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General Aptitude(10)Engineering Mathematics(8)Electric Circuits(6)Electromagnetic Fields(4)Signals and Systems(4)Electrical Machines(6)Power Systems(7)Control Systems(5)Electrical and Electronic Measurements(1)Analog and Digital Electronics(7)Power Electronics(7)

General Aptitude

10 Questions

GATE→2022→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

As you grow older, an injury to your ... may take longer to ... Select the correct homophones to fill the blanks.

(A)

heel/heel

(B)

heal/heel

(C)

heal/heal

(D)

heal/heal

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

In a 500 m race, P and Q have speeds in the ratio 3:4. Q starts when P has covered 140 m. What is the distance between P and Q when P wins?

(A)

20

(B)

40

(C)

60

(D)

140

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Bells P, Q, R ring every 20, 30, and 50 minutes. If rung together at 12:00 PM, when will they ring together next?

(A)

5:00 PM

(B)

5:30 PM

(C)

6:00 PM

(D)

6:30 PM

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Given 'Some bottles are cups' and 'All cups are knives', which conclusions (I. Some bottles are knives, II. Some knives are cups, etc.) are valid?

(A)

Only conclusion I and conclusion II are correct

(B)

Only conclusion II and conclusion III are correct

(C)

Only conclusion II and conclusion IV are correct

(D)

Only conclusion III and conclusion IV are correct

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

A disc with identical front/rear patterns is flipped w.r.t. axes 1-1, 2-2, or 3-3. What is the probability that it DOES NOT retain the same views?

(A)

0

(B)

1/3

(C)

2/3

(D)

1

Explanation

GATE→2022→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Based on the passage about altruism (motivated by social bonding/group identification, not empathy or guilt), which inference is correct?

(A)

Humans engage in altruism due to guilt but not empathy

(B)

Humans engage in altruism due to empathy but not guilt

(C)

Humans engage in altruism due to group identification but not empathy

(D)

Humans engage in altruism due to empathy but not familiarity

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Two dice with faces Q, R, S, T, U, V are thrown. What is the probability that both outcomes are chosen only from {Q, U, V}?

(A)

1/4

(B)

3/4

(C)

1/6

(D)

5/36

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Store S is 10% cheaper than M but charges 150 delivery (M is free). Buying from S saves 100. What is the price at store S?

(A)

2500

(B)

2250

(C)

1750

(D)

1500

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Letters P, Q, R, S, T, U are placed on the vertices of a regular hexagon with specific geometric relations. Which option is correct?

(A)

The line segment joining R and T is parallel to the line segment joining Q and S

(B)

The line segment joining T and Q is parallel to the line joining P and U

(C)

The line segment joining R and P is perpendicular to the line segment joining U and Q

(D)

The line segment joining Q and S is perpendicular to the line segment joining R and P

Explanation

GATE→2022→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

An ant at grid corner P moves towards the top-right such that distance strictly decreases. Which figure shows a valid trajectory part?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

Engineering Mathematics

8 Questions

GATE→2022→Engineering Mathematics→Calculus

Q11

MCQ[1 Mark]

For H(s) = (As + B)/(s^2 + Cs + D) with positive constants, which filter type can this system NOT operate as?

(A)

low pass filter.

(B)

high pass filter.

(C)

band pass filter.

(D)

an integrator.

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

Consider a 3x3 matrix A with elements a_{i,j} = (i - j)^3. The matrix A is

(A)

symmetric.

(B)

skew-symmetric.

(C)

unitary.

(D)

null.

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q13

MCQ[2 Marks]

For square matrix A with eigenvalue lambda and eigenvector v, are 'e^lambda is eigenvalue of e^A' and 'v is eigenvector of e^A' correct?

(A)

Statement 1 is true and statement 2 is false.

(B)

Statement 1 is false and statement 2 is true.

(C)

Both the statements are correct.

(D)

Both the statements are false.

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q14

MCQ[2 Marks]

For f(x) = integral from 0 to x of e^t (t-1)(t-2) dt, in which interval does f(x) decrease?

(A)

x in (1, 2)

(B)

x in (2, 3)

(C)

x in (0, 1)

(D)

x in (0.5, 1)

Explanation

GATE→2022→Engineering Mathematics→Linear Algebra

Q15

MCQ[2 Marks]

For matrix A = [1 0 0; 0 4 -2; 0 1 1], if 6A^{-1} = A^2 + cA + dI, find (c + d).

(A)

5

(B)

17

(C)

-6

(D)

11

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

Find the direction in which f(x,y,z) = 4x^2 + 7xy + 3xz^2 increases most rapidly at point P(1, 0, 2).

(A)

20i + 7j

(B)

20i + 7j + 12k

(C)

20i + 12k

(D)

20i

Explanation

GATE→2022→Engineering Mathematics→Calculus

Q17

MCQ[2 Marks]

Let R be a region enclosed by closed curve C counter-clockwise. Which expression does NOT represent the area of R?

(A)

double_integral_R dxdy

(B)

oint_C x dy

(C)

oint_C y dx

(D)

0.5 * oint_C (x dy - y dx)

Explanation

GATE→2022→Engineering Mathematics→Probability and Statistics

Q18

NAT[2 Marks]

If the probability density function of random variable x is f(x) = a * e^{-2|x|}, find the value of a.

Explanation

Electric Circuits

6 Questions

GATE→2022→Electric Circuits→Network Elements & Solution Methods

Q19

MCQ[1 Mark]

For a 3-phase unbalanced load with Z_A = 10 Ω and Z_B = 20∠60° Ω, find Z_C such that neutral voltage V_{nn'} = 0.

(A)

20∠-30°

(B)

20∠30°

(C)

20∠-60°

(D)

20∠60°

Explanation

GATE→2022→Electric Circuits→Network Theorems & AC/DC Transients

Q20

NAT[1 Mark]

An inductor with Q = 60 is in series with a capacitor with Q = 240. What is the overall Q-factor of the circuit?

Explanation

GATE→2022→Electric Circuits→Network Theorems & AC/DC Transients

Q21

NAT[1 Mark]

A parallel/series resonant network has f_r = 150 kHz and bandwidth BW = 600 Hz. Find its Q-factor.

Explanation

GATE→2022→Electric Circuits→Network Theorems & AC/DC Transients

Q22

NAT[1 Mark]

In the circuit with switch S closed at t = 0, find the magnitude of the steady-state voltage across the 6 Ω resistor in volts.

Explanation

GATE→2022→Electric Circuits→Network Elements & Solution Methods

Q23

NAT[1 Mark]

For two balanced 3-phase loads connected to 100*sqrt(3) V supply with Z1 and Z2, find the ammeter reading in amperes.

Explanation

GATE→2022→Electric Circuits→Network Elements & Solution Methods

Q24

NAT[2 Marks]

For the circuit with 75 V source, 2 kΩ resistor, 0.5 V_1 dependent source, and 8 kΩ resistor, find the magnitude of voltage V_1 in volts.

Explanation

Electromagnetic Fields

4 Questions

GATE→2022→Electromagnetic Fields→Electrostatics & Magnetostatics

Q25

MCQ[1 Mark]

For a long cylinder with current density J = J_a r^3 a_z for r < b, find magnetic field intensity H inside the conductor (r < b).

(A)

(J_a / 4) r^4

(B)

(J_a / 3) r^3

(C)

(J_a / 5) r^4

(D)

J_a r^3

Explanation

GATE→2022→Electromagnetic Fields→Electrostatics & Magnetostatics

Q26

MCQ[2 Marks]

Given H = x^2 i + x^2 y^2 j + x^2 y^2 z^2 k A/m, find the magnitude of current density J at (1, 2, 1) in A/m^2.

(A)

8

(B)

12

(C)

16

(D)

20

Explanation

GATE→2022→Electromagnetic Fields→Electrostatics & Magnetostatics

Q27

MCQ[2 Marks]

Evaluate the volume integral of div(E) dV over the unit cube for E = 2x^2 i + 5y j + 3z k.

(A)

3

(B)

8

(C)

10

(D)

5

Explanation

GATE→2022→Electromagnetic Fields→Electrostatics & Magnetostatics

Q28

MCQ[2 Marks]

Two concentric spherical shells at radii r = c and r = d have potentials V_1 and V_2. What is the potential V(r) in the region c < r < d?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

Signals and Systems

4 Questions

GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms

Q29

MCQ[2 Marks]

For a causal LTI system governed by y(t) + 0.25 (dy/dt) = 2 x(t), find its impulse response h(t).

(A)

2 e^{-0.25t} u(t)

(B)

2 e^{-4t} u(t)

(C)

8 e^{-0.25t} u(t)

(D)

8 e^{-4t} u(t)

Explanation

GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms

Q30

MCQ[2 Marks]

An input x(t) is passed through an LTI bandpass filter with impulse response h(t). What is the system output?

(A)

2 sin(10πt) + 5 cos(15πt)

(B)

5 cos(15πt) + 7 sin(42πt)

(C)

7 sin(42πt) + 4 cos(45πt)

(D)

2 sin(10πt) + 4 cos(45πt)

Explanation

GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms

Q31

MCQ[2 Marks]

For the continuous-time system defined by y(t) = x(e^t), the system is

(A)

linear and causal.

(B)

linear and non-causal.

(C)

non-linear and causal.

(D)

non-linear and non-causal.

Explanation

GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms

Q32

MCQ[2 Marks]

A periodic signal x[n] with period N=3 has non-zero Fourier coefficients a_{-3} = 2 and a_4 = 1. Which option represents the signal?

(A)

2 + 2*e^{-j(2*pi/6)n} cos((2*pi/6)n)

(B)

1 + 2*e^{j(2*pi/6)n} cos((2*pi/6)n)

(C)

1 + 2*e^{j(2*pi/3)n} cos((2*pi/6)n)

(D)

2 + 2*e^{j(2*pi/6)n} cos((2*pi/6)n)

Explanation

Electrical Machines

6 Questions

GATE→2022→Electrical Machines→DC & AC Machines

Q33

MCQ[1 Mark]

Which single-phase induction motor type has the highest power factor during steady-state running conditions?

(A)

split phase (resistance start).

(B)

shaded pole.

(C)

capacitor start.

(D)

capacitor start, capacitor run.

Explanation

GATE→2022→Electrical Machines→DC & AC Machines

Q34

NAT[1 Mark]

A 3-phase 8-pole induction motor has stator frequency 40 Hz and rotor frequency 1 Hz. Find motor speed in rpm.

Explanation

GATE→2022→Electrical Machines→DC & AC Machines

Q35

NAT[2 Marks]

A separately excited DC motor with R_a = 1 Ω draws 30 A at 1000 RPM (V = 280 V) driving a torque proportional to speed load. Find the speed in RPM if an extra 10 Ω is added in series with armature.

Explanation

GATE→2022→Electrical Machines→DC & AC Machines

Q36

NAT[2 Marks]

A 4-pole induction motor with J = 0.1 kg-m^2 drives a constant load torque T_L = 2 Nm. Speed increases linearly from 1000 to 1500 RPM in 4 s. Find energy consumed in Joules.

Explanation

GATE→2022→Electrical Machines→DC & AC Machines

Q37

NAT[2 Marks]

A star-connected synchronous motor (400 V, 50 kVA, X_s = 1 Ω) has shaft load 10 kW, 2 kW losses, 0.8 leading p.f. Find per-phase excitation emf E_f in volts.

Explanation

GATE→2022→Electrical Machines→DC & AC Machines

Q38

NAT[2 Marks]

An induction motor draws 5x starting current. To reduce starting current to 2x using a 3-phase autotransformer, find the transformation ratio x (or tapping percentage).

Explanation

Power Systems

7 Questions

GATE→2022→Power Systems→Fault Analysis, Protection & Stability

Q39

MCQ[1 Mark]

Which relay is most commonly used to protect an alternator against loss of excitation?

(A)

offset Mho relay.

(B)

over current relay.

(C)

differential relay.

(D)

Buchholz relay.

Explanation

GATE→2022→Power Systems→Generation, Transmission & Load Flow

Q40

MCQ[1 Mark]

Find the geometric mean radius (GMR) of a conductor having four equal strands of radius r arranged in a square bundle.

(A)

4r

(B)

1.414 r

(C)

2r

(D)

1.723 r

Explanation

GATE→2022→Power Systems→Fault Analysis, Protection & Stability

Q41

MCQ[1 Mark]

What are typical valid positive, negative, and zero sequence impedances (in p.u.) for a 220 kV fully transposed 3-phase transmission line?

(A)

1.1, 0.15 and 0.08

(B)

0.15, 0.15 and 0.35

(C)

0.2, 0.2 and 0.2

(D)

0.1, 0.3 and 0.1

Explanation

GATE→2022→Power Systems→Generation, Transmission & Load Flow

Q42

NAT[1 Mark]

If 5% of the supplied power reaches the output of a cable, what is the power loss in decibels?

Explanation

GATE→2022→Power Systems→Generation, Transmission & Load Flow

Q43

MCQ[2 Marks]

For two thermal power plants with given cost functions and incremental cost lambda = 8 Rs/MWh meeting 550 MW demand, find optimal P1 and P2.

(A)

200, 350

(B)

250, 300

(C)

325, 225

(D)

350, 200

Explanation

GATE→2022→Power Systems→Generation, Transmission & Load Flow

Q44

NAT[2 Marks]

Two generating units (250 MW, R=6% and 400 MW, R=6.4%) share a 500 MW load in parallel. Find the load shared by the 250 MW unit in MW.

Explanation

GATE→2022→Power Systems→Fault Analysis, Protection & Stability

Q45

NAT[2 Marks]

A 20 MVA, 50 Hz alternator has H = 15 MJ/MVA, P_m = 15 MW, P_e = 10 MW. Find angular acceleration in mechanical degrees/s^2.

Explanation

Control Systems

5 Questions

GATE→2022→Control Systems→Mathematical Modeling & LTI System Analysis

Q46

MCQ[1 Mark]

A first-order stable system has flat Bode magnitude and high-frequency phase of -180°. What are its pole-zero features?

(A)

one LHP pole and one RHP zero at the same frequency.

(B)

one LHP pole and one LHP zero at the same frequency.

(C)

two LHP poles and one RHP zero.

(D)

two RHP poles and one LHP zero.

Explanation

GATE→2022→Control Systems→Stability Criteria, Compensators & Controllers

Q47

MCQ[1 Mark]

For G(s) = k / (s^2 + 4s - 5) in a unity feedback system, find the range of k for closed-loop stability.

(A)

k > 3

(B)

k < 3

(C)

k > 5

(D)

k < 5

Explanation

GATE→2022→Control Systems→Mathematical Modeling & LTI System Analysis

Q48

MCQ[2 Marks]

For G(s) = 100/(s^2 + 0.1s + 10) and input r(t) = 1 + 0.1 sin(10t), find steady-state output parameters a and b.

(A)

a = 1, b = 10

(B)

a = 10, b = 1

(C)

a = 1, b = 100

(D)

a = 100, b = 1

Explanation

GATE→2022→Control Systems→Stability Criteria, Compensators & Controllers

Q49

MCQ[2 Marks]

For G(s) = 1/(s(s+1)) with the Nyquist contour indenting around the origin, find the number of encirclements N of (-1+j0).

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2022→Control Systems→Mathematical Modeling & LTI System Analysis

Q50

MCQ[2 Marks]

Find damping ratio zeta and natural frequency omega_n for the closed-loop system shown in the block diagram.

(A)

zeta = 0.5 and omega_n = 10 rad/s

(B)

zeta = 0.1 and omega_n = 10 rad/s

(C)

zeta = 0.707 and omega_n = 10 rad/s

(D)

zeta = 0.707 and omega_n = 100 rad/s

Explanation

Electrical and Electronic Measurements

1 Question

GATE→2022→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q51

MCQ[1 Mark]

For a balanced Wheatstone bridge with given arm resistances and tolerances, find R_CD and its accuracy.

(A)

30 Ω ± 3 Ω

(B)

30 Ω ± 0.9 Ω

(C)

3000 Ω ± 90 Ω

(D)

3000 Ω ± 3 Ω

Explanation

Analog and Digital Electronics

7 Questions

GATE→2022→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q52

MCQ[1 Mark]

For an ideal MOSFET biased in saturation, what is the magnitude of the small-signal current gain for a common-drain amplifier?

(A)

0

(B)

1

(C)

100

(D)

infinite

Explanation

GATE→2022→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q53

MCQ[1 Mark]

For the op-amp circuit with capacitor in feedback and 0.1 V DC input, what is the steady-state output V_out?

(A)

saturate to +V_DD

(B)

saturate to -V_EE

(C)

become equal to 0.1 V

(D)

become equal to -0.1 V

Explanation

GATE→2022→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q54

MCQ[1 Mark]

For the diode bridge/clipper circuit shown with ideal diodes D1 and D2, what is the output V_out?

(A)

V_out = V_in for V_in > 0

(B)

V_out = V_in for V_in < 0

(C)

V_out = -V_in for V_in > 0

(D)

V_out = -V_in for V_in < 0

Explanation

GATE→2022→Analog and Digital Electronics→Digital Logic & Converters

Q55

NAT[1 Mark]

Cascading a MOD 2 up-counter and a MOD 5 up-counter results in a MOD ... counter.

Explanation

GATE→2022→Analog and Digital Electronics→Digital Logic & Converters

Q56

NAT[1 Mark]

Find the maximum clock frequency in MHz for a 4-stage ripple counter where each flip-flop has a propagation delay of 20 ns.

Explanation

GATE→2022→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q57

MCQ[2 Marks]

How does the output impedance Z_out of a non-ideal op-amp configured as a voltage follower vary with increasing frequency f?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2022→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q58

MCQ[2 Marks]

Find the current gain I_out / I_in for the given switched-capacitor or op-amp current amplifier circuit with capacitors C_f and C_c.

(A)

C_f / C_c

(B)

-C_f / C_c

(C)

C_c / C_f

(D)

-C_c / C_f

Explanation

Power Electronics

7 Questions

GATE→2022→Power Electronics→Power Semiconductor Devices & Converters

Q59

MCQ[1 Mark]

A low-voltage high-frequency laptop charger (100 W, 20 V, 200 kHz) is best implemented using which power semiconductor device?

(A)

IGBT

(B)

Thyristor

(C)

MOSFET

(D)

BJT

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q60

NAT[1 Mark]

A single-phase full-bridge diode rectifier feeds R = 50 Ω from a 200 V, 50 Hz AC supply. Find active power drawn by load in watts.

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q61

NAT[1 Mark]

Given rectifier input voltage and current harmonic expressions, find the input power factor lagging.

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q62

NAT[2 Marks]

An ideal full-bridge single-phase inverter with 1000 V DC bus feeds load current i(t) = 10 sin(wt - pi/3) A with square-wave voltage (50% duty cycle). Find active power in watts.

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q63

NAT[2 Marks]

For the ideal single-phase bridge rectifier with I_dc = 15 A and firing angle alpha = 45°, find the amplitude of the fundamental source current component in amperes.

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q64

NAT[2 Marks]

A 3-phase grid-connected VSC with V_dc = 1000 V supplies S = -4000 - j3000 VA with phase current 10 A. Find the SPWM modulation index.

Explanation

GATE→2022→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q65

NAT[2 Marks]

For a DC-DC buck-boost converter with inductor current waveform (min 12 A, max 16 A over t_on = 20 us, t_off = 30 us) and output voltage ripple 1 V, find the output capacitance in µF.

Explanation