Electrical Engineering GATE 2025 Questions with Answer

Ques 27 Electronic Devices

Assuming ideal op-amps, the circuit represents a

Ques 28 Electronic Devices

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

Ques 29 Electronic Devices

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

Ques 30 Engineering Mathematics

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).

Ques 31 Engineering Mathematics

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).

Ques 32 Engineering Mathematics

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).

Ques 33 Engineering Mathematics

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?

Ques 34 Engineering Mathematics

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?

Ques 35 Engineering Mathematics

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

Ques 36 Engineering Mathematics

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

Ques 37 Engineering Mathematics

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

Ques 38 Engineering Mathematics

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

Ques 39 General Aptitude

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