large, the form of the output voltage for a very high frequency square wave input, is best represented by

A

B

C

D


(c) is the correct answer.

Ques 30 GATE 2025

Let (x,y)∈ℜ2. The rate of change of the real valued function, V(x,y)=x2+x+y2+1 at the origin in the direction of the point (1,2) is ______ (round off to the nearest integer).


(1) is the correct answer.

Ques 31 GATE 2025

Consider ordinary differential equations given by ẋ1(t)=2x2(t) and ẋ2(t)=r(t) with initial conditions x1(0)=1 and x2(0)=0.
If r(t)=1, t≥0; 0,t<0, then at t=1 x1(t)= ______ (round off to the nearest integer).


(2) is the correct answer.

Ques 32 GATE 2025

Let C be a clockwise oriented closed curve in the complex plane defined by |z|=1. Further, let f(z)=jz be a complex function, where j=√-1. Then, ∮f(z)dz= ______ (round off to the nearest integer).


(2) is the correct answer.

Ques 33 GATE 2025

Consider the set S of points (x,y)∈ℜ2 which minimize the real valued function f(x,y)=(x+y-1)2+(x+y)2
Which of the following statements is true about the set S?

A

The number of elements in the set S is finite and more than one.

B

The number of elements in the set S is infinite.

C

The set S is empty.

D

The number of elements in the set S is exactly one.


(b) is the correct answer.

Ques 34 GATE 2025

Let v1 and v2 be the two eigenvectors corresponding to distinct eigenvalues of a 3×3 real symmetric matrix. Which one of the following statements is true?

A

v1Tv2≠0

B

v1Tv2=0

C

v1+v2=0

D

v1-v2=0


(b) is the correct answer.

Ques 35 GATE 2025

Let Then, the system of linear equations Ax=b has

A

a unique solution.

B

infinitely many solutions.

C

a finite number of solutions.

D

no solution.


(b) is the correct answer.

Ques 36 GATE 2025

Let and let I be the identity matrix. Then P2 is equal to

A

2P-I

B

P2=I

C

P+I

D

P2=P-I


(a) is the correct answer.

Ques 37 GATE 2025

Consider discrete random variables X and Y with probabilities as follows:
P(X=0 and Y=0)=1/4
P(X=1 and Y=0)=1/8
P(X=0 and Y=1)=1/2
P(X=1 and Y=1)=1/8
Given X=1, the expected value of Y is

A

1/4

B

1/2

C

1/8

D

1/3


(b) is the correct answer.

Ques 38 GATE 2025

Let X and Y be continuous random variables with probability density functions PX(x) and PY(y), respectively. Further, let Y=X2 and PX(x) = 1, x∈(0,1]; 0, otherwise. Which one of the following options is correct?

A

PY(y) = 1/(2√y), y∈(0,1]; 0, otherwise

B

PY(y) = 1, y∈(0,1]; 0, otherwise

C

PY(y) = 1.5√y, y∈(0,1]; 0, otherwise

D

PY(y) = 2y, y∈(0,1]; 0, otherwise


(a) is the correct answer.

Ques 39 GATE 2025

Kavya ______ go to work yesterday as she ______ feeling well.
Select the most appropriate option to complete the above sentence.

A

didn't; isn't

B

wouldn't; wasn't

C

wasn't; wasn't

D

couldn't; wasn't


(d) is the correct answer.

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