Gate 2022
ELECTRICAL
MEMORY BASED QUESTIONS
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Aptitude
Q1. Some bottles are cups all cups are knives
(a) some bottles are knives
(b) some knives are cups
(c) All cups are bottles
(d) All Knives are cups
[Marks 1]
Solution
Ans: (a) and (b)
Q2. As you grow older, an injury to your may take longer to _______.
(a) heel/heel
(b) heal/heal
(c) heal/heel
(d) heel/heal
[Marks 1]
Solution
Ans: (d)
Q3. There are two identical dice with a single letter on each of the following Q, R, S, T, U
&V one on each of the faces. Any of the six outcomes are equally likely. The two dice are
thrown once independently at random. What is the probability that outcome on the dice were
composed only of any combination of the following letters Q, U & V?
[Marks 2]
Solution
Ans: (9/36 or 1/4)
Q4. Keep P, Q, R, S, T, U within the hexagonal. Line segment joining RS is greater than
segment joining PQ. Line segment RS is perpendicular to PQ and line segment RU is parallel
to line segment TQ. Find the correct option.
[Marks 2]
Solution
Ans: (RT is parallel to QS)
Q5. 2 shops are S and M. The person who buys from S is Cost price +150 delivery charge. If
the buys from M is Cost price +0 delivery charge.
Cost price (S) = 0.9* Cost price (M). A person buys the product from S and saves Rs. 100
What’s the cost price at S, excluding delivery charges?
[Marks 2]
Solution
Ans: (2250)
Q6. P and Q are in a race, Q starts when P is at 140 m and ratio of speed (Q) = ¾. The gap
between P and Q when P wins the race. Track length is 500m.
[Marks 1]
Solution
Ans: (20 m)
Q7. 3 Alarms buzz at every 20, 30, 50 mins. Simultaneously buzz at 12 noon, when they will
simultaneously buzz again?
[Marks 1]
Solution
Ans: (5 pm)
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Gate 2022
Electrical Engineering Solution Discussion
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Technical (EE)
Q1. Mathematics
1 0 0 
Consider a matrix A = 0 4 −2  the matrix A satisfies the equation
0 1 1 
–1
2
6A =A +CA +DI, where C & D are scalars and I is identity matrix. Then (C + D) =
_________.
[Marks 2]
Solution
Ans: (5)
Q2. Mathematics
Let the probability density function of a random variable x be given as f(x) = ae–2|x|. The value
of ‘a’ is ________.
[Marks 1]
Solution
Ans: (1)
Q3. Mathematics
Which not represent area.
(a)  xdy
c
 ydx
(c)  dxdy
(b)
R
(d)
1
( xdy − ydx )
2
[Marks 1]
Solution
Ans: (b)
Q4 Mathematics
Let, f(x,y,z) = 4x2 + 7xy + 3xz2. The direction in which the function f (x, y, z) increases most
rapidly at point P = (1, 0, 2) is
(a) 20iˆ + 7 ˆj + 12kˆ
(b) 20iˆ
(c) 20iˆ + 7 ˆj
(d) 20iˆ + 12kˆ
[Marks 1]
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Solution
Ans: (a)
Q.5 Mathematics:
x
Let f ( x ) =  et ( t − 1)( t − 2 ) dt . Then f ( x ) decreases in the interval.
0
(a) x  ( 0.5,1)
(b) x  (1, 2 )
(c) x  ( 0,1)
(d) x  ( 2,3 )
[Marks 1]
Solution
Ans: (b)
Q.6 Mathematics:
Consider 3 × 3 matrix A where (i, j)th element aij = (i - j)3 the matrix is.
(a) Symmetrical
(b) Skew symmetric
(c) null
(d) skull
[Marks 1]
Solution
Ans: (b)
Q7. Mathematics:
The fig below shows the front and rear views of a disc, which is should with identical
patterns. The disc is flipped once with respect to any one if the fixed axes 1 – 1, 2 – 2 or 3 – 3
chosen uniformly at random.
What is the probability that the disc does not retain the same front and rear view after the
flipping operation?
[Marks 2]
(a) 1
(b) 0
(c) 2/3
(d) 1/3
Solution
Ans: (c)
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Q8. Power electronics
A charger supplies 100W at 20V for charging the battery of a laptop. The power device used
in the converter inside the charger, operate at a switching frequency of 200KHz. Which
power device is belt suited for this purpose?
[Marks 1]
(a) IGBT
(b) MOSFET
(c) BJT
(d) Thyristor
Solution
Ans: (b)
Q9. Power system
The fuel cost functions in rupees 600 MW thermal power plants are given by
Plant 1 : C1 = 350 + 6 P1 + 0.004 P12
Plant 2 : C2 = 450 + aP1 + 0.003P22
where 𝑃1 and 𝑃2 are power generated by plant 1 and plant 2, respectively, in MW and a is
constant. The incremental cost of power (  ) is 8 rupees per MWh. The two thermal power
plants together meet a total power demand of 550 MW. The optional generation of plant 1
plant 2 in MW, respectively are
[Marks 2]
(a) 200, 350
(b) 350, 200
(c) 325, 225
(d) 250, 300
Solution
Ans: (d)
Q10. Power Electronics
The steady state current flowing through inductor of a DC-DC buck boost converter is below.
If peak to peak ripple in output voltage of converter is 1V, then value of output capacitor is
_________ (µF)
[Marks 2]
Solution
Ans: (168)
Q11. Power Electronics:
A single-phase fill bridge diode rectifier feeds a resistive load of 50Ω from a 200V, 50 Hz.
single-phase AC supply If the diode are ideal then the active power in watts drawn because
the load is _________. (Round of to nearest integer)
[Marks 1]
Solution
Ans: (800)
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Q12. Power Electronics:
The volt at the input of an AC – DC rectifier is given by V(t) = 230 2 sin ωt where ω = 2π ×
50 rad is. The input current drawn by the rectifier is given by
i(t)=10 sin (ωt – π/3) + 4 sin (3ωt – π/6) + 3 sin (5ωt – π/3) the input power factor is
________.
[Marks 2]
Solution
Ans: (0.44)
Q13. Analog Electronics:
Ideal MOSFET is in saturation under CD AMP so small signal current gain
(a) 0
(b) 
(c) 1
(d) 100
Solution
Ans: (b)
[Marks 1]
Q14. Analog Electronics:
For the circuit shown below with ideal diodes, the output will be
[Marks 1]
(a) Vout = Vin for Vin < 0
(c) Vout = -Vin for Vin > 0
Solution
Ans: (d)
(b) Vout = -Vin for Vin < 0
(d) Vout = Vin for Vin > 0
Q15. Analog Electronics:
The current gain (Iout/Iin) in the circuit will an ideal current amplifier given below is
[Marks 1]
CF
Cc
C
(c) c
CF
Solution
Ans: (c)
(a)
−CF
Cc
−Cc
(d)
CF
(b)
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Q16. Analog Electronics:
The O/P impedance of Non ideal op-Amp is donated by Zout The variation in the magnitudes
of Zout with increasing frequency of in the circuit shown in below is best represented by
(a)
(b)
[Marks 1]
(c)
(d)
Solution
Ans: (a)
Q17 Analog Electronics:
The steady state output (Vout) of the ckt show below
(a) become equal to 0.1 V
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(b) Saturate to +VDD
(c) Saturated to – VEE
(d) become equal to – 0.1 V
[Marks 1]
Solution
Ans: (c)
Q.18 Power system:
A 20 MVA, 11.2kV, 4-pole, 50Hz alternator has an inertia constant of 15MJ/MVA. If the
input and output power of the alternator are 15 MW and 10 MW, respectively, the angular
acceleration in mechanical degree/s2 is __________. (Round off to nearest integer).
[Marks 2]
Solution
Ans: (75)
Q.19 Signal & System:
Let an input x(t) = 2sin (10πt ) +5cos (15πt ) +7sin ( 42πt ) +4cos ( 45πt ) is passed through an
LTI system having an impulse response
 sin (10πt ) 
h ( t ) =2 
 cos ( 40πt )
πt


The output of the system is
[Marks 2]
Solution
Ans: (𝟕 𝐬𝐢𝐧(𝟒𝟐𝝅𝒕) + 𝟒𝐜𝐨𝐬(𝟒𝟓𝛑𝐭))
Q.20 Signal & system:
The transfer function of a real system H(S) is given as H ( S) =
are positive constants, The system cannot operate as
(a) HPF
(b) LPF
(c) BPF
(d) Integrator
As+B
where, A, B, C, D
s +Cs+D
2
[Marks 1]
Solution
Ans: (a)
Q21. Digital Electronics:
The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flop, with
each flip-flop having a propagation delay of 20ns, is ____________.
[Marks 1]
Solution
Ans: (12.5 MHz)
Q22. Signal & system:
Consider the signal system as shown below
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Where Y ( t ) =x ( e t ) system is ____
[Marks 1]
(a) linear & causal
(b) non-linear & causal
(c) Non-linear & non causal
(d) Linear & non-causal
Solution
Ans: (d)
Q23. Digital Electronics:
A MOD 2 and a MOD 5 up counter when cascaded together results in a MOD __________
counter.
[Marks 1]
Solution
Ans: (10)
Q24. Power system:
Which relay protects from loss of excitation of alternator?
(a) Mho relay
(b) Directional relay
(c) Over current relay
(d) Buchholz relay
[Marks 1]
Solution
Ans: (a)
Q25. Electromagnetic Fields:
If the magnetic field intensity (H) in a conducting region is given by the expression
H=x 2 a x +x 2 y 2a y +x 2 y 2 z 2a z A/m. The magnitude of current density, in A/ m2 at x = 1m, y =
2m & z = 1m is __________.
(a) 20
(b) 8
(c) 16
(d) 12
[Marks 1]
Solution
Ans: (d)
Q26. Power Systems:
If only 5% of the supplied power to a cable reaches the output terminal the power loss in the
cable, in decibels is ________ (round off the nearest integer)
[Marks 1]
Solution
Ans: (–0.22)
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Q. 27 Power System:
The valid positive negative and zero sequence impedance, respectively for a 220 kV, fully
transposed three phase transmission line from the given choices are
(a) 0.15, 0.15 and 0.35
[Marks 1]
(b) 0.2, 0.2 and 0.2
(c) 1.1, 0.15 and 0.08
(d) 0.1, 0.3 and 0.1
Solution
Ans: (a)
Q28. Electromagnetic Fields:
A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density
is J=J a r 3a z for the region r < b where r is the distance (H) for the region inside the conductor
(i.e. r < b) is ________
J
(a) a r 3
[Marks 1]
3
J
(b) a r 4
5
J
(c) a r 3
J
(d) a r 4
4
Solution
Ans: (b)
Q29. Signals and Systems:
A Discrete time Fourier series representation of signal x(n) with period m is written as
N-1
x ( n ) =  a k e j( 2knπ/m ) A discrete time period signal with period N = 3 has the non – zero
k=0
Fourier coefficients a -3 = 2 and a 4 = 1 . The signal is
(a) 2 + 2e
 -j2π 
n

 6 
 j2π 
n

6 
 2π 
cos  n 
 6 
 j2π 
n

 6 
 2π 
cos  n 
 6 
 j2π 
n

 3 
 2π 
cos  n 
 6 
(b) 1 + 2e
(c) 2 + 2e
(d) 1 + 2e
 2π 
cos  n 
 6 
Solution
Ans: (b)
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[Marks 2]
Q30. Control Systems:
1
G (s) =
s ( s + 1)
Find encirclement of (-1, 0)
(a) 1
(b) 3
(c) 2
(d) 0
Solution
Ans: (a)
[Marks 1]
Q31. Measurements:
A balanced Wheatstone bridge ABCD has following arm resistance: RAB = 1k + 2.1%
RBC = 100  0  5% RCD is unknown resistance
RDA = 300  0.4% . The value of RCD its accuracy is
(a) 30  0.9
(b) 3000  90
(c) 3000  3
(d) 30  3
[Marks 1]
Solution
Ans: (d)
Q32. Control Systems:
The steady state output of the systems to input of the system
100
G (s) = 2
s + 0.19 + 100
y ( t ) = a + b sin (10t +  )
r ( t ) = 1 + 0.1sin10t
a = 100
b =1
a = 10
(c)
b =1
(a)
[Marks 2]
a =1
b = 10
a =1
(d)
b = 100
(b)
Solution
Ans: (b)
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Q33. Electrical machines:
Rotor current frequency given as 1Hz and stator current frequency if 40Hz, find out the speed
of induction motor having 8 poles.
[Marks 1]
Solution
Ans: (585 rpm)
Q34. Electrical Circuits:
Find 𝑉1 across 8kΩ resistance.
[Marks 2]
Solution
Ans: (100V)
Q35. Electrical Measurements:
A 3–ϕ, 50Hz, circuit is operating, with z1 = (18 + j24 )  and z2 = ( 6 + j8 ) . Find the current
through the circuit.
[Marks 2]
Solution
Ans: (20A)
Q36. Control Systems:
The O.L.T.F of a unity gain negative feedback system has G ( s ) =
for which the system is stable is
(a) k < 5
(b) k < 3
(c) k > 5
(d) k >3
Solution
Ans: (c)
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k
. The range of k
s + 4s − 5
2
[Marks 1]
Q37. Control Systems:
A 4-pole induction motor with inertial of 0.1 kg-m2 drives a constant load torque of 2 Nm.
The speed of the motor is increased linearly form 1000 rpm to 1500 rpm in 4 second as
shown in the figure below, neglect losses in the motor. The energy in joules, consumed by the
motor during the speed change is __________. (Round oof to nearest integer)
[Marks 2]
Solution
Ans: (1047.19 J)
Q38. Control Systems:
The damping ratio and undamped frequency of a closed loop system as below.
(a)  = 0.707, n = 10 rad/s
[Marks 2]
(b)  = 0.707, n = 100 rad/s
(c)  = 0.1, n = 10 rad/s
(d)  = 0.5, n = 10 rad/s
Solution
Ans: (d)
Q39. Electrical Circuits:
The network shown has resonant frequency of 150Hz and B.W = 600Hz. The Q-factor is
______.
[Marks 1]
Solution
Ans: (250)
Q40. Electrical Circuits:
An inductor having Q-factor of 60 is connected in series with a capacitor having a Q-factor of
240. The overall Q-factor of circuit is ______.
[Marks 1]
Solution
Ans: (48)
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Q41. Electrical Circuits:
In the circuit shown below the switch S is closed at t = 0. The magnitude of steady state
voltage in volts across the 6Ω resistor is ________.
(Round of to decimal place).
[Marks 1]
Solution
Ans: (5V)
Q42. Electrical Machines:
A 3 – ϕ, 415V, 50Hz I.M, draws 5 times the rated current at rated voltage at starting. It is
required to bring down the starting current from the supply to 2 times of rated current using a
3 – ϕ auto transformer neglect all losses, find transformation ratio of autotransformer
_________.
[Marks 1]
Solution
Ans: (0.632)
Q43. Electrical Machines:
A 280V, separately excited DC motor with armature resistance Ra = 1Ω and constant field
excitation drives a load. load torque (TL) ∝ speed. Motor draws a current of 30A when
running at a speed 1000 rpm. Neglect frictional loss. What will be speed (in rpm) when
additional resistance (𝑅𝑒𝑥𝑡 ) = 10Ω connected in series __________.
[Marks 2]
Solution
Ans: (482.76)
Q44. Electrical Machines:
A star connected 3 – ϕ, 400V, 50 kVA, 50Hz synchronous motor has synchronous reactance
= 1Ω /ph with negligible Ra. The shaft load of motor is 10 kW, while the power factor is 0.8
leading. The loss in motor is 2kW. The magnitude of per phase excitation Emf ________.
[Marks 2]
Solution
Ans: (244.54)
Q45. Electrical Machines:
The type of 1 – ϕ I.M expected to have the maximum power factor during steady state
running condition
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(a) Shaded pole
(b) Split phase (resistance start)
(c) Capacitor start
(d) Capacitor start and capacitor run.
[Marks 1]
Solution
Ans: (d)
Q46. Control Systems:
Let a causal LTI signal system be governed by the following differential equation
1 dy
y (t ) +
= 2 x ( t ) where x(t) and y(t) are the input and out respectively its impulse
4 dt
response is
(a) 8e
1
− t
4
u (t )
1
− t
4
u (t )
(b) 2e
(c) 8e −4t u ( t )
(d) 2e−4t u ( t )
[Marks 1]
Solution
Ans: (c)
Q47. Electrical Machines:
Consider an ideal full-bridge single phase DC-AC inverter with a DC bus voltage magnitude
of 1000V. The inverter output voltage v(t) shown below, is obtained when diagonal switches
of the inverter are switched with 50% duty cycle. The inverter feeds a load with a sinusoidal
2


current given by, i ( t ) = 10sin  t −  A , where  =
. The active power in watts,
T
3

delivered to the load is ________. (Rounded off to nearest integer)
[Marks 2]
Solution
Ans: (3183.09)
Q48. Control Systems:
The bode magnitude plot of a first order stable single system is constant with frequency, the
asymptotic value of the high frequency phase, for the signal system is –180° the signal
system has
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(a) One LHP pole, 1 LHP zero at the same frequency
(b) 2 RHP poles, 1 LHP zero
(c) 1 LHP pole and 1 RHP zero at the same frequency
(d) Two LHP pole and 1 RHP zero
[Marks 2]
Solution
Ans: (c)
Q49. Power Electronics:
For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is
I dc = 15A and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude
of the fundamental component of the source current, the amperes, is ________. (Rounded off
to two decimal places)
[Marks 2]
Solution
Ans: (17.65A)
Q50. Power System:
A 3-pahse grid-connected voltage source converter with DC link voltage of 1000V is
switched using sinusoidal pulse width modulation (PWM) technique. If the grid phase current
is 10A and the 3-phase complex power supplied by the converted is given by (–4000–j3000)
VA, then the modulation index used is sinusoidal PWM is _______. (Rounded off to two
decimal places)
[Marks 2]
Solution
Ans: (0.4714)
Q51. Power System:
The GMR of the bundle conductors given below is _______ r.
[Marks 1]
Solution
Ans: (1.723)
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