Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electrical Engineering 11th Feb 2017 Session 2

Subject Name: Electrical Engineering

Duration : 180

Total Marks: 100

1. In the circuit shown, the diodes are ideal, the inductance is small, and I_o ≠ Which one of the following statements is true?

(A) D₁ conducts for greater than 180° and D₂ conducts for greater than 180°

(B) D₂ conducts for more than 180° and D₂ conducts for 180°

(D) D₁ conducts for more than 180° and D₂ conducts for 180°

Ans: (A)

2. For a 3-input logic circuit shown below, the output Z can be expressed as

(A)

(B)

(C)

(D)

Ans: (C)

3. An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

(A) 1/2

(B) 4/9

(D) 6/9

Ans: (A)

4. When a unit ramp input is applied to the unity feedback system having closed loop transfer function the steady state error will be

(A)

(B)

(C)

(D)

Ans: (D)

5. A three-phase voltage source inverter with ideal devices operating in o 180 conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is V_dc. The peak of the fundamental component of the phase voltage is

(A)

(B)

(C)

(D)

Ans: (B)

6. The figures show diagrammatic representations of vector fields respectively. Which one of the following choices is true?

(A)

(B)

(C)

(D)

Ans: (C)

7. Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Ans: (0.9)

8. Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

(A) uniformly over the entire volume of the sphere

(B) uniformly over the outer surface of the sphere

(D) along a straight line passing through the centre of the sphere

Ans: (B)

9. The transfer function C(s) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

(A) 0.1 < ω < 1

(B) 1 < ω < 10

(D) ω > 100

Ans: (A)

10. The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.

For the given circuit, Y_bus and Z_bus are bus admittance matrix and bus impedance matrix, respectively, each of size 2× 2. Which one of the following statements is true?

(A) Both Y_bus and Z_bus are symmetric

(B) Y_bus is symmetric and Z_bus is unsymmetric

(D) Both Y_bus and Z_bus are unsymmetric

Ans: (D)

11. A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

(A) 25

(B) 50

(D) 300

Ans: (C)

12. Let x and y be integers satisfying the following equations

2x² + y² = 34

x + 2y = 11

The value of (x + y) is ________.

Ans: (7)

13. Consider a function f(x, y, z) given by

f(x, y, z) = (x² + y² – 2z²) (y² + z²)

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ________

Ans: (40)

14. For the given 2-port network, the value of transfer impedance Z₂₁ in ohms is_______

Ans: (3)

15. The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

Ans: (100)

16. The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T₁ and T₂ are 90° and 270°, respectively.

The RMS value of the current through diode D₃ in amperes is ________

Ans: (0)

17. In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100× If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.

Ans: (61)

18. A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

(A) 1500

(B) 1470

(D) 154

Ans: (C)

19. Two resistors with nominal resistance values R₁ and R₂ have additive uncertainties ∆R₁ and ∆R₂, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

(A)

(B)

(C)

(D)

Ans: (A)

20. The nominal- π circuit of a transmission line is shown in the figure.

Impedance and reactance X = 3300Ω. The magnitude of the characteristic impedance of the transmission line, in Ω, is _______________. (Give the answer up to one decimal place.)

Ans: (406.2)

21. The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems?

(A) All three are high-pass filters.

(B) All three are band-pass filters.

(D) P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter.

Ans: (B)

22. The mean square value of the given periodic waveform f (t) is_________

Ans: (6)

23. A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHZ. The frequency of the vertical input is

(A) 1.5 kHz

(B) 2 kHz

(D) 4.5 kHz

Ans: (D)

24. Let y² – 2y + 1 = x and √x + y = 5. The value of x + √y equals ______. (Give the answer up to three decimal places)

Ans: (5.732)

25. If a synchronous motor is running at a leading power factor, its excitation induced voltage (E_f) is

(A) equal to terminal voltage V_t

(B) higher than the terminal voltage V_t

(D) dependent upon supply voltage V_t

Ans: (B)

26. Which of the following systems has maximum peak overshoot due to a unit step input?

(A)

(B)

(C)

(D)

Ans: (C)

27. Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length D_ab = D_bc = D_ca = 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/ km (rounded off to three decimal places) is ________

Ans: (0.289)

28. Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is _______ MW.

Ans: (400)

29. For the network given in figure below, the Thevenin‟s voltage V_ab is

(A) −1.5 V

(B) −0.5 V

(D) 1.5 V

Ans: (A)

30. The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

(A) 1000 samples/s

(B) 1500 sample/s

(D) 3000samples/s

Ans: (B)

31. A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance R_a = 0.02Ω. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is

(A) 34.2 A

(B) 30 A

(D) 4.84 A

Ans: (B)

32. A cascade system having the impulse responses is shown in the figure below, where symbol ↑ denotes the time origin.

The input sequence x (n) for which the cascade system produces an output sequence is

(A)

(B)

(C)

(D)

Ans: (D)

33. For the circuit shown in the figure below, it is given that The transistor has β = 29 and V_BE = 0.7 V when the B-E junction is forward biased.

For this circuit, the value of is

(A) 43

(B) 92

(D) 129

Ans: (D)

34. A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.

Ans: (12.7)

35. For the circuit shown below, assume that the OPAMP is ideal.

Which one of the following is TRUE?

(A) V_o = v_s

(B) v_o = 1.5v_s

(D) v_o = 5v_s

Ans: (C)

36. The root locus of the feedback control system having the characteristic equation s² + 6Ks + 2s + 5 = 0 where K > 0, enters into the real axis at

(A) s = −1

(B) s = −√5

(D) s = √5

Ans: (B)

37. For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions

The minimum number of clock cycles after which the output Z would again become zero is ________

Ans: (6)

38. In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

(A) 1 nF

(B) 1 μF

(D) 10 mF

Ans: (D)

39. In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ________. (Give the answer up to one decimal place.)

Ans: (40)

40. In the circuit shown in the figure, the diode used is ideal. The input power factor is _______. (Give the answer up to two decimal places.)

Ans: (0.707)

41. Consider the system described by the following state space representation

If u(t) is a unit step input and the value of output y(t) at t = 1 sec (rounded off to three decimal places) is ________

Ans: (1.2838)

42. A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R₁ = 0.3Ω, R₂ = 0.3Ω, X₁ = 0.41Ω, X₂ = 0.41Ω Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3-phase AC source is __________.

Ans: (71.04)

43. A 25 kVA, 400 V, ∆ – connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.

Ans: (−14.6)

44. If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. Y− ∆ transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_____.

Ans: (37.879)

45. For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

(A) 33∠−53.1°Ω

(B) 60∠53.1°Ω

(D) 180∠−53.1°Ω

Ans: (C)

46. A thin soap bubble of radius R = 1 cm, and thickness a = 3.3μm(a <<R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is 4πR²a and that of the drop is The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)

Ans: (10.03)

47. The value of the contour integral in the complex-plane

Along the contour |Z| = 3, taken counter-clockwise is

(A) −18πi

(B) 0

(D) 48πi

Ans: (C)

48. Let

Consider the composition of f and g, i.e., (f ∘ g) (x) = f(g(x)). The number of discontinuities in (f ∘ g) present in the interval (−∞, 0) is:

(A) 0

(B) 1

(D) 4

Ans: (A)

49. A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω, and the shunt field resistance is 240Ω. The no load speed, in rpm, is ________.

Ans: (1241.82)

50. A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.

Ans: (10000)

51. A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equals

(A)

(B)

(C)

(D)

Ans: (C)

52. The figure below shows a half-bridge voltage source inverter supplying an RL-load with The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. M = 0.6. At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage V_DC in volts is

(A) 300√2

(B) 500

(D) 1000√2

Ans: (C)

53. The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is

(A) 0 < K < 6

(B) 0 < K < 16

(D) 6 < K < 16

Ans: (A)

54. The eigen values of the matrix given below are

(A) (0, −1, −3)

(B) (0, −2, −3)

(D) (0, 1, 3)

Ans: (A)

55. A 3-phase 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25Ω and 3.925Ω If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

Ans: (0.737)

56. There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle?

(A) V

(B) W

(D) Y

Ans: (A)

57. Saturn is _________ to be seen on a clear night with the naked eye.

(A) enough bright

(B) bright enough

(D) bright as enough

Ans: (B)

58. Choose the option with words that are not synonyms.

(A) aversion, dislike

(B) luminous, radiant

(D) yielding, resistant

Ans: (D)

59. There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

(A) 1/5

(B) 7/30

(D) 4/15

Ans: (D)

60. A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

(A) 12

(B) 15

(D) 19

Ans: (B)

61. An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

(A) P

(B) Q

(D) S

Ans: (C)

62. There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

(A) The box labelled “Apples”

(B) The box labelled “Apples and Oranges”

(D) Cannot be determined

Ans: (B)

63. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

(A) ‘culture’

(B) ‘seemingly’

(D) ‘political’

Ans: (B)

64. X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number 3 X will have

(A) 90 digits

(B) 91 digits

(D) 93 digits

Ans: (A)

65. The number of roots of e^x + 0.5x² – 2 = 0 in the range [−5, 5] is

(A) 0

(B) 1

(D) 3

Ans: (C)

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