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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Electric Circuits(6)Electromagnetic Fields(2)Signals and Systems(7)Electrical Machines(4)Power Systems(7)Control Systems(6)Electrical and Electronic Measurements(1)Analog and Digital Electronics(6)Power Electronics(7)

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '->' denotes increasing order of intensity, then the meaning of the words [talk -> shout -> scream] is analogous to [please -> ... -> pander]. Which one of the given options is appropriate to fill the blank?

(A)

flatter

(B)

flutter

(C)

fritter

(D)

frizzle

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

P wants a study table near the window for bird watching, and Q wants his bed close to the ceiling fan. Which room arrangement suits them best?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Express the decimal number 108 in the octal number system.

(A)

168

(B)

108

(C)

150

(D)

154

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

A customer pays 3,186.00 per shirt including 18% tax. The shopkeeper sells at 20% profit. What was the cost price from the producer?

(A)

2,500.00

(B)

1,975.40

(C)

2,250.00

(D)

2,548.80

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

If x:y = (a+1):(a-1) for a > 1, find the ratio (x^2 - y^2):(x^2 + y^2).

(A)

2a : (a^2 + 1)

(B)

a : (a^2 + 1)

(C)

2a : (a^2 - 1)

(D)

a : (a^2 - 1)

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Select the correct prepositions to fill the blanks in the sentence.

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Given geometric figure with rhombus AFCD and dimensions, find the length of BF in cm.

(A)

3

(B)

2

(C)

4

(D)

6

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

Based on the chart showing car purchases by Millennials and Gen X and fuel consumption from 2010 to 2020, which statement is true?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

If rack A translates towards the right in the pinion-rack gear assembly, which statement is correct?

(A)

Object B translates towards the right direction.

(B)

Object B translates towards the left direction.

(C)

Object R rotates in the anticlockwise direction.

(D)

Object Q rotates in the clockwise direction.

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

In triangle ABC with base AB = 200 m and base angles 87.8°, find the distance of vertex C from the center of AB.

(A)

2603

(B)

2606

(C)

2306

(D)

2063

Explanation

Engineering Mathematics

9 Questions

GATE→2024→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Which of the given 3x3 matrices has an inverse (i.e., non-zero determinant)?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q12

MSQ[1 Mark]

For X uniformly distributed over integers from -10 to 10, which transformations are uniformly distributed?

(A)

X^2

(B)

X^3

(C)

(X-5)^2

(D)

(X+10)^2

Explanation

GATE→2024→Engineering Mathematics→Complex Variables

Q13

MSQ[1 Mark]

Which of the given complex functions are analytic on the entire complex plane?

(A)

f(z) = j Re(z)

(B)

f(z) = Im(z)

(C)

f(z) = e^|z|

(D)

f(z) = z^2 - z

Explanation

GATE→2024→Engineering Mathematics→Complex Variables

Q14

NAT[1 Mark]

Find the coefficient of z^5 in the Taylor series expansion of f(z) = cos(z) + e^{z^2} about the origin.

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q15

NAT[1 Mark]

Find the sum of eigenvalues of the matrix A = ([1 2; 3 4])^2.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

Find the directional derivative of f(x,y,z) = 2 ln(xy) + ln(yz) + 3 ln(xz) at (1,1,1) in the direction of vector u = 2i + j + 2k.

(A)

0

(B)

7/(5*sqrt(2))

(C)

7

(D)

21

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q17

MSQ[2 Marks]

If f(t) has a positive second derivative everywhere (-inf < t < inf), which statements are always true?

(A)

f(t) has at least one local minimum.

(B)

f(t) cannot have two distinct local minima.

(C)

f(t) has at least one local maximum.

(D)

The minimum value of f(t) cannot be negative.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q18

MSQ[2 Marks]

For f(t) = (max(0, t))^2, which of the following statements is/are true?

(A)

f(t) is not differentiable.

(B)

f(t) is differentiable and its derivative is continuous.

(C)

f(t) is differentiable but its derivative is not continuous.

(D)

f(t) and its derivative are differentiable.

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q19

MSQ[2 Marks]

Which of the given differential equations are nonlinear?

(A)

t x(t) + dx(t)/dt = t^2 e^t, x(0) = 0

(B)

0.5 e^t + x(t) dx(t)/dt = 0, x(0) = 0

(C)

x(t) cos(t) - (dx(t)/dt) sin(t) = 1

(D)

x(t) + e^{(dx(t)/dt)} = 1

Explanation

Electric Circuits

6 Questions

GATE→2024→Electric Circuits→Network Elements & Solution Methods

Q20

MCQ[1 Mark]

Determine the number of essential junctions (nodes) in the given circuit diagram.

(A)

6

(B)

7

(C)

8

(D)

9

Explanation

GATE→2024→Electric Circuits→Network Elements & Solution Methods

Q21

MCQ[1 Mark]

Find the power delivered by the 10 V source in the given circuit.

(A)

0

(B)

50

(C)

100

(D)

dependent on the value of a

Explanation

GATE→2024→Electric Circuits→Network Theorems & AC/DC Transients

Q22

MCQ[1 Mark]

For the circuit with switch S, find the time constant in seconds after S is closed.

(A)

1.25

(B)

0

(C)

1

(D)

1.5

Explanation

GATE→2024→Electric Circuits→Network Elements & Solution Methods

Q23

NAT[2 Marks]

Two two-port networks P and Q are cascaded. Given Z_P and Y_Q, find parameter alpha of the overall ABCD matrix.

Explanation

GATE→2024→Electric Circuits→Network Theorems & AC/DC Transients

Q24

NAT[2 Marks]

For the circuit with magnetically coupled inductors at omega = 5000 rad/s, find Thevenin's impedance Z_th between terminals P and Q in ohms.

Explanation

GATE→2024→Electric Circuits→Network Theorems & AC/DC Transients

Q25

NAT[2 Marks]

For the 3-phase two-wattmeter method circuit with loads Z_1 and Z_2 supplied by 400 V source, find the magnitude of the difference between W_1 and W_2 readings in watts.

Explanation

Electromagnetic Fields

2 Questions

GATE→2024→Electromagnetic Fields→Electrostatics & Magnetostatics

Q26

NAT[2 Marks]

Three point charges Q, Q, and alpha Q are at (-1,0,0), (1,0,0), and (0,-1,0). Find alpha such that the electric field at (0, 0.5, 0) is zero.

Explanation

GATE→2024→Electromagnetic Fields→Electrostatics & Magnetostatics

Q27

NAT[2 Marks]

For the magnetic field vector H to be curl-free (source-free magnetic dipole field) in free space, find the value of P.

Explanation

Signals and Systems

7 Questions

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q28

MCQ[1 Mark]

If y(t) = x(-t), which statement is always true for the convolution of x(t) and y(t)?

(A)

It is an even signal.

(B)

It is an odd signal.

(C)

It is a causal signal.

(D)

It is an anti-causal signal.

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q29

MCQ[1 Mark]

Find the ROC of the Laplace transform for the finite-duration signal x(t) = e^{t^2} [u(t-1) - u(t-10)].

(A)

-inf < Re(s) < inf

(B)

Re(s) >= 10

(C)

Re(s) <= 1

(D)

1 <= Re(s) <= 10

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q30

NAT[1 Mark]

Find the value of the derivative of X(omega) at omega = 0 for x(t) = e^{-t^4} cos(t).

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q31

MCQ[2 Marks]

For the system with relation y(t) = e^{-t} integral_{-inf}^t e^tau x(tau) dtau, the system is

(A)

nonlinear.

(B)

linear and time-invariant.

(C)

linear but not time-invariant.

(D)

noncausal.

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q32

MCQ[2 Marks]

Consider discrete-time systems T1 and T2 defined by partial sums. Which statement is true regarding BIBO stability?

(A)

T1 and T2 are BIBO stable.

(B)

T1 and T2 are not BIBO stable.

(C)

T1 is BIBO stable but T2 is not BIBO stable.

(D)

T1 is not BIBO stable but T2 is BIBO stable.

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q33

MCQ[2 Marks]

If X(z) is the Z-transform of x[n], what is the Z-transform of y[n] = x[2n]?

(A)

Y(z) = X(z^2)

(B)

Y(z) = 0.5[X(z^{-1/2}) + X(-z^{-1/2})]

(C)

Y(z) = 0.5[X(z^{1/2}) + X(-z^{1/2})]

(D)

Y(z) = 0.5[X(z^2) + X(-z^2)]

Explanation

GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms

Q34

NAT[2 Marks]

If energy of x(t) is E, and energy of y(t) = 2x(2t-1) is cE, find the value of c.

Explanation

Electrical Machines

4 Questions

GATE→2024→Electrical Machines→DC & AC Machines

Q35

MCQ[1 Mark]

A 3-phase, 50 Hz, 6-pole induction motor runs at 960 rpm with negligible stray losses. Find its percentage efficiency.

(A)

92

(B)

94

(C)

96

(D)

98

Explanation

GATE→2024→Electrical Machines→Transformers & Energy Conversion

Q36

MCQ[1 Mark]

Which option represents correct voltage polarities and induced EMFs in a single-phase two-winding transformer?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2024→Electrical Machines→DC & AC Machines

Q37

NAT[2 Marks]

For a slip-ring induction motor with given parameters, find the extra rotor resistance per phase required for maximum starting torque.

Explanation

GATE→2024→Electrical Machines→DC & AC Machines

Q38

NAT[2 Marks]

For a 5 kW, 220 V DC shunt motor with R_a = 0.5 ohm, I_nl = 3 A, I_f = 1 A, find the armature current for maximum efficiency at rated load.

Explanation

Power Systems

7 Questions

GATE→2024→Power Systems→Generation, Transmission & Load Flow

Q39

MCQ[1 Mark]

For the 4-bus network with branch impedances 4z, z, 2z, 4z, which branch should be opened for minimum loss?

(A)

b_1

(B)

b_2

(C)

b_3

(D)

b_4

Explanation

GATE→2024→Power Systems→Generation, Transmission & Load Flow

Q40

NAT[1 Mark]

Using the incremental cost curves for Gen A and Gen B, find the common load in MW when incremental cost is Rs. 7400/MWh.

Explanation

GATE→2024→Power Systems→Generation, Transmission & Load Flow

Q41

MCQ[2 Marks]

A synchronous generator supplies an inductive load (pf = sqrt(3)/2) through a line (X = 5 ohm). With X_s = 30 ohm at rated voltage and current, find the generator terminal power factor.

(A)

0.63 lagging.

(B)

0.87 lagging.

(C)

0.63 leading.

(D)

0.87 leading.

Explanation

GATE→2024→Power Systems→Generation, Transmission & Load Flow

Q42

MCQ[2 Marks]

For the 3-bus lossless network with given reactances and P_1 = m P_2, if power flow from bus 1 to bus 2 is 0 pu, which condition holds?

(A)

gamma = m beta

(B)

beta = m gamma

(C)

alpha = m gamma

(D)

alpha = m beta

Explanation

GATE→2024→Power Systems→Fault Analysis, Protection & Stability

Q43

MSQ[2 Marks]

For Clarke's transformation expressing phase voltages in terms of alpha-beta components, which matrices S are valid?

(A)

[1 1; 1 -1]

(B)

[1 1; 1 1]

(C)

[1 1; 1 0]

(D)

[-1 1; 1 1]

Explanation

GATE→2024→Power Systems→Generation, Transmission & Load Flow

Q44

MSQ[2 Marks]

Which options are correct regarding Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR)?

(A)

AGC response has a local effect on frequency while AVR response has a global effect on voltage.

(B)

AGC response has a global effect on frequency while AVR response has a local effect on voltage.

(C)

AGC regulates the field current of the synchronous generator while AVR regulates the generator's mechanical power input.

(D)

AGC regulates the generator's mechanical power input while AVR regulates the field current of the synchronous generator.

Explanation

GATE→2024→Power Systems→Fault Analysis, Protection & Stability

Q45

NAT[2 Marks]

For the single-machine infinite bus system with critical clearing angle pi/2 and given pre/during/post-fault power curves, find the accelerating area in terms of P_max.

Explanation

Control Systems

6 Questions

GATE→2024→Control Systems→Mathematical Modeling & LTI System Analysis

Q46

MCQ[1 Mark]

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

(A)

G(s) / (1 + 2G(s))

(B)

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

(C)

G(s) / (1 - 2G(s))

(D)

G(s) / (1 - 2G(s))

Explanation

GATE→2024→Control Systems→Mathematical Modeling & LTI System Analysis

Q47

MCQ[1 Mark]

Compare settling times of System 1 (omega_n = 3, angle theta = 60°) and System 2 (omega_n = 1, angle theta = 70°).

(A)

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

(B)

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

(C)

Settling times of both the systems are the same.

(D)

Settling time cannot be computed from the given information.

Explanation

GATE→2024→Control Systems→Mathematical Modeling & LTI System Analysis

Q48

MCQ[1 Mark]

For the cascaded transfer function (1/(s+1)) * ((s+40)/(s+20)), find a first-order pole-only approximation with matching steady-state step response.

(A)

1/(s+1)

(B)

2/(s+1)

(C)

1/(s+20)

(D)

2/(s+20)

Explanation

GATE→2024→Control Systems→Stability Criteria, Compensators & Controllers

Q49

NAT[2 Marks]

Find the angle of departure of the root locus branch from the complex pole (-1 + j2) for G(s) = K(s^2 - 2s + 2)/(s^2 + 2s + 5).

Explanation

GATE→2024→Control Systems→Mathematical Modeling & LTI System Analysis

Q50

NAT[2 Marks]

For the stable closed-loop system with given Bode plot characteristics, find the steady-state error for a unit ramp input.

Explanation

GATE→2024→Control Systems→Stability Criteria, Compensators & Controllers

Q51

NAT[2 Marks]

Using the tabulated frequency response of G(s), find the integral gain K_I for a phase margin of 50°.

Explanation

Electrical and Electronic Measurements

1 Question

GATE→2024→Electrical and Electronic Measurements→Bridges, Meters & Instrumentation

Q52

MCQ[1 Mark]

Match the instrument transformers (CT, PT) with their correct operational features.

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

Analog and Digital Electronics

6 Questions

GATE→2024→Analog and Digital Electronics→Digital Logic & Converters

Q53

MCQ[1 Mark]

Simplify the Boolean function F(P,Q,R,S) = not(P)not(Q) + not(P)QS + P not(Q)not(R)not(S) + P not(Q)R not(S).

(A)

not(P)S + not(Q)not(S)

(B)

not(P)not(Q) + not(Q)not(S)

(C)

not(P)Q + R not(S)

(D)

P not(S) + Q not(R)

Explanation

GATE→2024→Analog and Digital Electronics→Digital Logic & Converters

Q54

MCQ[1 Mark]

With initial Z = 1, X = 1, Y = 0, and S = X XOR Y XOR Z, find S and Z after clock edge.

(A)

S = 0, Z = 0

(B)

S = 0, Z = 1

(C)

S = 1, Z = 0

(D)

S = 1, Z = 1

Explanation

GATE→2024→Analog and Digital Electronics→Digital Logic & Converters

Q55

MCQ[1 Mark]

To implement F(X,Y) = X not(Y) + not(X) using a 4:1 multiplexer with select lines X, Y, what should inputs PQRS be?

(A)

1010

(B)

1110

(C)

1011

(D)

0110

Explanation

GATE→2024→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q56

MCQ[2 Marks]

For the BJT biasing circuit with V_CC = 12 V, R_1 = 100 kΩ, R_2 = 50 kΩ, R_C = 2 kΩ, R_E = 1 kΩ, beta = 100, find quiescent V_CE and I_C.

(A)

4.6 V and 2.46 mA

(B)

3.5 V and 2.46 mA

(C)

2.61 V and 3.13 mA

(D)

4.6 V and 3.13 mA

Explanation

GATE→2024→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q57

NAT[2 Marks]

For the given diode circuit with ideal diodes, find the current I through diode D1 in milliamperes.

Explanation

GATE→2024→Analog and Digital Electronics→Analog Circuits, Op-Amps & Filters

Q58

NAT[2 Marks]

Calculate the CMRR in dB for the given difference amplifier with resistor values 10.5 kΩ, 101 kΩ, 9.5 kΩ, and 101.5 kΩ.

Explanation

Power Electronics

7 Questions

GATE→2024→Power Electronics→Power Semiconductor Devices & Converters

Q59

MCQ[1 Mark]

Among the given power switching devices with similar ratings, which is the fastest?

(A)

SCR

(B)

GTO

(C)

IGBT

(D)

Power MOSFET

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q60

MCQ[1 Mark]

For a triac AC voltage controller feeding RL load (R = 10 ohm, L = 18.37 mH at 50 Hz), find the minimum triggering angle for controllable output.

(A)

30°

(B)

45°

(C)

60°

(D)

90°

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q61

NAT[1 Mark]

Calculate the turn-off time available to thyristor Th in microseconds for the given step-down chopper circuit.

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q62

NAT[2 Marks]

For a single-phase half-controlled bridge converter with alpha = 60° and ripple-free load current, find the ratio of fundamental input current RMS to total input current RMS.

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q63

NAT[2 Marks]

A single-phase full-bridge VSI with 100 V DC input feeds L = 20 mH at 50 Hz. Find the peak-to-peak load current in amperes.

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q64

NAT[2 Marks]

For the given DC-DC converter with f_s = 500 Hz, L = 2 mH, V_i = 20 V, V_o = 40 V, R = 10 ohm, find the peak inductor current in amperes.

Explanation

GATE→2024→Power Electronics→Inverters & AC-DC/DC-DC Topologies

Q65

NAT[2 Marks]

For regenerative braking of a DC motor at 600 rpm with armature current at rated 10 A, find the converter bridge triggering angle in degrees.

Explanation