Electrical Engineering Gate Yearwise 




Electrical Engineering Gate 2023 Questions with Answer

Ques 53 GATE 2023

A 50 Hz, 275 kV line of length 400 km has the following parameters:
Resistance, R=0.035 Ω/km;
Inductance, L=1 mH/km;
Capacitance, C=0.01 μF/km.
The line is represented by the nominal-π model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by VS and VR, respectively) maintained at 275 kV, the phase angle difference (δ) between VS and VR required for maximum possible active power to be delivered to the receiving end, in degrees, is _______. (Round off to 2 decimal places).


(31.44) is the correct answer.

Ques 54 GATE 2023

A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is -400 W and the line current is IR=2 A (rms), then the power factor of the load per phase is _______.

A

Unity

B

0.5 leading

C

0.866 leading

D

0.707 lagging


(c) is the correct answer.

Ques 55 GATE 2023

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is an infinite bus having a voltage of magnitude |V3|=1.0 p.u. and an angle of -15°. A variable current source, |I|∠φ, is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, φ=θ1±π/2, where θ1 is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as _______.

A

Bus 1: Slack bus,
Bus 2: PV bus,
Bus 3: PQ bus

B

Bus 1: PV bus,
Bus 2: PV bus,
Bus 3: Slack bus

C

Bus 1: PQ bus,
Bus 2: Slack bus,
Bus 3: PQ bus

D

Bus 1: PV bus,
Bus 2: PQ bus,
Bus 3: Slack bus


(d) is the correct answer.

Ques 56 GATE 2023

The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ transformer. The positive, negative, and zero-sequence diagrams of the system are shown in figures (ii), (iii), and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases 'b' and 'c' at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase 'b' to 'c') in p.u. is _______. (Round off to 2 decimal places).


(3.09) is the correct answer.

Ques 57 GATE 2023

A balanced delta connected load consisting of the series connection of one resistor (R=15 Ω) and a capacitor (C=212.21 μF) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of L=31.83 mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals VAB in Volts is _______. (Round off to the nearest integer).


(390) is the correct answer.

Ques 58 GATE 2023

A continuous-time system that is initially at rest is described by

where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is _______.

A

3e-2t

B

(1/3)e-2tu(t)

C

2e-3tu(t)

D

2e-3t


(c) is the correct answer.

Ques 59 GATE 2023

The Fourier transform X(ω) of the signal x(t) is given by X(ω)=1, for

Which one of the following statements is true?

A

x(t) tends to be an impulse as W0→∞.

B

x(0) decreases as W0 increases.

C

At t=π/(2W0), x(t)=-1/π.

D

At t=π/(2W0), x(t)=1/π.


(a) is the correct answer.

Ques 60 GATE 2023

The Z-transform of a discrete signal x[n] is

with ROC=R. Which one of the following statements is true?

A

Discrete-time Fourier transform of x[n] converges if R is |z|>3.

B

Discrete-time Fourier transform of x[n] converges if R is 2/3<|z|<3.

C

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a left-sided sequence.

D

Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a right-sided sequence.


(a) is the correct answer.

Ques 61 GATE 2023

Which of the following statement(s) is/are true?

A

If an LTI system is causal, it is stable.

B

A discrete time LTI system is causal if and only if its response to a step input u[n] is 0 for n<0.

C

If a discrete time LTI system has an impulse response h[n] of finite duration, the system is stable.

D

If the impulse response 0<|h[n]|<1 for all n, then the LTI system is stable.


(b) is the correct answer.

Ques 62 GATE 2023

For the signals x(t) and y(t) shown in the figure, z(t)=x(t)y(t) is maximum at t=T1. Then T1 in seconds is _______. (Round off to the nearest integer).


(1) is the correct answer.

Ques 63 GATE 2023

The period of the discrete-time signal x[n] described by the equation

is N=___________. (Round off to the nearest integer).


(48) is the correct answer.

Ques 64 GATE 2023

The discrete-time Fourier transform of a signal x[n] is X(Ω)=(1+cos Ω)e-jΩ. Consider that xp[n] is a periodic signal of period N=5 such that

Note that xp[n]=ΣN-1k=0akej2πkn/N. The magnitude of the Fourier series coefficient a3 is _______. (Round off to 3 decimal places).


(0.363) is the correct answer.

Ques 65 GATE 2023

A signal x(t)=2cos(180πt)cos(60πt) is sampled at 200 Hz and then passed through an ideal low pass filter having a cut-off frequency of 100 Hz. The maximum frequency present in the filtered signal in Hz is _______. (Round off to the nearest integer).


(90) is the correct answer.

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