GATE Electrical Engineering Test Online

1. For a periodic square wave, which one of the following statements is TRUE?

2. Given a system of equations:

x + 2y + 2z = b₁

5x + y + 3z = b₂

Which of the following is true regarding its solutions?

3. In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

4. The palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighboring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighboring regions of Kerala having higher summer temperatures. What can be inferred from this passage?

5. Which of the following options is the closest in meaning to the phrase underlined in the sentence below?

It is fascinating to see life forms cope with varied environmental conditions.

6. A star connected 400 V. 50 Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results: Open circuit test: V_oc = 400 V (rms, line-to-line) at field current, I_f = 2.3 A

Short circuit test: I_sc = 10 A (rms, phase) at field current, I_f = 1.5 A

The value of per phase synchronous impedance in Ω at rated voltage is _______.

7. Let g : [0, ∞) → [0, ∞) be a function defined by g(x) = x – [x], where [x] represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of g(x) is ___________.

8. A distribution feeder of 1 km length having resistance, but negligible reactance, is fed from both the ends by 400 V, 50 Hz balanced sources. Both voltage sources S₁ and S₂ are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

The contributions of S₁ and S₂ in 100 A current supplied at location P respectively, as

9. The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is _______________

10. Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is र 100, a group of 5 tourists purchasing round-trip tickets will be charge र ___________.

11. In an oscilloscope screen, linear sweep is applied at the

12. A three-phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is R-Y-B and that of incoming generator voltage is R’-Y’-B’.

It was found that the lamps are becoming dark in the sequence La-Lb-Lc. It means that the phase sequence of incoming generator is

13. An incandescent lamp is marked 40 W, 240 V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is 4.5 x 10⁻³/°C, then its ‘ON’ state filament temperature in °C is approximately __________.

14. A two bus power system shown in the figure supplies load of 1.0 + j0.5 p.u.

The values of V₁ in p.u. and δ₂ respectively are

15. The undesirable property of an electrical insulating material is

16. A cascade of three identical modulo-5 counters has an overall modulus of

17. The function shown in the figure can be represented as

18. Power consumed by a balanced 3-phase, 3-wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is

19. In a press meet on the recent scam, the minister said, “The buck stops here”. What did the minister convey by the statement?

20. The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230 V, 50 Hz input. The core loss is again measured to be 500 W for 138 V, 30 Hz input. The hysteresis and eddy current losses of the transformer for 230 V, 50 Hz input are respectively,

21. A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n – 3) is

22. An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 700 rpm. The frequency of the rotor current of the motor in Hz is ____________.

23. The root locus of a unity feedback system is shown in the figure

The closed loop transfer function of the system is

24. For a specified input voltage and frequency. If the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is

25. A combination of 1μF capacitor with an initial voltage V_c(0) = – 2 V in series with a 100 Ω resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage V_s across the current source over the next few seconds?

26. When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal places are created with these lines?

27. Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}). Consider the function f(z) = z z* where z* denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

28. Let f(x) = x e⁻^x. The maximum value of the function in the interval (0, ∞) is

29. In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ________.

30. A 3-phase, 50 Hz, six pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is

31. The overcurrent relays for the line protection and loads connected at the buses are shown in the figure.

The relays are IDMT in nature having the characteristic

top = 0.14xTime Multiplier Setting/(Plug Setting Multiplier)⁰ ͘⁰² – 1  

The maximum and minimum fault currents at bus B are 2000 A and 500 A respectively. Assuming the time multiplier setting and plug setting for relay RB to be 0.1 and 5A respectively, the operating time of RB (in seconds) is __________.

32. Choose the most appropriate word from the options given below to complete the following sentence.

He could not understand the judges awarding her the first prize, because he thought that her performance was quite ____________.

33. In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when

34. Let X(s) = 3s + 5/s² + 10s + 21 be the Laplace Transform of a signal x(t). Then, x(0⁺) is

35. The roots of ax² + bx + c = 0 are real and positive. a, b and c are real. Then ax² + b |x| + c = 0 has

36. Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely?

37. Let X(z) = 1/1 – z ⁻³ be the Z-transform of a causal signal x[n]. Then, the values of x [2] and x [3] are

38. The fuel cost functions of two power plants are

Plant P₁ : C₁ = 0.05Pg²₁ + APg₁ + B

Plant P₂ : C₂ = 0.10Pg²₂ + 3APg₂ + 2B where, Pg₁ and Pg₂ are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 100 MW load at incremental fuel cost of र 100/MWh, the ratio of load shared by plants P₁ and P₂ is

39. The line integral of function F = yzi, in the counterclockwise direction, along the circle x² + y² = 1 at z = 1 is

40. The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 Wb/m², and the area of the coil is 80 mm². The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is ________.