GATE Electrical Sample Paper

Questions And Answers


No. Question
1 The RMS value of the voltage u(t) =3 + 4cos (3t) is
Options
A)
Ö (17)
V
B) 5 V
C) 7 V D) (3 + 2
Ö 2
) V
Correct Answer A
2 The open loop transfer function of a unity feed back control system is given as

G(s) =

as + 1
s2

The value of ‘a’ to give a phase margin of 45° is equal to

Options
A) 0.141 B) 0.441
C) 0.841 D) 1.141
Correct Answer C
3 The armature resistance of a permanent magnet dc motor is 0.8 W. At no load, the motor draws 1.5 A from a supply voltage of 25 V and runs at 1500 rpm. The efficiency of the motor while it is operating on load at 1500 rpm drawing a current of 3.5 A from the same source will be
Options
A) 48.0% B) 57.1%
C) 59.2% D) 88.8%
Correct Answer A
4 The solution of the first order differential equation x(t) = -3x(t), x (0) = x0 is
Options
A) x (t) = x0 e-3t B) x (t) = x0 e-3
C) x (t) = x0 e-1/3 D) x (t) = x0 e-1
Correct Answer A
5 The unit impulse response of a second order under-damped system starting from rest is given by
c(t) = 12.5 e-6t sin 8 t, t 0
The steady-state value of the unit step response of the system is equal to
Options
A) 0 B) 0.25
C) 0.5 D) 1.0
Correct Answer D
6 A single-phase, 230 V, 50 Hz, 4 pole, capacitor-start induction motor has the following stand-still impedances
Main winding Zm = 6.0 + j4.0 W

Auxiliary winding Za = 8.0 + j6.0 W
The value of the starting capacitor required to produce 90° phase difference between the currents in the main and auxiliary windings will be

Options
A) 176.84 mF B) 187.24 mF
C) 265.26 mF D) 280.86 mF
Correct Answer A
7 A single-phase half-controlled rectifier is driving a separately excited dc motor. The dc motor has a back emf constant of 0.5 V/rpm. The armature current is 5 A without any ripple. The armature resistance is 2W. The converter is working from a 280 V, single phase ac source with a firing angle of 80°. Under this operating condition, the speed of the motor will be
Options
A) 339 rpm B) 359 rpm
C) 366 rpm D) 386 rpm
Correct Answer C
8 The 8085 assembly language instruction that stores the content of H and L registers into the memory locations 2050H and 2051H, respectively, is
Options
A) SPHL 2050H B) SPHL2051H
C) SHLD 2050H D) STAX 2050H
Correct Answer C
9 A 50 Hz, 4-pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing is electric power output by 40%. Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MNm at the time of the fault will be
Options
A) 1.528 B) 1.018
C) 0.848 D) 0.509
Correct Answer A
10 The Nyquist plot of loop transfer function G(s) H(s) of a closed loop control system passes through the point (-1, j0) in the G(s) H(s) plane. The phase margin of the system is
Options
A) B) 45°
C) 90° D) 180°
Correct Answer D
11 A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately.
Options
A) 25kW in (i) and 75kW in (ii) B) 25kW in (i) and 50kW in (ii)
C) 50kW in (i) and 75kW in (ii) D) 50kW in (i) and 50kW in (ii)
Correct Answer B
12 A hydraulic turbine having rated speed of 250 rpm is connected to a synchronous generator. In order to produce power at 50 Hz, the number of poles required in the generator are
Options
A) 6 B) 12
C) 16 D) 24
Correct Answer D
13 For the equation x(t)+3 x(t) +2x(t) = 5, the solution x (t) approaches which of the following values as t ® ¥ ?
Options
A) 0 B)
5
2
C) 5 D) 10
Correct Answer B
14 The following motor definitely has a permanent magnet rotor
Options
A) DC commutator motor B) Brushless dc motor
C) Stepper motor D) Reluctance motor
Correct Answer C
15 A110 kV, single core coaxial, XLPE insulated power cable delivering power at 50Hz, has a capacitance of 125 nF/km. If the dielectric loss tangent of XLPE is 2 x 10-4, the dielectric power loss in this cable in W/km is
Options
A) 5.0 B) 31.7
C) 37.8 D) 189.0
Correct Answer D
16 The simultaneous application of signals x(t) and y(t) to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-8 display. If P and Q are constants, and x(t) = P sin (4t + 30), then y(t) is equal to
Options
A) Q sin (4t - 30) B) Q sin (2t + 15)
C) Q sin (8t + 60) D) Q sin (4t + 30)
Correct Answer B
17 A 500 MW 3-phase Y-connected synchronous generator has a rated voltage of 21.5 kV at 0.85pf. The line current when operating at full load rated conditions will be
Options
A) 13.43 kA B) 15.79 kA
C) 23.25 kA D) 27.36 kA
Correct Answer B
18 Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is
Options
A) zero B) constant
C) pulsating with zero average D) pulsating with non-zero average
Correct Answer B
19 The equivalent circuit of a transformer has leakage reactances X1 , X
Options
A) X1>> X B) X1<<>
C) X1» X D) X1» X
Correct Answer D
20 If P and Q are two random events, then the following is TRUE
Options
A) Independence of P and Q implies that probability (P Q ) = 0
B) Probability (P Q ) Probability (P) + Probability (Q)
C) If P and Q are mutually exclusive, then they must be independent
D) Probability (P Q ) Probability (P)
No. Question
1 For the scalar field u =
x2
2
+
y2
3
, magnitude of the gradient at the point (1,3) is
Options
A)
Ö 13/9
B)
Ö 9/2
C)
Ö 5
D)
9
2
Correct Answer C
2 A digital-to-analog converter with a full-scale output voltage of 3.5 V has a resolution close to 14m V. Its bit size is
Options
A) 4 B) 8
C) 16 D) 32
Correct Answer B
3 A single-phase half-controlled rectifier is driving a separately excited dc motor. The dc motor has a back emf constant of 0.5 V/rpm. The armature current is 5 A without any ripple. The armature resistance is 2W. The converter is working from a 280 V, single phase ac source with a firing angle of 80°. Under this operating condition, the speed of the motor will be
Options
A) 339 rpm B) 359 rpm
C) 366 rpm D) 386 rpm
Correct Answer C
4 In relation to the synchronous machines, which one of the following statements is false?
Options
A) In salient pole machines, the direct-axis synchronous reactance is greater than the quadrature-axis synchronous reactance B) The damper bars help the synchronous motor self start
C) Short circuit ratio is the ratio of the field current required to produce the rated voltage on open circuit to the rated armature current
D) The V-curve of a synchronous motor represents the variation in the armature current with field excitation, at a given output power
Correct Answer C
5 The 8085 assembly language instruction that stores the content of H and L registers into the memory locations 2050H and 2051H, respectively, is
Options
A) SPHL 2050H B) SPHL2051H
C) SHLD 2050H D) STAX 2050H
Correct Answer C
6 If
E
is the electric field intensity, Ñ(Ñ x
E
) is equal to
Options
A)
E
B) |
E
|
C) null vector D) zero
Correct Answer D
7 For the function f(x) = x2 e-x, the maximum occurs when x is equal to
Options
A) 2 B) 1
C) 0 D) -1
Correct Answer B
8 Two wattmeters, which are connected to measure the total power on a three -phase system supplying a balanced load, read 10.5 kW and - 2.5 kW, respectively. The total powere and the power factor, respectively, are
Options
A) 13.0 kW, 0.334 B) 13.0 kW, 0.684
C) 8.0 kW, 0.52 D) 8.0 kW, 0.334
Correct Answer D
9 The insulation strength of an EHV transmission line is mainly governed by
Options
A) load power factor B) switching over-voltages
C) harmonics D) corona
Correct Answer B
10 For the equation,
s3 - 4s2+ s + 6 = 0
the number of roots in the left half of s-plane will be
Options
A) zero B) one
C) two D) three
Correct Answer C
11 A dc potentiometer is designed to measure up to about 2 V with a slide wire of 800 mm. A standard cell of emf 1.18 V obtains balance at 600 mm. A test cell is seen to obtain balance at 680 mm. The emf of the test cell is
Options
A) 1.00V B) 1.34V
C) 1.50V D) 1.70V
Correct Answer B
12 High Voltage DC (HVDC) transmission is mainly used for
Options
A) bulk power transmission over very long distances
B) inter-connecting two systems with the same nominal frequency
C) eliminating reactive power requirement in the operation D) minimizing harmonics at the converter stations
Correct Answer A
13 A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, for the BJT
Options
A) both the base-emitter and base-collector junctions are reverse biased B) the base-emitter junction is reverse biased, and the base-collector junction is forward biased
C)

the base-emitter junction is forward biased, and the base-collector junction is reverse biased

D) both the base-emitter and base-collector junctions are forward biased
Correct Answer D
14 The Q - meter works on the principle of
Options
A) mutual inductance B) self inductance
C) series resonance D) parallel resonance
Correct Answer C
15 A 800 kV transmission line is having per phase line inductance of 1.1 mH/km and per phase line capacitance of 11.68 nF/km. Ignoring the length of the line, its ideal power transfer capability in MW is
Options
A) 1204 MW B) 1504 MW
C) 2085 MW D) 2606 MW
Correct Answer C
16 If the following program is executed in a icroprocessor, the number of instruction cycles it will take from START to HALT is

START MVI A, 14H ; Move 14H to register A
SHIFT RLC ; Rotate left without carry
JNZ SHIFT ; Jump on non-zero to SHIFT
HALT

Options
A) 4 B) 8
C) 13 D) 16
Correct Answer C
17 A moving iron ammeter produces a full scale torque of 240 mNm with a deflection of 120° at a current of 10 A. The rate of change of self inductance (mH/radian) of the instrument at full scale is
Options
A) 2.0 mH/radian B) 4.8 mH/radian
C) 12.0 mH/radian D) 114.6 mH/radian
Correct Answer B
18 At an industrial sub-station with a 4 MW load, a capacitor of 2 MVAR is installed to maintain the load power factor at 0.97 lagging. If the capacitor goes out of serivce, the load power factor becomes
Options
A) 0.85 B) 1.00
C) 0.80 lag D) 0.90 lag
Correct Answer C
19 The conduction loss versus device current characteristic of a power MOSFET is best approximated by
Options
A) a parabola
B) a straight line
C) a rectangular hyperbola
D) an exponentially decaying function
Correct Answer A
20 If P and Q are two random events, then the following is TRUE
Options
A) Independence of P and Q implies that probability (P Q ) = 0
B) Probability (P Q ) Probability (P) + Probability (Q)
C) If P and Q are mutually exclusive, then they must be independent
D) Probability (P Q ) Probability (P)
Correct Answer D





Questions And Answers


No. Question
1 A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately.
Options
A) 25kW in (i) and 75kW in (ii) B) 25kW in (i) and 50kW in (ii)
C) 50kW in (i) and 75kW in (ii) D) 50kW in (i) and 50kW in (ii)
Correct Answer B
2 A fair coin is tossed three times in succession. If the first toss poduces a head, then the probability of getting exactly two heads in three tosses is
Options
A)
1
8
B)
1
2
C)
3
8
D)
3
4
Correct Answer D
3 In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x:
Options
A) Augmented matrix [Pq] must have the same rank as matrix P
B) Vector q must have only non-zero elements
C) Matrix P must be singular
D) Matrix P must be square
Correct Answer A
4 At an industrial sub-station with a 4 MW load, a capacitor of 2 MVAR is installed to maintain the load power factor at 0.97 lagging. If the capacitor goes out of serivce, the load power factor becomes
Options
A) 0.85 B) 1.00
C) 0.80 lag D) 0.90 lag
Correct Answer C
5 In the GH(s) plane, the Nyquist plot of the loop transfer function
G(s)H(s) =
p e-0.25
s
asses through the negative real axis at the point
Options
A) (-0.25, j0) B) (-0.5, j0)
C) (-l, j0) D) (-2, j0)
Correct Answer B
6 If S =
ò
¥
x-3 dx, then S has the value
1
Options
A)
-1
3
B)
1
4
C)
1
2
D) 1
Correct Answer C
7 The following motor definitely has a permanent magnet rotor
Options
A) DC commutator motor B) Brushless dc motor
C) Stepper motor D) Reluctance motor
Correct Answer C
8 The conduction loss versus device current characteristic of a power MOSFET is best approximated by
Options
A) a parabola
B) a straight line
C) a rectangular hyperbola
D) an exponentially decaying function
Correct Answer A
9 A digital-to-analog converter with a full-scale output voltage of 3.5 V has a resolution close to 14m V. Its bit size is
Options
A) 4 B) 8
C) 16 D) 32
Correct Answer B
10 A 50 Hz, bar primary CT has a secondary with 500 turns. The secondary supplies 5 A current into a purely resistive burden of l W. The magnetizing ampere-turns is 200. The phase angle between the primary and secondary current is
Options
A) 4.6°
B) 85.4°
C) 94.6°
D) 175.4°
Correct Answer A
11 The armature resistance of a permanent magnet dc motor is 0.8 W. At no load, the motor draws 1.5 A from a supply voltage of 25 V and runs at 1500 rpm. The efficiency of the motor while it is operating on load at 1500 rpm drawing a current of 3.5 A from the same source will be
Options
A) 48.0% B) 57.1%
C) 59.2% D) 88.8%
Correct Answer A
12 A bipolar junction transistor (BJT) is used as a power control switch by biasing it in the cut-off region (OFF state) or in the saturation region (ON state). In the ON state, for the BJT
Options
A) both the base-emitter and base-collector junctions are reverse biased B) the base-emitter junction is reverse biased, and the base-collector junction is forward biased
C)

the base-emitter junction is forward biased, and the base-collector junction is reverse biased

D) both the base-emitter and base-collector junctions are forward biased
Correct Answer D
13 For the equation,
s3 - 4s2+ s + 6 = 0
the number of roots in the left half of s-plane will be
Options
A) zero B) one
C) two D) three
Correct Answer C
14 The Q - meter works on the principle of
Options
A) mutual inductance B) self inductance
C) series resonance D) parallel resonance
Correct Answer C
15 A 800 kV transmission line is having per phase line inductance of 1.1 mH/km and per phase line capacitance of 11.68 nF/km. Ignoring the length of the line, its ideal power transfer capability in MW is
Options
A) 1204 MW B) 1504 MW
C) 2085 MW D) 2606 MW
Correct Answer C
16 The insulation strength of an EHV transmission line is mainly governed by
Options
A) load power factor B) switching over-voltages
C) harmonics D) corona
Correct Answer B
17 If the following program is executed in a icroprocessor, the number of instruction cycles it will take from START to HALT is

START MVI A, 14H ; Move 14H to register A
SHIFT RLC ; Rotate left without carry
JNZ SHIFT ; Jump on non-zero to SHIFT
HALT

Options
A) 4 B) 8
C) 13 D) 16
Correct Answer C
18 A moving iron ammeter produces a full scale torque of 240 mNm with a deflection of 120° at a current of 10 A. The rate of change of self inductance (mH/radian) of the instrument at full scale is
Options
A) 2.0 mH/radian B) 4.8 mH/radian
C) 12.0 mH/radian D) 114.6 mH/radian
Correct Answer B
19 The output voltage waveform of a three-phase square-wave inverter contains
Options
A) only even harmonics B) both odd and even harmonics
C) only odd harmonics D) only triplen harmonics
Correct Answer C
20 If P and Q are two random events, then the following is TRUE
Options
A) Independence of P and Q implies that probability (P Q ) = 0
B) Probability (P Q ) Probability (P) + Probability (Q)
C) If P and Q are mutually exclusive, then they must be independent
D) Probability (P Q ) Probability (P)
Correct Answer D

D











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