Electrical Engineering GATE 2024 Questions with Answer

Ques 1 Control Systems

Consider the standard second-order system of the form ω_n²/(s²+2ζω_ns+ω_n²) with the poles p and p having negative real parts.
The pole locations are also shown in the figure. Now consider two such second-order systems as defined below: System 1: ω_n=3 rad/sec and θ=60° System 2: ω_n=1 rad/sec and θ=70°
Which one of the following statements is correct?

Settling time of System 1 is more than that of System 2.

Settling time of System 2 is more than that of System 1.

Settling times of both the systems are the same.

Settling time cannot be computed from the given information.

Ques 2 Control Systems

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are the same?

1/(s+1)

2/(s+1)

1/(s+20)

2/(s+20)

Ques 3 Control Systems

Consider the closed-loop system shown in the figure with

The root locus for the closed-loop system is to be drawn for 0≤K<∞. The angle of departure (between 0° and 360°) of the root locus branch drawn from the pole (-1+j2), in degrees, is _______. (rounded off to the nearest integer)

143 is the correct answer.

Ques 4 Control Systems

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of G(s) has a constant slope of -20 dB/decade at least till 100 rad/sec with the gain crossover frequency being 10 rad/sec. The asymptotic Bode phase plot remains constant at -90° at least till ω=10 rad/sec. The steady-state error of the closed-loop system for a unit ramp input is _______. (rounded off to 2 decimal places)

0.10 is the correct answer.

Ques 5 Control Systems

Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s) are given in the table. The value of the gain K_I(>0) for a 50° phase margin is _______. (rounded off to 2 decimal places)

0.50 is the correct answer.

Ques 6 Digital Circuits

Simplified form of the Boolean function
F(P,Q,R,S)=P̅Q̅+P̅QS+PQ̅R̅S̅+PQ̅RS̅ is _______.
is

P̅S+Q̅S

P̅Q̅+Q̅S

P̅Q+RS̅

PS̅+QR̅

Ques 7 Digital Circuits

In the circuit, the present value of Z is 1. Neglecting the delay in the combinatorial circuit, the values of S and Z, respectively, after the application of the clock will be _______. Z X=1 S=X⊕Y⊕Z S Clock Y=0 Combinatorial Circuit D Flip-flop.

S=0, Z=0

S=0, Z=1

S=1, Z=0

S=1, Z=1

Ques 8 Digital Circuits

To obtain the Boolean function F(X,Y)=XY̅+X̅, the inputs PQRS in the 4:1 Multiplexer with select lines S₁ and S₀ should be _______.

1010

1110

0101

1001

Ques 9 Electric Circuits

In the circuit shown, Z₁=50∠-90° Ω and Z₂=200∠-30° Ω. It is supplied by a three-phase 400 V source with the phase sequence being R-Y-B. Assume the wattmeters W₁ and W₂ to be ideal. The magnitude of the difference between the readings of W₁ and W₂ in watts is _______. (rounded off to 2 decimal places)

5196.15 is the correct answer.

Ques 10 Electric Circuits

In the (x, y, z) coordinate system, three point-charges Q, Q, and αQ are located in free space at (-1,0,0), (1,0,0), and (0,-1,0), respectively. The value of α for the electric field to be zero at (0,0.5,0) is _______. (rounded off to 1 decimal place)

-0.5 is the correct answer.

Ques 11 Electric Circuits

The given equation represents a magnetic field strength H̅(r,θ,φ) in the spherical coordinate system, in free space. Here, r̂ and θ̂ represent the unit vectors along r and θ, respectively. The value of P in the equation H̅(r,θ,φ)=(1/r³)(r̂P cos θ+θ̂ sin θ) should be _______. (rounded off to the nearest integer)