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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Electric Circuits(3)Electromagnetic Fields(4)Signals and Systems(6)Electrical Machines(5)Power Systems(6)Control Systems(6)Electrical and Electronic Measurements(4)Analog and Digital Electronics(6)Power Electronics(6)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Kavya didn't go to work yesterday as she ... feeling well. Select the most appropriate option to complete the sentence.

(A)

didn't; isn't

(B)

wouldn't; wasn't

(C)

wasn't; wasn't

(D)

couldn't; wasn't

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Good : Evil :: Genuine : ... Select the most appropriate option to complete the analogy.

(A)

Counterfeit

(B)

Contraband

(C)

Counterfoil

(D)

Counterpart

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The relationship between variables x and y is given by x + py + q = 0 and shown in the representative figure. Find p and q.

(A)

p = -1/2, q = 2

(B)

p = 2, q = -2

(C)

p = 1/2, q = 4

(D)

p = 2, q = 4

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Match the items in Column-I (such as Animals, Zebra, Giraffe) with the appropriate Venn diagram representations in Column-II.

(A)

(1)-(Q); (2)-(R); (3)-(S); (4)-(P)

(B)

(1)-(Q); (2)-(P); (3)-(S); (4)-(R)

(C)

(1)-(S); (2)-(P); (3)-(R); (4)-(Q)

(D)

(1)-(R); (2)-(S); (3)-(Q); (4)-(P)

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

What is the value of ((3^81) / (27^4))^(1/3)?

(A)

3^13

(B)

3^96

(C)

3^23

(D)

3^69

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Identify the correct sentence sequence to form a coherent paragraph about tigers and deer hunting.

(A)

S -> P -> R -> Q

(B)

R -> P -> S -> Q

(C)

Q -> S -> R -> P

(D)

P -> Q -> S -> R

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

In the given circular coded figure where EF = 30 and HJ = 80, find the appropriate values for entries (i) and (ii).

(A)

(i) EH; (ii) 40

(B)

(i) JK; (ii) 36

(C)

(i) EG; (ii) 42

(D)

(i) PS; (ii) 14

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

Based on the course scores of students P and Q given in the table, which statement is INCORRECT?

(A)

Average score of P is less than the average score of Q.

(B)

Median score of P is same as the median score of Q.

(C)

Difference between the maximum and minimum scores of P is greater than that of Q.

(D)

Median score and the average score of Q are same.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

For unit diameter spheres at integer coordinates (l, m, n), let x be distance to nearest sphere and y to next nearest. Find y/x.

(A)

2*sqrt(2)

(B)

1/sqrt(2)

(C)

sqrt(2)

(D)

2

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

In triangle PQR with PT:TR = 3:2 and ST parallel to QR, semicircles on PS and PQ form shaded area PQS. Which statement is true?

(A)

16/9 times the area of the semicircle with the diameter PS.

(B)

The shaded area is equal to the area of the semicircle with the diameter PS.

(C)

14/9 times the area of the semicircle with the diameter PS.

(D)

14/25 times the area of the semicircle with the diameter PQ.

Explanation

Engineering Mathematics

9 Questions

GATE→2025→Engineering Mathematics→Calculus

Q11

MCQ[1 Mark]

Consider points in R^2 minimizing f(x, y) = (x + y - 1)^2 + (x + y)^2. What is true about set S?

(A)

The number of elements in the set S is finite and more than one.

(B)

The number of elements in the set S is infinite.

(C)

The set S is empty.

(D)

The number of elements in the set S is exactly one.

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

Let v_1 and v_2 be eigenvectors corresponding to distinct eigenvalues of a 3x3 real symmetric matrix. Which statement is true?

(A)

v_1^T v_2 != 0

(B)

v_1^T v_2 = 0

(C)

v_1 + v_2 = 0

(D)

v_1 - v_2 = 0

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q13

MCQ[1 Mark]

Given matrix A and vector b, determine whether the system Ax = b has a unique, infinite, finite, or no solution.

(A)

a unique solution.

(B)

infinitely many solutions.

(C)

a finite number of solutions.

(D)

no solution.

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q14

MCQ[1 Mark]

Let P be the given 3x3 matrix and I be the identity matrix. P^2 is equal to

(A)

2P - I

(B)

P + I

(C)

P

(D)

I

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q15

MCQ[1 Mark]

Given discrete random variables X and Y with specified joint probabilities, find E[Y | X = 1].

(A)

1/4

(B)

1/2

(C)

1/8

(D)

1/3

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q16

MCQ[2 Marks]

If Y = X^2 and X is uniform on (0, 1], find the probability density function P_Y(y).

(A)

P_Y(y) = 1/(2*sqrt(y)) for y in (0, 1], 0 otherwise

(B)

P_Y(y) = 1 for y in (0, 1], 0 otherwise

(C)

P_Y(y) = 1.5*sqrt(y) for y in (0, 1], 0 otherwise

(D)

P_Y(y) = 2y for y in (0, 1], 0 otherwise

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q17

NAT[2 Marks]

Find the directional derivative of V(x, y) = x^2 + x + y^2 + 1 at the origin in the direction of point (1, 2).

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q18

NAT[2 Marks]

Solve the system of differential equations with given initial conditions at t = 1.

Explanation

GATE→2025→Engineering Mathematics→Complex Variables

Q19

NAT[2 Marks]

Evaluate the contour integral of f(z) = jz over clockwise circle |z| = 1.

Explanation

Electric Circuits

3 Questions

GATE→2025→Electric Circuits→Network Elements & Solution Methods

Q20

MCQ[1 Mark]

The I-V characteristics of the element between nodes X and Y (1 A current source in parallel with 1 kΩ resistor) is best depicted by

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2025→Electric Circuits→Network Elements & Solution Methods

Q21

MCQ[1 Mark]

A series combination of a nullator and a resistor of value R will behave as a

(A)

resistor of value R.

(B)

nullator.

(C)

open circuit.

(D)

short circuit.

Explanation

GATE→2025→Electric Circuits→Network Theorems & AC/DC Transients

Q22

NAT[2 Marks]

For the RC circuit with 100 V source, 25 ohm resistor, and 5 F capacitor where switch S closes at t = 0, find time to charge capacitor to 50 V.

Explanation

Electromagnetic Fields

4 Questions

GATE→2025→Electromagnetic Fields→Electrostatics & Magnetostatics

Q23

MCQ[1 Mark]

Which figure correctly represents the radial electric field E_R due to a spherical cloud of negative volume charge density for 0 <= R <= a?

(A)

Fig. (i)

(B)

Fig. (ii)

(C)

Fig. (iii)

(D)

Fig. (iv)

Explanation

GATE→2025→Electromagnetic Fields→Electrostatics & Magnetostatics

Q24

MCQ[2 Marks]

An air cylindrical capacitor has capacitance C_0. If a dielectric of relative permittivity epsilon_r fills 50% of the annular volume, find epsilon_r to make new capacitance 5 C_0.

(A)

4

(B)

5

(C)

9

(D)

10

Explanation

GATE→2025→Electromagnetic Fields→Electrostatics & Magnetostatics

Q25

MSQ[2 Marks]

For which value(s) of n is the divergence of radial vector field F(R) = a_R (1 / R^n) independent of R in spherical coordinates?

(A)

-2

(B)

-1

(C)

1

(D)

2

Explanation

GATE→2025→Electromagnetic Fields→Electrostatics & Magnetostatics

Q26

MSQ[2 Marks]

Two coupled circuits with L_1, L_2, M (k=1) carry I_1, I_2. At which value(s) of I_1/I_2 is stored magnetic energy minimum?

(A)

M/L_1

(B)

-M/L_2

(C)

-L_1/M

(D)

-L_2/M

Explanation

Signals and Systems

6 Questions

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q27

MCQ[1 Mark]

For a discrete-time LTI system with impulse response h[n] = 1 for n in {0, 1, 2}, find the output y[n] for input x[n].

(A)

x[n] + x[n-1] + x[n-2]

(B)

x[n-1] + x[n] + x[n+1]

(C)

x[n] + x[n+1] + x[n+2]

(D)

x[n+1] + x[n+2] + x[n+3]

Explanation

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q28

MCQ[1 Mark]

Evaluate the integral of x(t) delta(t+3) dt from -inf to inf for x(t) = -t^2 {u(t+4) - u(t-4)}.

(A)

-9

(B)

9

(C)

3

(D)

-3

Explanation

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q29

NAT[1 Mark]

For the periodic signal x(t) = 1 + 2 cos(2 pi t) + 2 cos(4 pi t) + 2 cos(6 pi t), find the mean squared value over its period T.

Explanation

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q30

MCQ[2 Marks]

For y(t) = x_1(t) * x_2(t) (convolution of given trapezoidal/triangular signals), find the integral of y(t) from -inf to inf.

(A)

1.5

(B)

2.5

(C)

3.5

(D)

4

Explanation

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q31

MCQ[2 Marks]

If impulse response of LTI system S is u(t), which statement is true about BIBO stability?

(A)

Every bounded input signal applied to S results in a bounded output signal.

(B)

It is possible to find a bounded input signal which when applied to S results in an unbounded output signal.

(C)

On applying any input signal to S, the output signal is always bounded.

(D)

On applying any input signal to S the output signal is always unbounded.

Explanation

GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms

Q32

NAT[2 Marks]

For an ideal low-pass filter with cutoff frequency 200 pi rad/s, find h(0) in the time domain.

Explanation

Electrical Machines

5 Questions

GATE→2025→Electrical Machines→DC & AC Machines

Q33

MCQ[2 Marks]

For the induction motor operating region and load torque curve, which trajectory from O to S takes the shortest time?

(A)

O-Q-R-S

(B)

O-P-S

(C)

O-E-S

(D)

O-F-S

Explanation

GATE→2025→Electrical Machines→DC & AC Machines

Q34

NAT[1 Mark]

A 3.3 kV synchronous motor has load angle deflection of 2° mechanical, X_s = 2 ohm. Find armature current magnitude in amperes.

Explanation

GATE→2025→Electrical Machines→Transformers & Energy Conversion

Q35

MCQ[2 Marks]

For the given 3-phase transformer connection with 2:1 turns ratio, find the magnitude and phase relation between I_A and I_ad.

(A)

|I_A|/|I_ad| = 1/(2*sqrt(3)) and I_ad lags I_A by 30°

(B)

|I_A|/|I_ad| = 1/(2*sqrt(3)) and I_ad leads I_A by 30°

(C)

|I_A|/|I_ad| = 2*sqrt(3) and I_ad lags I_A by 30°

(D)

|I_A|/|I_ad| = 2*sqrt(3) and I_ad leads I_A by 30°

Explanation

GATE→2025→Electrical Machines→DC & AC Machines

Q36

MCQ[2 Marks]

A DC series motor drives a load where T_L proportional to N^3. Fed from 400 V, draws 40 A. Find external resistance to reduce speed by half.

(A)

23.28

(B)

4.82

(C)

46.7

(D)

0

Explanation

GATE→2025→Electrical Machines→DC & AC Machines

Q37

MCQ[2 Marks]

For a 3-phase induction motor with R_r' = 1 ohm, X_eq = 4 ohm, find V and f for maximum starting torque under V/f control.

(A)

400 V and 50 Hz

(B)

200 V and 25 Hz

(C)

100 V and 12.5 Hz

(D)

300 V and 37.5 Hz

Explanation

Power Systems

6 Questions

GATE→2025→Power Systems→Generation, Transmission & Load Flow

Q38

MCQ[1 Mark]

During power failure, a household UPS supplying power to lights and fans is represented in NR load-flow as a

(A)

Slack bus

(B)

PV bus

(C)

PQ bus

(D)

PQV bus

Explanation

GATE→2025→Power Systems→Generation, Transmission & Load Flow

Q39

NAT[1 Mark]

For a distribution feeder with R/X = 5, find the load power factor at which maximum voltage drop occurs.

Explanation

GATE→2025→Power Systems→Fault Analysis, Protection & Stability

Q40

NAT[1 Mark]

Given Z_bus for a 3-bus system, find the voltage at bus 1 during a symmetrical fault at bus 2 with fault impedance j0.007 pu.

Explanation

GATE→2025→Power Systems→Fault Analysis, Protection & Stability

Q41

MCQ[2 Marks]

For a temporary fault and clearance in a single-machine infinite bus system, which P-delta curve diagram best indicates rotor accelerating and decelerating areas?

(A)

Fig. (i)

(B)

Fig. (ii)

(C)

Fig. (iii)

(D)

Fig. (iv)

Explanation

GATE→2025→Power Systems→Generation, Transmission & Load Flow

Q42

NAT[2 Marks]

A 3-phase 4 kV induction motor draws 390 kVA at 0.77 pf lag. Shunt capacitors correct pf to 0.85 pf lag. Find capacitor bank line current in A.

Explanation

GATE→2025→Power Systems→Generation, Transmission & Load Flow

Q43

NAT[2 Marks]

Given incremental cost data for two generating units, find total plant output at incremental cost of 11,800 Rs/MWh without exceeding unit capacities.

Explanation

Control Systems

6 Questions

GATE→2025→Control Systems→Mathematical Modeling & LTI System Analysis

Q44

MCQ[1 Mark]

Given step response data points for a stable first-order LTI system, find the closest time constant in seconds.

(A)

1

(B)

2

(C)

3

(D)

4

Explanation

GATE→2025→Control Systems→Stability Criteria, Compensators & Controllers

Q45

MCQ[1 Mark]

The Nyquist plot of strictly stable G(s) with numerator (s-3) encircles -1 once anti-clockwise. The closed-loop system is

(A)

The system stability cannot be ascertained.

(B)

The system is marginally stable.

(C)

The system is stable.

(D)

The system is unstable.

Explanation

GATE→2025→Control Systems→Stability Criteria, Compensators & Controllers

Q46

MSQ[1 Mark]

For G(s) = Ks(s+2)/((s+5)(s+7)), which real axis points are on the root locus for K >= 0?

(A)

-1

(B)

-4

(C)

-6

(D)

-10

Explanation

GATE→2025→Control Systems→Stability Criteria, Compensators & Controllers

Q47

MCQ[2 Marks]

For G(s) = 1/((s+1)(s+2)) and forward/feedback transfer function K(s-1)G(s), determine closed-loop stability for K.

(A)

stable for all K > 2

(B)

unstable for all K > 2

(C)

unstable for all K > 1

(D)

stable for all K > 1

Explanation

GATE→2025→Control Systems→Mathematical Modeling & LTI System Analysis

Q48

NAT[2 Marks]

Given state-space matrix A, find the sum of the magnitudes of the system poles.

Explanation

GATE→2025→Control Systems→Stability Criteria, Compensators & Controllers

Q49

NAT[2 Marks]

For plant G(s) and controller D(s) = 1 + K_D s, find K_D to yield 45° phase margin at gain crossover frequency omega_gc = 10 rad/s.

Explanation

Electrical and Electronic Measurements

4 Questions

GATE→2025→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q50

MSQ[1 Mark]

Which instrument(s) are required to synchronize an alternator to the grid?

(A)

Voltmeter

(B)

Wattmeter

(C)

Synchroscope

(D)

Stroboscope

Explanation

GATE→2025→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q51

NAT[1 Mark]

Find the maximum percentage error in the equivalent resistance of 100 ohm and 900 ohm parallel resistors with 5% error each.

Explanation

GATE→2025→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q52

NAT[2 Marks]

Using three-voltmeter method with R = 2 ohm, V_source = 200 V, V_R = 9 V, V_load = 199 V, find load active power in W.

Explanation

GATE→2025→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q53

NAT[2 Marks]

For the Wheatstone bridge with R = 50 ohm, S = 5 kohm, P = 10 ohm, Q = 1 kohm, source = 10 V, find sensitivity dE/dR in mV/ohm.

Explanation

Analog and Digital Electronics

6 Questions

GATE→2025→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q54

MCQ[1 Mark]

Which statement is true about small signal voltage gain of MOSFET single-stage amplifiers?

(A)

Common source and common gate amplifiers are both inverting amplifiers

(B)

Common source and common gate amplifiers are both non-inverting amplifiers

(C)

Common source amplifier is inverting and common gate amplifier is non-inverting amplifier

(D)

Common source amplifier is non-inverting and common gate amplifier is inverting amplifier

Explanation

GATE→2025→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q55

MCQ[1 Mark]

Assuming ideal op-amps, what does the given multi op-amp circuit represent?

(A)

summing amplifier.

(B)

difference amplifier.

(C)

logarithmic amplifier.

(D)

buffer.

Explanation

GATE→2025→Analog and Digital Electronics→Digital Logic & Converters

Q56

MCQ[2 Marks]

Simplify the given Boolean function in Product of Sums (POS) form.

(A)

not(u) and not(w)

(B)

not(u) or not(w)

(C)

not(v) and not(x)

(D)

v or x

Explanation

GATE→2025→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q57

MCQ[2 Marks]

Find the small-signal output impedance of the given cascode/current source transistor circuit.

(A)

2*r_ds

(B)

1/g_m + r_ds

(C)

g_m * r_ds^2 + 2*r_ds

(D)

infinity

Explanation

GATE→2025→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q58

MCQ[2 Marks]

For large R and C values, what is the output voltage waveform for a high-frequency square wave input?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2025→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q59

NAT[2 Marks]

Find the voltage gain of the given ideal multi op-amp circuit with 10 kΩ resistors.

Explanation

Power Electronics

6 Questions

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q60

MCQ[2 Marks]

Given converter input voltage v(t) and current i(t) with harmonics, find the input power factor.

(A)

0.845

(B)

0.867

(C)

0.887

(D)

1.0

Explanation

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q61

NAT[1 Mark]

For a DC-DC converter setup where MOSFET has duty cycle 0.4, current source I = 10 A, voltage V = 15 V, find power delivered by current source.

Explanation

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q62

MCQ[2 Marks]

In a 3-phase SPWM inverter with modulation index M = 0.8 and DC link voltage 600 V, find per phase fundamental RMS motor voltage.

(A)

169.71

(B)

300.00

(C)

424.26

(D)

212.13

Explanation

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q63

MCQ[2 Marks]

An AC voltage source feeds an inductor L = 100 mH through an SCR with firing angle alpha = 0°. Find the peak inductor current.

(A)

20.71

(B)

0

(C)

10.35

(D)

7.32

Explanation

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q64

MCQ[2 Marks]

Given converter average voltage V_o and resistor power dissipation 64 W (with R = 1 ohm and 500 V DC source in circuit), find firing angle alpha in degrees.

(A)

35.9

(B)

46.4

(C)

41.4

(D)

0

Explanation

GATE→2025→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q65

NAT[2 Marks]

For a DC-DC buck converter in CCM with V_in = 30 V and capacitor current ripple waveform parameters, find inductor value in mH.

Explanation