GATE EE 2025: Electrical Engineering
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Electrical Engineering (EE)
General Aptitude
Q.1 – Q.5 Carry ONE mark Each
Q.1 Kavya _________ go to work yesterday as she __________ feeling well.
Select the most appropriate option to complete the above sentence.
(A) didn’t; isn’t
(B) wouldn’t; wasn’t
(C) wasn’t; wasn’t
(D) couldn’t; wasn’t
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Electrical Engineering (EE)
Q.2 Good : Evil :: Genuine : _______
Select the most appropriate option to complete the analogy.
(A) Counterfeit
(B) Contraband
(C) Counterfoil
(D) Counterpart
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Electrical Engineering (EE)
Q.3 The relationship between two variables x and y is given by x + py + q = 0 and is
shown in the figure. Find the values of p and q.
Note: The figure shown is representative.
12
10
8
y 6
4
2
0
-4 -3 -2 -1 0 1 2 3 4
x
(A) 1
p= − ; q= 2
2
(B) p = 2 ; q = −2
(C) 1
p= ;q= 4
2
(D) p= 2; q = 4
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Electrical Engineering (EE)
Q.4 Each row of Column-I has three items and each item is represented by a circle in
Column-II. The arrangement of circles in Column-II represents the relationship
among the items in Column-I.
Identify the option that has the most appropriate match between Column-I and
Column-II.
Note: The figures shown are representative.
Column-I Column-II
(1) Animals, Zebra, Giraffe (P)
(2) Director, Producer, Actor (Q)
(3) Word, Sentence, Novel (R)
(4) Pianist, Guitarist, Instrumentalist (S)
(A) (1) – (Q); (2) – (P); (3) – (S); (4) – (R)
(B) (1) – (Q); (2) – (R); (3) – (S); (4) – (P)
(C) (1) – (S); (2) – (P); (3) – (R); (4) – (Q)
(D) (1) – (R); (2) – (S); (3) – (Q); (4) – (P)
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Electrical Engineering (EE)
1
Q.5
381 3
What is the value of ( ) ?
274
(A) 313
(B) 396
(C) 323
(D) 369
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Electrical Engineering (EE)
Q.6 – Q.10 Carry TWO marks Each
Q.6 Identify the option that has the most appropriate sequence such that a coherent
paragraph is formed:
P. It is because deer, like most of the animals that tigers normally prey on, run
much faster! It simply means, another day of empty stomach for the big cats.
Q. Tigers spend most of their life searching for food.
R. If they trace the scent of deer, tigers follow the trail, chase the deer for a
mile or two in the dark, and yet may not catch them.
S. For several nights, they relentlessly prowl through the forest, hunting for a
trail that may lead to their prey.
(A) S→ P→R→Q
(B) R→P→S→Q
(C) Q→S→R→P
(D) P→Q→S→R
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Electrical Engineering (EE)
Q.7 In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one
among the given options is most appropriate for the entries marked (i) and (ii) ?
EF HJ
FG (i)
35 (ii)
80 30
(A) (i) EH; (ii) 40
(B) (i) JK; (ii) 36
(C) (i) EG; (ii) 42
(D) (i) PS; (ii) 14
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Electrical Engineering (EE)
Q.8 Scores obtained by two students P and Q in seven courses are given in the table
below. Based on the information given in the table, which one of the following
statements is INCORRECT?
P 22 89 50 45 78 60 39
Q 35 65 60 56 81 45 50
(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 the
difference between the maximum and minimum scores of Q.
(D) Median score and the average score of Q are same.
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Electrical Engineering (EE)
Q.9 Spheres of unit diameter are centered at (l, m, n) where l, m, and n take every possible
integer values.
The distance between two spheres is computed from the center of one sphere to the
center of the other sphere. For a given sphere, x is the distance to its nearest sphere and
y
y is the distance to its next nearest sphere. The value of x is:
(A) 2√2
(B) 1
√2
(C) √2
(D) 2
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Electrical Engineering (EE)
Q.10 In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2.
ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as
shown in the figure.
Which one of the following statements is true about the shaded area PQS?
Note: The figure shown is representative.
(A) 16
The shaded area is times the area of the semicircle with the diameter PS.
9
(B) The shaded area is equal to the area of the semicircle with the diameter PS.
(C) 14
The shaded area is times the area of the semicircle with the diameter PS.
9
(D) 14
The shaded area is times the area of the semicircle with the diameter PQ.
25
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Q.11 – Q.35 Carry ONE mark Each
Q.11 Consider the set S of points (x, y) ∈ ℜ2 which minimize the real valued function
f(x, y) = (x + y − 1)2 + (x + y)2
Which of the following statements is true about the 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.
Q.12 Let v1 and v2 be the two eigenvectors corresponding to distinct eigenvalues of a
3 × 3 real symmetric matrix. Which one of the following statements is true?
(A) vT1 v2 ≠ 0
(B) vT1 v2 = 0
(C) v1 + v2 = 0
(D) v1 − v2 = 0
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Q.13 1 1 1 1/3
Let A = [−1 −1 −1], and b = [−1/3]. Then, the system of linear equations
0 1 −1 0
Ax = b has
(A) a unique solution.
(B) infinitely many solutions.
(C) a finite number of solutions.
(D) no solution.
Q.14 2 1 0
Let P = [−1 0 0] and let I be the identity matrix. Then P2 is equal to
0 0 1
(A) 2P − I
(B) P
(C) I
(D) P+I
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Q.15 Consider discrete random variables X and Y with probabilities as follows:
1
P(X = 0 and Y = 0) =
4
1
P(X = 1 and Y = 0) =
8
1
P(X = 0 and Y = 1) =
2
1
P(X = 1 and Y = 1) =
8
Given X = 1, the expected value of Y is
(A) 1
4
(B) 1
2
(C) 1
8
(D) 1
3
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Electrical Engineering (EE)
Q.16 Which one of the following statements is true about the small signal voltage gain of
a MOSFET based single stage amplifier?
(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
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Electrical Engineering (EE)
Q.17 Assuming ideal op-amps, the circuit represents a
+VDD
+VDD
-VEE
Vout
Vin -VEE
(A) summing amplifier.
(B) difference amplifier.
(C) logarithmic amplifier.
(D) buffer.
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Electrical Engineering (EE)
Q.18 The I-V characteristics of the element between the nodes X and Y is best depicted
by
X IXY
1A 1 kΩ
Y
(A) IXY
1A
0 VXY
(B) IXY
1A
0 VXY
(C) IXY
1A
0 VXY
(D) IXY
1A
0 VXY
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Electrical Engineering (EE)
Q.19 A nullator is defined as a circuit element where the voltage across the device and
the current through the device are both zero. 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.
Q.20 Consider a discrete-time linear time-invariant (LTI) system S, where
y[n] = S{x[n]}
Let
1, n ∈ {0, 1, 2}
S{δ[n]} = {
0, otℎerwise
where δ[n] is the discrete-time unit impulse function. For an input signal x[n], the
output y[n] is
(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]
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Electrical Engineering (EE)
Q.21 Consider a continuous-time signal
x(t) = −t 2 {u(t + 4) − u(t − 4)}
where u(t) is the continuous-time unit step function. Let δ(t) be the continuous-
time unit impulse function. The value of
∞
∫ x(t)δ(t + 3)dt
−∞
is
(A) −9
(B) 9
(C) 3
(D) −3
Q.22 Selected data points of the step response of a stable first-order linear time-invariant
(LTI) system are given below. The closest value of the time-constant, in sec, of the
system is
Time (sec) 0.6 1.6 2.6 10 ∞
Output 0.78 1.65 2.18 2.98 3
(A) 1
(B) 2
(C) 3
(D) 4
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Electrical Engineering (EE)
Q.23 The Nyquist plot of a strictly stable G(s) having the numerator polynomial as
(s − 3) encircles the critical point −1 once in the anti-clockwise direction. Which
one of the following statements on the closed-loop system shown in figure, is
correct?
Input + Output
G(s)
_
(A) The system stability cannot be ascertained.
(B) The system is marginally stable.
(C) The system is stable.
(D) The system is unstable.
Q.24 During a power failure, a domestic household uninterruptible power supply (UPS)
supplies AC power to a limited number of lights and fans in various rooms. As per
a Newton-Raphson load-flow formulation, the UPS would be represented as a
(A) Slack bus
(B) PV bus
(C) PQ bus
(D) PQV bus
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Electrical Engineering (EE)
Q.25 Which one of the following figures represents the radial electric field distribution
ER caused by a spherical cloud of electrons with a volume charge density,
ρ = −3ρ0 for 0 ≤ R ≤ a (both ρ0 , a are positive and R is the radial distance) and
ρ = 0 for R > a ?
(A) Fig. (i)
(B) Fig. (ii)
(C) Fig. (iii)
(D) Fig. (iv)
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Electrical Engineering (EE)
Q.26 The operating region of the developed torque (Tem ) and speed (ω) of an induction
motor drive is given by the shaded region OQRE in the figure. The load torque (TL )
characteristic is also shown. The motor drive moves from the initial operating point
O to the final operating point S. Which one of the following trajectories will take
the shortest time?
Tem
Q R
P S
TL
F
ω
O E
(A) O−Q−R−S
(B) O−P−S
(C) O−E−S
(D) O−F−S
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Electrical Engineering (EE)
Q.27 The input voltage v(t) and current i(t) of a converter are given by,
v(t) = 300 sin(ωt) V
π π π
i(t) = 10 sin (ωt − ) + 2 sin (3ωt + ) + sin (5ωt + ) A
6 6 2
where, ω = 2π × 50 rad/s. The input power factor of the converter is closest to
(A) 0.845
(B) 0.867
(C) 0.887
(D) 1.0
Q.28 Instrument(s) required to synchronize an alternator to the grid is/are
(A) Voltmeter
(B) Wattmeter
(C) Synchroscope
(D) Stroboscope
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Electrical Engineering (EE)
Q.29 The open-loop transfer function of the system shown in the figure, is
Ks(s + 2)
G(s) =
(s + 5)(s + 7)
For K ≥ 0, which of the following real axis point(s) is/are on the root locus?
Input + Output
G(s)
_
(A) −1
(B) −4
(C) −6
(D) −10
Q.30 A continuous time periodic signal x(t) is
x(t) = 1 + 2 cos 2πt + 2 cos 4πt + 2 cos 6πt .
1 T
If T is the period of x(t), then ∫ |x(t)|2 dt =____________ (round off to the
T 0
nearest integer).
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Electrical Engineering (EE)
Q.31 The maximum percentage error in the equivalent resistance of two parallel-
connected resistors of 100 Ω and 900 Ω with each having a maximum 5% error is
____________ % (round off to nearest integer value).
Q.32 Consider a distribution feeder, with R/X ratio of 5. At the receiving end, a 350 kVA
load is connected. The maximum voltage drop will occur from the sending end to
the receiving end, when the power factor of the load is ___________(round off to
three decimal places).
Q.33 The bus impedance matrix of a 3-bus system (in pu) is
j0.059 j0.061 j0.038
Zbus = [j0.061 j0.093 j0.066]
j0.038 j0.066 j0.110
A symmetrical fault (through a fault impedance of j0.007 pu) occurs at bus 2.
Neglecting pre-fault loading conditions, the voltage at bus 1, during the fault is
________ pu (round off to three decimal places).
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Electrical Engineering (EE)
Q.34 In the circuit with ideal devices, the power MOSFET is operated with a duty cycle
of 0.4 in a switching cycle with I =10 A and V =15 V. The power delivered by the
current source, in W, is ____________ (round off to the nearest integer).
Q.35 The induced emf in a 3.3 kV, 4 pole, 3-phase star connected synchronous motor is
considered to be equal and in phase with the terminal voltage under no load
condition. On application of a mechanical load, the induced emf phasor is deflected
by an angle of 2° mechanical with respect to the terminal voltage phasor. If the
synchronous reactance is 2 Ω, and stator resistance is negligible, then the motor
armature current magnitude, in ampere, during loaded condition is closest to,
____________ (round off to two decimal places).
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Electrical Engineering (EE)
Q.36 – Q.65 Carry TWO marks Each
Q.36 Let X and Y be continuous random variables with probability density functions
PX (x) and PY (y), respectively. Further, let Y = X 2 and
1, x ∈ (0,1]
PX (x) = { .
0, otℎerwise
Which one of the following options is correct?
(A) 1
, y ∈ (0,1]
PY (y) = {2√y
0, otℎerwise
(B) 1, y ∈ (0,1]
PY (y) = {
0, otℎerwise
(C) 1.5 √y, y ∈ (0,1]
PY (y) = {
0, otℎerwise
(D) 2y, y ∈ (0,1]
PY (y) = {
0, otℎerwise
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Electrical Engineering (EE)
Q.37 A Boolean function is given as
f = (u̅ + v̅ + w
̅ + x̅ ). (u̅ + v̅ + w
̅ + x). (u̅ + v + w
̅ + x̅ ). (u̅ + v + w
̅ + x)
The simplified form of this function is represented by
(A) u f
w
(B) u f
w
(C)
v f
x
(D)
v f
x
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Electrical Engineering (EE)
Q.38 In the circuit, IDC is an ideal current source. The transistors M1 and M2 are assumed
to be biased in saturation, wherein Vin is the input signal and VDC is fixed DC
voltage. Both transistors have a small signal resistance of rds and trans-conductance
of gm . The small signal output impedance of this circuit is
VDD
IDC
VDC Vout
M2
Vin
M1
(A) 2rds
(B) 1
+ rds
gm
2
(C) gm rds + 2rds
(D) infinity
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Electrical Engineering (EE)
Q.39 In the circuit, shown below, if the values of R and C are very large, the form of the
output voltage for a very high frequency square wave input, is best represented by
(A) Vout
1V
t
-1 V
(B) Vout
1V
t
-1 V
(C) Vout
1V
t
-1 V
(D) Vout
1V
t
-1 V
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Electrical Engineering (EE)
Q.40 Let continuous-time signals x1 (t) and x2 (t) be
1, t ∈ [0,1] t, t ∈ [0,1]
x1 (t) = { 2 − t, t ∈ [1,2] and x2 (t) = { 2 − t, t ∈ [1,2]
0, otℎerwise 0, otℎerwise
∞
Consider the convolution y(t) = x1 (t) ∗ x2 (t). Then ∫−∞ y(t)dt is
(A) 1.5
(B) 2.5
(C) 3.5
(D) 4
Q.41 1
Let G(s) = . Then the closed-loop system shown in the figure below,
(s+1)(s+2)
is
Input + Output
K(s-1)G(s)
_
(A) stable for all K > 2.
(B) unstable for all K > 2.
(C) unstable for all K > 1.
(D) stable for all K > 1.
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Electrical Engineering (EE)
Q.42 The continuous-time unit impulse signal is applied as an input to a continuous-time
linear time-invariant system S. The output is observed to be the continuous-time
unit step signal u(t). Which one of the following statements is true?
(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.
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Electrical Engineering (EE)
Q.43 The transformer connection given in the figure is part of a balanced 3-phase circuit
where the phase sequence is “abc”. The primary to secondary turns ratio is 2:1. If
(Ia + Ib + Ic = 0), then the relationship between IA and Iad will be
IA
Iad
A a
Ic Icd
Ia c
Ib
IB Ibd
B IC b
C
primary secondary
(A) |IA | 1
|Iad |
= 2√3 and Iad lags IA by 30°.
(B) |IA | 1
|Iad |
= 2√3 and Iad leads IA by 30°.
(C) |IA |
|Iad |
= 2√3 and Iad lags IA by 30°.
(D) |IA |
|Iad |
= 2√3 and Iad leads IA by 30°.
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Q.44 A DC series motor with negligible series resistance is running at a certain speed
driving a load, where the load torque varies as cube of the speed. The motor is fed
from a 400 V DC source and draws 40 A armature current. Assume linear magnetic
circuit. The external resistance, in Ω, that must be connected in series with the
armature to reduce the speed of the motor by half, is closest to
(A) 23.28
(B) 4.82
(C) 46.7
(D) 0
Q.45 A 3-phase, 400 V, 4 pole, 50 Hz star connected induction motor has the following
parameters referred to the stator:
Rr′ = 1Ω, Xs = Xr′ = 2Ω
Stator resistance, magnetizing reactance and core loss of the motor are neglected.
The motor is run with constant V/f control from a drive. For maximum starting
torque, the voltage and frequency output, respectively, from the drive, is closest to,
(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
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Q.46 The 3-phase modulating waveforms (va (t), vb (t) and vc (t)), used in sinusoidal
PWM in a Voltage Source Inverter (VSI) are
va (t) = 0.8 sin (ωt) V
2π
vb (t) = 0.8 sin (ωt − 3 ) V
2π
vc (t) = 0.8 sin (ωt + 3 ) V
where ω = 2π × 40 rad/s is the fundamental frequency. The modulating
waveforms are compared with a 10 kHz triangular carrier whose magnitude varies
between +1 and −1. The VSI has a DC link voltage of 600 V and feeds a star
connected motor. The per phase fundamental RMS motor voltage, in volts, is closest
to
(A) 169.71
(B) 300.00
(C) 424.26
(D) 212.13
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Q.47 An ideal sinusoidal voltage source v(t) = 230√2 sin(2π × 50t) V feeds an ideal
inductor L through an ideal SCR with firing angle α = 0°. If L = 100 mH, then the
peak of the inductor current, in ampere, is closest to
(A) 20.71
(B) 0
(C) 10.35
(D) 7.32
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Electrical Engineering (EE)
Q.48 In the following circuit, the average voltage
cos α
Vo = 400 (1 + ) V,
3
where α is the firing angle. If the power dissipated in the resistor is 64 W, then the
closest value of α in degrees is
(A) 35.9
(B) 46.4
(C) 41.4
(D) 0
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Electrical Engineering (EE)
In the system shown below, the generator was initially supplying power to the grid.
Q.49 A temporary LLLG bolted fault occurs at F very close to circuit breaker 1. The
circuit breakers open to isolate the line. The fault self-clears. The circuit breakers
reclose and restore the line. Which one of the following diagrams best indicates the
rotor accelerating and decelerating areas?
F CB2
CB1
CB 1
Gen fault Grid
Fig. (i) Fig. (ii)
Fig. (iii) Fig. (iv)
(A) Fig. (i)
(B) Fig. (ii)
(C) Fig. (iii)
(D) Fig. (iv)
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Q.50 An air filled cylindrical capacitor (capacitance C0 ) of length L, with a and b as its
inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its
cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a
dielectric material of relative permittivity εr is inserted inside 50% of the annular
region as shown in Fig. (ii). The value of εr for which the capacitance of the
capacitor in Fig. (ii), becomes 5C0 is
a a
b b
0 0 0 r
Fig. (i) Fig. (ii)
(A) 4
(B) 5
(C) 9
(D) 10
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Q.51 Let aR be the unit radial vector in the spherical co-ordinate system. For which of
1
the following value(s) of n, the divergence of the radial vector field f(R) = aR
Rn
is independent of R?
(A) −2
(B) −1
(C) 1
(D) 2
Q.52 Consider two coupled circuits, having self-inductances L1 and L2 , that carry non-
zero currents I1 and I2 , respectively. The mutual inductance between the circuits is
M with unity coupling coefficient. The stored magnetic energy of the coupled
I1
circuits is minimum at which of the following value(s) of ?
I2
(A) M
−
L1
(B) M
−
L2
(C) L
− 1
M
(D) L
− 2
M
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Q.53 Let (x, y) ∈ ℜ2 . The rate of change of the real valued function,
V(x, y) = x 2 + x + y 2 + 1
at the origin in the direction of the point (1,2) is ___________ (round off to the
nearest integer).
Q.54 Consider ordinary differential equations given by
ẋ 1 (t) = 2x2 (t)
ẋ 2 (t) = r(t)
with initial conditions x1 (0) = 1 and x2 (0) = 0.
1, t ≥ 0
If r(t) = { , then at t = 1, x1 (t) =__________ (round off to the nearest
0, t < 0
integer).
Q.55 Let C be a clockwise oriented closed curve in the complex plane defined by
|z| = 1. Further, let f(z) = jz be a complex function, where j = √−1. Then,
∮C f(z)dz = _______ (round off to the nearest integer).
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Q.56 The op-amps in the following circuit are ideal. The voltage gain of the circuit is
____ (round off to the nearest integer).
Q.57 The switch (S) closes at t = 0 sec. The time, in sec, the capacitor takes to charge to
50 V is _____ (round off to one decimal place).
5F
S
100 V 25 Ω 3A
2Ω
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Electrical Engineering (EE)
Q.58 In an experiment to measure the active power drawn by a single-phase RL Load
connected to an AC source through a 2 Ω resistor, three voltmeters are connected
as shown in the figure below. The voltmeter readings are as follows:
VSource = 200 V, VR = 9 V, VLoad = 199 V. Assuming perfect resistors and ideal
voltmeters, the Load-active power measured in this experiment, in W, is ________
(round off to one decimal place).
2
VR
V
V
VSource
VLoad V RL Load
Q.59 In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of
change in balancing voltage E for unit change in the resistance R, in mV/Ω, is
______________ (round off to two decimal places).
Ω P=
R= 10
50 Ω
10 V E
S=
5 kΩ
kΩ Q=
1
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Electrical Engineering (EE)
Q.60 The steady state capacitor current of a conventional DC-DC buck converter,
working in CCM, is shown in one switching cycle. If the input voltage is 30 V, the
value of the inductor used, in mH, is _____________ (round off to one decimal
place).
Q.61 An ideal low pass filter has frequency response given by
1, |ω| ≤ 200π
H(jω) = {
0, otℎerwise
Let ℎ(t) be its time domain representation. Then ℎ(0) = ________ (round off to the
nearest integer).
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Electrical Engineering (EE)
Q.62 Consider the state-space model
ẋ (t) = Ax(t) + Br(t),
y(t) = Cx(t)
where x(t), r(t) , y(t) are the state, input and output, respectively. The matrices
A, B, C are given below
0 1 0
A=[ ], B = [ ], C = [1 0]
−2 −3 1
The sum of the magnitudes of the poles is _______________ (round off to nearest
integer).
Q.63 Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor
(drawing 390 kVA at 0.77 pf lag) is to be corrected to 0.85 pf lag. The line current
of the capacitor bank, in A, is ____________ (round off to one decimal place).
Q.64 Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch.
When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to
50 MW and 80 MW respectively. At an overall incremental cost of
10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW,
respectively. The total plant MW-output (without overloading any unit) at an overall
incremental cost of 11,800 Rs./MWh is ________ (round off to the nearest integer).
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Electrical Engineering (EE)
Q.65 A controller D(s) of the form (1 + KD s) is to be designed for the plant
1000√2
G(s) = s(s+10)2 as shown in the figure. The value of KD that yields a phase margin
of 45° at the gain cross-over frequency of 10 rad/sec is ________________ (round
off to one decimal place).
Input + Output
D(s) G(s)
_
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Electrical Engineering (EE)
EXTRA (BUFFER) Questions
Q.1A – Q.1E Carry ONE mark only
Q.1A In a power system, following a sudden increase in load, the frequency will settle at
a lower steady-state value if
(A) rotational inertia of the power system reduces.
(B) a major proportion of the connected load is resistive.
(C) all generation units for frequency regulation also have voltage regulators enabled.
(D) the pre-disturbance tie-line power flows are increased.
Q.1B A coil of inductance 100 mH and series resistance 100 Ω is connected across a
20 V, 1 kHz supply. The quality factor of the coil at 1 kHz is
(A) π
(B) 2π
(C) 10−3
(D) 1
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Electrical Engineering (EE)
Q.1C A device (single-phase, 50 Hz, AC) yields the following measurements at its
terminals: voltage = 141.4 ∠ − 10° V, current = 0.7∠ − 55° A. The power factor
of the device is______(round off to three decimal places).
Q.1D The current, i, in the circuit shown below, in A, is _________ (round off to the
nearest integer).
6A
i
1Ω
4V 10 V
3Ω
1Ω 2Ω
Q.1E In the circuit, both Q1 and Q2 have a current gain of 100 and VBE = 0.7 V. The small
signal voltage gain is _______ (round off to two decimal places).
10 V
100 kΩ
Vin Q1
1 pF Q2
100 kΩ Vout
1 kΩ
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Electrical Engineering (EE)
Q.2A – Q.2E Carry TWO marks only
Q.2A The bilateral z-transform of a discrete-time signal x[n] is
(1 − a2 )
X(z) =
(z − a)(z −1 − a)
with 0 < a < 1, and the region of convergence
1
a < |z| < a .
Let u[n] be the discrete-time unit step signal. Then, for n ≥ 0, the signal x[n] is
(A) an u[n]
(B) 1
u[n − 1]
an
(C) an (u[n] − u[n − 1])
(D) −an (u[n] − u[n − 1])
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Electrical Engineering (EE)
Q.2B 1
Let G(s) = . Then the closed-loop system shown in the figure below,
(s+1)(s+2)
is
Input + Output
K(s-1)G(s)
_
(A) stable for all K > 2.
(B) unstable for all K > 2.
(C) unstable for all K > 1.
(D) stable for all K > 1.
Q.2C Consider the two statements given below, and select the correct option.
Statement 1: A directional relay relies on the principle that the CT currents due to
fault location on either side of the CT, always differ from each other by a phase of
90°.
Statement 2: Directional relays are generally deployed in distribution feeders, with
their direction towards the source/substation.
(A) Both the Statements are FALSE.
(B) Both the Statements are TRUE.
(C) Statement 1 is FALSE, while Statement 2 is TRUE.
(D) Statement 1 is TRUE, while Statement 2 is FALSE.
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Electrical Engineering (EE)
Q.2D In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of
change in balancing voltage E for unit change in the resistance R, in mV/Ω, is
______________ (round off to two decimal places).
Ω P=
50 10
R= Ω
10 V E
S= kΩ
5 1
kΩ Q=
Q.2E Given F = ax (3y + k1 z) + ay (k2 x − 2z) + az (k3 y − x), where ax , ay and
az are the unit vectors in Cartesian coordinate system. The product k1 k2 k3 for
which F is irrotational is __________(round off to nearest integer).
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Answer Key for Electrical Engineering (EE)
Q. No. Session Q. Type Section Key/Range Marks
1 4 MCQ GA D 1
2 4 MCQ GA A 1
3 4 MCQ GA A 1
4 4 MCQ GA B 1
5 4 MCQ GA C 1
6 4 MCQ GA C 2
7 4 MCQ GA C 2
8 4 MCQ GA B 2
9 4 MCQ GA C 2
10 4 MCQ GA A 2
11 4 MCQ EE B 1
12 4 MCQ EE B 1
13 4 MCQ EE B 1
14 4 MCQ EE A 1
15 4 MCQ EE B 1
16 4 MCQ EE C 1
17 4 MCQ EE D 1
18 4 MCQ EE B 1
19 4 MCQ EE B 1
20 4 MCQ EE A 1
21 4 MCQ EE A 1
22 4 MCQ EE B 1
23 4 MCQ EE D 1
24 4 MCQ EE A 1
25 4 MCQ EE C 1
26 4 MCQ EE A 1
27 4 MCQ EE A 1
28 4 MSQ EE A;C 1
29 4 MSQ EE A;C 1
30 4 NAT EE 7 to 7 1
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31 4 NAT EE 5 to 5 1
32 4 NAT EE 0.975 to 0.985 1
33 4 NAT EE 0.380 to 0.400 1
34 4 NAT EE 90 to 90 1
35 4 NAT EE 66.25 to 66.75 1
36 4 MCQ EE A 2
37 4 MCQ EE A 2
38 4 MCQ EE C 2
39 4 MCQ EE C 2
40 4 MCQ EE A 2
41 4 MCQ EE B 2
42 4 MCQ EE B 2
43 4 MCQ EE A 2
44 4 MCQ EE A 2
45 4 MCQ EE C 2
46 4 MCQ EE A 2
47 4 MCQ EE A 2
48 4 MCQ EE A 2
49 4 MCQ EE B 2
50 4 MCQ EE C 2
51 4 MSQ EE B;D 2
52 4 MSQ EE A;D 2
53 4 NAT EE 0 to 1 2
54 4 NAT EE 2 to 2 2
55 4 NAT EE 0 to 0 2
56 4 NAT EE 2 to 2 2
57 4 NAT EE 4.0 to 4.2 2
58 4 NAT EE 78.0 to 81.0 2
59 4 NAT EE -2.00 to -1.94 OR 1.94 to 2.00 2
60 4 NAT EE 1.7 to 1.9 2
61 4 NAT EE 200 to 200 2
62 4 NAT EE 3 to 3 2
63 4 NAT EE 8.5 to 10.0 2
64 4 NAT EE 216 to 216 2
65 4 NAT EE 0.1 to 0.1 2
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Source: GATE. Question paper published by GATE.