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# GATE Electrical Engineering Sample Question Paper - I

1 The RMS value of the voltage u(t) =3 + 4cos (3t) is

A) Ö (17) V

B) 5 V

C) 7 V

D) (3 + 2Ö2) V

2. 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

A) 48.0%

B) 57.1%

C) 59.2%

D) 88.8%

3. The solution of the first order differential equation x(t) = -3x(t), x (0) = x0 is

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

4. The unit impulse response of a second order under-damped system starting from rest is given by c(t) = 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:

A) 0

B) 0.25

C) 0.5

D) 1.0

5. 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

A) 176.84 mF

B) 187.24 mF

C) 265.26 mF

D) 280.86 mF

6. 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

A) 339 rpm

B) 359 rpm

C) 366 rpm

D) 386 rpm

7. The 8085 assembly language instruction that stores the content of H and L registers into the memory locations 2050H and 2051H, respectively, is

A) SPHL 2050H

B) SPHL 2051H

C) SHLD 2050H

D) STAX 2050H

8. 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

A) 1.528

B) 1.018

C) 0.848

D) 0.509

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

A) 1.528

B) 1.018

C) 0.848

D) 0.509

10. 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.

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)

11. 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:

A) 6

B) 12

C) 16

D) 24

12. For the equation x(t)+3 x(t) +2x(t) = 5, the solution x (t) approaches which of the following values as t ® ¥ ?

A) 0

B) 5/2

C) 5

D) 10

13. The following motor definitely has a permanent magnet rotor:

A) DC commutator motor

B) Brushless dc motor

C) Stepper motor

D) Reluctance motor

14. 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:

A) 5.0

B) 31.7

C) 37.8

D) 189.0

15. 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:

A) Q sin (4t - 30)

B) Q sin (2t + 15)

C) Q sin (8t + 60)

D) Q sin (4t + 30)

16. 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:

A) 13.43 kA

B) 15.79 kA

C) 23.25 kA

D) 27.36 kA

17. Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is:

A) zero

B) constant

C) pulsating with zero average

D) pulsating with non-zero average

18. The equivalent circuit of a transformer has leakage reactances X1 , X:

A) X1>> X

B) X1<< X

C) X1» X

D) X1» X

19. If P and Q are two random events, then the following is TRUE:

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) D) Probability (P Q ) Probability (P)

A) Ö (17) V

B) 5 V

C) 7 V

D) (3 + 2Ö2) V

2. 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

A) 48.0%

B) 57.1%

C) 59.2%

D) 88.8%

3. The solution of the first order differential equation x(t) = -3x(t), x (0) = x0 is

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

4. The unit impulse response of a second order under-damped system starting from rest is given by c(t) = 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:

A) 0

B) 0.25

C) 0.5

D) 1.0

5. 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

A) 176.84 mF

B) 187.24 mF

C) 265.26 mF

D) 280.86 mF

6. 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

A) 339 rpm

B) 359 rpm

C) 366 rpm

D) 386 rpm

7. The 8085 assembly language instruction that stores the content of H and L registers into the memory locations 2050H and 2051H, respectively, is

A) SPHL 2050H

B) SPHL 2051H

C) SHLD 2050H

D) STAX 2050H

8. 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

A) 1.528

B) 1.018

C) 0.848

D) 0.509

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

A) 1.528

B) 1.018

C) 0.848

D) 0.509

10. 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.

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)

11. 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:

A) 6

B) 12

C) 16

D) 24

12. For the equation x(t)+3 x(t) +2x(t) = 5, the solution x (t) approaches which of the following values as t ® ¥ ?

A) 0

B) 5/2

C) 5

D) 10

13. The following motor definitely has a permanent magnet rotor:

A) DC commutator motor

B) Brushless dc motor

C) Stepper motor

D) Reluctance motor

14. 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:

A) 5.0

B) 31.7

C) 37.8

D) 189.0

15. 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:

A) Q sin (4t - 30)

B) Q sin (2t + 15)

C) Q sin (8t + 60)

D) Q sin (4t + 30)

16. 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:

A) 13.43 kA

B) 15.79 kA

C) 23.25 kA

D) 27.36 kA

17. Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is:

A) zero

B) constant

C) pulsating with zero average

D) pulsating with non-zero average

18. The equivalent circuit of a transformer has leakage reactances X1 , X:

A) X1>> X

B) X1<< X

C) X1» X

D) X1» X

19. If P and Q are two random events, then the following is TRUE:

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) D) Probability (P Q ) Probability (P)