Back to Years

Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Electric Circuits(5)Electromagnetic Fields(1)Signals and Systems(8)Electrical Machines(7)Power Systems(7)Control Systems(6)Electrical and Electronic Measurements(1)Analog and Digital Electronics(5)Power Electronics(5)

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Rafi told Mary, "I am thinking of watching a film this weekend." Report this statement in indirect speech: Rafi told Mary that he ... of watching a film that weekend.

(A)

thought

(B)

is thinking

(C)

am thinking

(D)

was thinking

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Complete the analogy based on word meanings: Permit : ... :: Enforce : Relax

(A)

Allow

(B)

Forbid

(C)

License

(D)

Reinforce

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

What is the probability of rolling a '1' on the first roll and a '4' on the second roll of a fair six-sided die?

(A)

1/36

(B)

1/6

(C)

5/6

(D)

1/3

Explanation

GATE→2023→General Aptitude→Data Interpretation

Q4

MCQ[1 Mark]

Based on the survey showing 65% advised to stop and 3 out of 10 attempting to stop, which statement can be logically inferred?

(A)

A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B)

A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(C)

Approximately 30% of tobacco users successfully stopped consuming tobacco.

(D)

Approximately 65% of tobacco users successfully stopped consuming tobacco.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

How many triangles are present in the given figure?

(A)

12

(B)

16

(C)

20

(D)

24

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q6

MCQ[2 Marks]

Based on registration rules and the fact that none from Human Sciences registered, which statements can be logically inferred?

(A)

(i) and (ii)

(B)

(i) and (iii)

(C)

only (i)

(D)

only (iii)

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Which of the following options represents the given graph?

(A)

f(x) = x^2 2^{-|x|}

(B)

f(x) = x 2^{-|x|}

(C)

f(x) = |x| 2^{-x}

(D)

f(x) = x 2^{-x}

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q8

MCQ[2 Marks]

Which option does NOT describe or follow from the passage about cancer and cellular machinery metaphors?

(A)

It is a reflection of why cancer seems so modern to most of us.

(B)

It tells us that modern cell biology uses and promotes metaphors of machinery.

(C)

Modern cell biology encourages metaphors of machinery, and cancer is often imagined as a machine.

(D)

Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

What is the unit's place digit of the product 3^{999} * 7^{1000}?

(A)

7

(B)

1

(C)

3

(D)

9

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

A square of side 6 cm has two semicircles on its sides as boundaries. Find the area of the shaded region.

(A)

9*pi

(B)

18

(C)

20

(D)

9*pi (or other values)

Explanation

Engineering Mathematics

9 Questions

GATE→2023→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

For vector w = [1 2 3]^T, find a vector normal to the plane defined by w^T X = 1.

(A)

[-2 -2 2]^T

(B)

[3 0 -1]^T

(C)

[3 2 1]^T

(D)

[1 2 3]^T

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

Find the 2D rotation/transformation matrix A that relates vector u to vector v (Au = v).

(A)

[4/5 3/5; -3/5 4/5]

(B)

[3/5 4/5; -4/5 3/5]

(C)

[4/5 -3/5; 3/5 4/5]

(D)

[3/5 -4/5; 4/5 3/5]

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q13

MCQ[1 Mark]

For sample variance estimators hat{sigma}_1^2 (divided by N) and hat{sigma}_2^2 (divided by N-1), which statement is true?

(A)

E(hat{sigma}_2^2) = sigma_0^2

(B)

E(hat{sigma}_2) = sigma_0

(C)

E(hat{sigma}_1^2) = sigma_0^2

(D)

E(hat{sigma}_1) = E(hat{sigma}_2)

Explanation

GATE→2023→Engineering Mathematics→Differential Equations

Q14

NAT[1 Mark]

Solve dy/dt = e^{-alpha t} / (2 + alpha t) with alpha = 0.01 and y(0) = 0 at t = 1.

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

Find the slope of the best-fit straight line in the least squares sense for points (-1, 0.8), (0, 2.2), and (1, 2.8).

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q16

MSQ[2 Marks]

For the curve |x_1|^p + |x_2|^p = 1 in 2-D space for p > 0, which statements are true?

(A)

When p = 2 the area enclosed by the curve is pi.

(B)

When p tends to infinity, the area enclosed by the curve tends to 4.

(C)

When p tends to 0, the area enclosed by the curve is 1.

(D)

When p = 1, the area enclosed by the curve is 2.

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q17

NAT[2 Marks]

For a biased coin where the expected number of trials for the first head is 4, find the probability that the first head occurs on the second trial.

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q18

NAT[2 Marks]

Find the magnitude of the line integral of F = -y i + x j around the cardioid r = 1 + cos(theta).

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q19

NAT[2 Marks]

Find the magnitude of the maximum rate of change of f(x_1, x_2) = x_1^2 + 2x_2^2 + 3x_1 + 3x_2 + x_1 x_2 + 1 at the point (1,1).

Explanation

Electric Circuits

5 Questions

GATE→2023→Electric Circuits→Network Theorems & AC/DC Transients

Q20

NAT[1 Mark]

For the RLC circuit with switch K opened at t = 0, find the voltage across the inductor V_L at t = 0+ in volts.

Explanation

GATE→2023→Electric Circuits→Network Elements & Solution Methods

Q21

NAT[1 Mark]

For the circuit with V_1 = 8 V and I_1 = 8 A, find the voltage V_ab in volts.

Explanation

GATE→2023→Electric Circuits→Network Elements & Solution Methods

Q22

NAT[2 Marks]

For the given circuit with i = sin(1000t), find the instantaneous Thevenin equivalent voltage across terminals a-b at t = 5 ms in volts.

Explanation

GATE→2023→Electric Circuits→Network Elements & Solution Methods

Q23

NAT[2 Marks]

Given y-parameters of a two-port network connected to 20 V source with 3 ohm series resistance at port 1 and R_L = 6 ohm at port 2, find power delivered to R_L in watts.

Explanation

GATE→2023→Electric Circuits→Network Theorems & AC/DC Transients

Q24

NAT[2 Marks]

Find the minimum switching time t_1 in milliseconds such that no transient occurs in the 100 uF capacitor voltage upon switching.

Explanation

Electromagnetic Fields

1 Question

GATE→2023→Electromagnetic Fields→Electrostatics & Magnetostatics

Q25

NAT[2 Marks]

Find the magnitude of magnetic field intensity H at point (1,1,1) due to infinite sheet current K = 5 a_x A/m on the x-y plane.

Explanation

Signals and Systems

8 Questions

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q26

MCQ[1 Mark]

Find the impulse response of the LTI system described by dy/dt + 3y(t) = 2x(t) starting from rest.

(A)

3 e^{-2t}

(B)

(1/3) e^{-2t} u(t)

(C)

2 e^{-3t} u(t)

(D)

2 e^{-3t}

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q27

MCQ[1 Mark]

For X(omega) = rect(omega / 2W_0), which statement is true about x(t)?

(A)

x(t) tends to be an impulse as W_0 -> infinity.

(B)

x(0) decreases as W_0 increases.

(C)

At t = pi / (2W_0), x(t) = -1 / pi

(D)

At t = pi / (2W_0), x(t) = 1 / pi

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q28

MCQ[1 Mark]

For X(z) = 4z / ((z - 1/5)(z - 2/3)(z - 3)), which statement regarding ROC and DTFT convergence 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

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q29

MSQ[1 Mark]

Which of the following statements regarding discrete-time LTI systems 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.

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q30

NAT[1 Mark]

For the given signals x(t) and y(t), their convolution z(t) = x(t) * y(t) is maximum at t = T_1. Find T_1 in seconds.

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q31

NAT[2 Marks]

Find the fundamental period N of the discrete-time signal x[n] = 1 + 3 sin(15*pi*n/8 + 3*pi/4) - 5 sin(pi*n/3 - pi/4).

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q32

NAT[2 Marks]

For the periodic signal x_p[n] of period N=5 formed from x[n] with DTFT X(Omega) = (1 + cos Omega)e^{-j Omega}, find the magnitude of Fourier series coefficient |a_3|.

Explanation

GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms

Q33

NAT[2 Marks]

A signal x(t) = 2 cos(180 pi t) cos(60 pi t) is sampled at 200 Hz and filtered by a 100 Hz low-pass filter. Find the maximum frequency in Hz in the filtered signal.

Explanation

Electrical Machines

7 Questions

GATE→2023→Electrical Machines→DC & AC Machines

Q34

MCQ[1 Mark]

Match the induction machine modes of operation (a. Generator, b. Motor, c. Plugging) with their slip ranges (p: 0 to 1, q: 1 to 2, r: -1 to 0).

(A)

a-r, b-p, c-q

(B)

a-r, b-q, c-p

(C)

a-p, b-r, c-q

(D)

a-q, b-p, c-r

Explanation

GATE→2023→Electrical Machines→DC & AC Machines

Q35

MCQ[1 Mark]

A 10-pole, 50 Hz single-phase induction motor runs at 540 RPM. Find the frequency of induced rotor currents due to the backward rotating field.

(A)

100 Hz

(B)

95 Hz

(C)

10 Hz

(D)

5 Hz

Explanation

GATE→2023→Electrical Machines→Transformers & Energy Conversion

Q36

MCQ[1 Mark]

For the rotating machine with stator DC conductors and rotor coils, rotating at omega rad/s, what can be said about induced EMFs E_{a-a'} and E_{b-b'}?

(A)

E_{a-a'} and E_{b-b'} have finite magnitudes and are in the same phase

(B)

E_{a-a'} and E_{b-b'} have finite magnitudes with E_{b-b'} leading E_{a-a'}

(C)

E_{a-a'} and E_{b-b'} have finite magnitudes with E_{a-a'} leading E_{b-b'}

(D)

E_{a-a'} = E_{b-b'} = 0

Explanation

GATE→2023→Electrical Machines→DC & AC Machines

Q37

NAT[1 Mark]

A separately excited DC motor drives constant torque load at 1500 RPM (400 V, 15 A, R_a = 1.2 ohm). If supply voltage drops by 10%, find the new speed in RPM.

Explanation

GATE→2023→Electrical Machines→DC & AC Machines

Q38

NAT[2 Marks]

A 3-phase synchronous motor with Z_s = 0.1 + j0.3 pu has a static stability limit of 2.5 pu. Find the corresponding excitation voltage E_f in pu.

Explanation

GATE→2023→Electrical Machines→DC & AC Machines

Q39

NAT[2 Marks]

A 3-phase induction motor running at 960 RPM has its supply voltage and frequency reduced by 20%. Find the new speed in RPM.

Explanation

GATE→2023→Electrical Machines→Transformers & Energy Conversion

Q40

NAT[2 Marks]

For the single-phase transformer with given core dimensions, B_max, and permeability, find the self-inductance of winding a-b in millihenry.

Explanation

Power Systems

7 Questions

GATE→2023→Power Systems→Fault Analysis, Protection & Stability

Q41

MCQ[1 Mark]

For the 3-bus power system protection scheme, what is the necessary condition regarding directional overcurrent relays?

(A)

R_3 and R_4 are directional overcurrent relays blocking faults towards bus 2

(B)

R_3 and R_4 are directional overcurrent relays blocking faults towards bus 2 and R_7 is directional overcurrent relay blocking faults towards bus 3

(C)

R_3 and R_4 are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively...

(D)

R_3 and R_4 are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively.

Explanation

GATE→2023→Power Systems→Generation, Transmission & Load Flow

Q42

MCQ[1 Mark]

When parameter 'a' in the fuel cost function of unit 1 increases by 10% under economic dispatch, what happens to P_G1 and total cost F?

(A)

P_G1 will decrease and F will increase

(B)

Both P_G1 and F will increase

(C)

P_G1 will increase and F will decrease

(D)

Both P_G1 and F will decrease

Explanation

GATE→2023→Power Systems→Generation, Transmission & Load Flow

Q43

MSQ[1 Mark]

Given the Y_bus matrix of a 3-bus power system with no shunt reactors, which statements can NOT be true regarding line charging and shunt capacitors?

(A)

Line charging capacitor of finite value is present in all three lines

(B)

Line charging capacitor of finite value is present in line 2-3 only

(C)

Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 1 only

(D)

Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 3 only

Explanation

GATE→2023→Power Systems→Generation, Transmission & Load Flow

Q44

NAT[1 Mark]

For a 400 km, 275 kV transmission line represented by nominal-pi model, find the phase angle difference delta for maximum active power delivery in degrees.

Explanation

GATE→2023→Power Systems→Generation, Transmission & Load Flow

Q45

MCQ[2 Marks]

For the 3-bus power system with specified generation, infinite bus, and controlled current source, categorize buses 1, 2, and 3 for load flow analysis.

(A)

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

(B)

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

(C)

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

(D)

Bus 1: PV bus, Bus 2: P-Q bus, Bus 3: Slack bus

Explanation

GATE→2023→Power Systems→Fault Analysis, Protection & Stability

Q46

NAT[2 Marks]

For a bolted line-to-line fault between phases b and c at bus 1 in the 2-bus power system, find the magnitude of the fault current in p.u.

Explanation

GATE→2023→Power Systems→Generation, Transmission & Load Flow

Q47

NAT[2 Marks]

For a balanced delta load supplied through line inductance L = 31.83 mH per phase from a 415 V source, find the magnitude of terminal voltage V_AB in volts.

Explanation

Control Systems

6 Questions

GATE→2023→Control Systems→Mathematical Modeling & LTI System Analysis

Q48

MCQ[1 Mark]

For the given block diagram, find the closed-loop transfer function Y(s)/R(s).

(A)

(s + 1) / (3s + 2)

(B)

(3s + 2) / (s - 1)

(C)

(s + 1) / (3s + 2)

(D)

(3s + 2) / (s + 1)

Explanation

GATE→2023→Control Systems→Stability Criteria, Compensators & Controllers

Q49

MCQ[1 Mark]

For G(s)H(s) = (3s+5)/(s-1), where does the infinite semi-circular arc of the Nyquist contour map in the G(s)H(s) plane?

(A)

G(s)H(s) = infinity

(B)

G(s)H(s) = 0

(C)

G(s)H(s) = 3

(D)

G(s)H(s) = -5

Explanation

GATE→2023→Control Systems→Mathematical Modeling & LTI System Analysis

Q50

MCQ[1 Mark]

For a unity-gain feedback system with G(s) = 1/(s-1) and PI controller (Kp=3, Ki=1), find final values of controller output and plant output for unit step input.

(A)

(8, 0)

(B)

(1, 0)

(C)

(1, -1)

(D)

(-1, 1)

Explanation

GATE→2023→Control Systems→Mathematical Modeling & LTI System Analysis

Q51

MCQ[2 Marks]

From the given magnitude and phase plots of an LTI system, identify its transfer function.

(A)

2.51 e^{-0.032s} / (s + 1)

(B)

e^{-2.514s} / (s + 1)

(C)

1.04 e^{-2.514s} / (s + 1)

(D)

2.51 e^{-1.047s} / (s + 1)

Explanation

GATE→2023→Control Systems→Stability Criteria, Compensators & Controllers

Q52

MCQ[2 Marks]

A lead compensator produces maximum phase lead at omega_m = 4 rad/s with a gain of 6 dB at that frequency. Find parameters a and beta.

(A)

(1, 16)

(B)

(2, 4)

(C)

(3, 5)

(D)

(2.66, 2.25)

Explanation

GATE→2023→Control Systems→Mathematical Modeling & LTI System Analysis

Q53

NAT[2 Marks]

For the given state-space system, find the input frequency omega > 0 for which the steady-state sinusoidal output is zero.

Explanation

Electrical and Electronic Measurements

1 Question

GATE→2023→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q54

MCQ[2 Marks]

A 3-phase star-connected balanced load has line current 2 A from 400 V source. A wattmeter reads -400 W. Find the per-phase load power factor.

(A)

Unity

(B)

0.5 leading

(C)

0.866 leading

(D)

0.707 lagging

Explanation

Analog and Digital Electronics

5 Questions

GATE→2023→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q55

MCQ[2 Marks]

For the op-amp clipper/limiter circuit with 5 V Zener and V_in = 10 sin(1000t) V, find the maximum and minimum values of output voltage V_0.

(A)

The maximum and minimum values of the output voltage V_o are +15 V and -10 V, respectively.

(B)

The maximum and minimum values of the output voltage V_o are +5 V and -15 V, respectively.

(C)

The maximum and minimum values of the output voltage V_o are +10 V and -5 V, respectively.

(D)

The maximum and minimum values of the output voltage V_o are +5 V and -10 V, respectively.

Explanation

GATE→2023→Analog and Digital Electronics→Digital Logic & Converters

Q56

MCQ[2 Marks]

An 8-bit ADC has range 0 to +5 V. For V_in = 1.9922 V, find the corresponding digital output in hexadecimal.

(A)

64H

(B)

65H

(C)

66H

(D)

67H

Explanation

GATE→2023→Analog and Digital Electronics→Digital Logic & Converters

Q57

NAT[2 Marks]

Find the decimal equivalent of the initial binary state [ABCD] that remains unchanged upon clock pulses in the given sequential logic circuit.

Explanation

GATE→2023→Analog and Digital Electronics→Digital Logic & Converters

Q58

NAT[2 Marks]

For microcontroller registers R0 = 0x60 and R1 = 0x46, execute ADD R0, R1 and find the decimal equivalent of flag pattern [CAOP].

Explanation

GATE→2023→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q59

NAT[2 Marks]

For the transistor-Zener regulator circuit with beta = 99 and 5 V Zener, find the current through the 20 ohm resistance in milliamperes.

Explanation

Power Electronics

5 Questions

GATE→2023→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q60

MCQ[1 Mark]

A chopper feeds a 5 A DC constant current source with f_s = 100 kHz and given gate duty cycles. Find the average voltage across the 5 A source.

(A)

10 V

(B)

6 V

(C)

12 V

(D)

20 V

Explanation

GATE→2023→Power Electronics→Power Semiconductor Devices & Converters

Q61

MSQ[1 Mark]

Which semiconductor switch combinations can block unidirectional voltage (V > 0) and carry bidirectional current?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2023→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q62

MSQ[2 Marks]

For the given circuit with diodes and current/voltage sources, which statements regarding switch S states are true?

(A)

When switch S is ON, both D1 and D2 conduct and D3 is reverse biased

(B)

When switch S is ON, D1 conducts and both D2 and D3 are reverse biased

(C)

When switch S is OFF, D1 is reverse biased and both D2 and D3 conduct

(D)

When switch S is OFF, D1 conducts, D2 is reverse biased and D3 conducts

Explanation

GATE→2023→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q63

NAT[2 Marks]

A thyristor is turned ON in the RLC resonant circuit with V = 100 V, C = 1 uF, L = 4 uH, R = 4 ohm. Find the conduction duration in microseconds before turn-off.

Explanation

GATE→2023→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q64

NAT[2 Marks]

For the single-phase thyristor-diode rectifier feeding 10 A load with given firing angles and input V_in = 100 sin(100 pi t) V, find average load voltage V_0.

Explanation