GATE Electrical Engineering Test 3 Online Question Answers

1. Three friends, R, s and T shared toffee from a bowl. R took 1/3^rd of the toffee from a bowl. S took 1/4^th of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees were originally there in the bowl?

2. The transistor used in the circuit shown below has a β of 30 and I_CBO is negligible

If the forward voltage drop of diode is 0.7 V, then the current through collector will be

3. In the above system, the three-phase fault MVA at the bus 3 is

4. Given two continuous time signals x(t) = e⁻^t and y(t) = e⁻²^t which exist for t > 0, the convolution z(t) = x(t)* y(t) is

(a) e⁻^t – e⁻²^t

(b) e⁻³

(c) e⁺^t

(d) e⁻^t + e⁻²^t

5. The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is

6.

7. For enhancing the power transmission in along EHV transmission line, the most preferred method is to connect a

8. A solar energy installation utilize a three-phase bridge converter to feed energy into power system through into power system through a transformer of 400 V/400 V, as shown below.

The energy is called in a bank of 400 V battery and is connected to converter through a large filter choke of resistance 10Ω.

The maximum current through the battery will be

9. The open loop transfer function G(s) of a unity feedback control system is given G(s) = k(s + 2/3)/s²(s + 2)

From the root locus, it can be inferred that when k tends to positive infinity,

10. An open loop system represented by the transfer function G(s) = (s – 1)/(s + 2)(s + 3) is

11. Choose the most appropriate word from the options given below to complete the following sentence: It was her view that the country’s problems had been ___________ by foreign technocrats, so that to invite them to come back would be counter-productive,

12. The r.m.s value of the current i(t) in the circuit shown below is

13. A load center of 120 MW derives power from two power stations connected by 220 kV transmission lines of 25km and 75km as shown in the4 figure below. The three generators G1, G2 and G3 are of 100 MW capacity each and have identical fuel cost schedule for supplying the 120 MW load is

P1 = 80MW + losses

14. The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way. It can be inferred from the passage that horses were

15. With K as a constant, the possible solution for the first order differential equation dy/dx = e⁻³^x is

(a) – 1/3 e⁻³^x +K

(b) – 1/3 e³^x +K

(c) 1/3 e⁻³^x +K

(d) – 1/3 e⁻^x +K

16. Choose the word from the options given below that is most nearly opposite in meaning to the given word:

17. A lossy capacitor C_x, rated for operation at 5 kV, 50 Hz is represented by an equivalent circuit with an ideal capacitor C_p in parallel with a resistor R_p. The value C_p is found to be 0.102 μF and the value of R_p = 1.25 MΩ. Then the power loss and tan  of the lossy capacitor operating at the rated voltage, respectively, are

18. The bridge circuit shown in the figure below is used for the measurement of an unknown element ZX. The bridge circuit is best suited when ZX is a

19. A negative sequence relay is commonly used to protect

20. An RLC circuit with relevant data is given below.

The power dissipated in the resistor R is

21. The response h(t) of a linear time invariant system to an impulse δ(t), under initially relaxed condition is h(t) = e⁻^t + e⁻²^t. The response of this system for a unit step input u(t) is

(a) u(t) + e⁻^t + e⁻²^t

(b) (e⁻^t + e⁻²^t) u(t)

(c) (1.5 – e⁻^t – 0.5e⁻²^t) u(t)

(d) e⁻¹ δ(t) + e⁻²^t u(t)

22. There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

23. Consider the following statement

(i) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the current coil.

(ii) The compensating coil of a low power factor wattmeter compensates the effect of the impedance of the voltage coil circuit.

24. A capacitor is made with a polymeric dielectric having an ɛ_r of 2.26 and a dielectric breakdown strength of 50 KV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of the capacitor have a width of 20cm and a length of 40 cm, then the maximum electric charge in the capacitor is

25. The voltage applied to a circuit is 100√2 cos (100πt) volts and the circuit draws a current of 10√2 sin (100πt + π/4) amperes. Taking the voltage as the reference phasor, the phasor representation of the current in amperes is

26. A three-phase, salient pole synchronous motor is connected to an infinite bus. Ig is operated at no load a normal excitation. The field excitation of the motor is first reduced to zero and then increased in reverse direction gradually. Then the armature current

27. A low-pass filter with a cut-off frequency of 30Hz is cascaded with a high-pass filter with a cut-off frequency of 20Hz. The resultant system of filters will function as

28. The input voltage given to a converter is

v_i = 100√2 sin (100πt) V

The current drawn by the converter is

i_i = 10√2 sin (100πt – π/3) + 5√2 sin 300πt + π/4 2√sin (500πt – π/6)A

The input power factor of the converter is

29. An RLC circuit with relevant data is given below.

The current Ic in the figure above is

30. Roots of the algebraic equation x³ + x² + x + 1 = 0 are

31. The function f(x) = 2x – x² – x³ + 3 has

32. A voltage commutated chopper circuit, operated at 500 Hz, is shown below.

If the maximum value of load current is 10A, then the maximum current through the main (M) and auxiliary (A) thyristors will be

(a) i_{M max} = 12A and i_{A max} = 10A

(b) i_{M max} = 12A and i_{A max} = 2A

(c) i_{M max} = 10A and i_{A max} = 12A

(d) i_{M max} = 10A and i_{A max} = 8A

33. A three-phase 440V, 6 pole, 50Hz, squirrel cage induction motor is running at a slip of 5%. The speed of stator magnetic field to rotor magnetic field and speed of root with respect to stator magnetic field are

34. Let the Laplace transform of a function F(t) which exists for t > 0 be F₁(s) and the Laplace transform of its delayed version f(1 – τ) be F₂(s). Let F₁*(s) be the complex conjugate of F₁(s) with the Laplace variable set as s = σ + jw. If G(s) = F₂(s).F₁*(s)/|F₁(s)|² , then the inverse Laplace transform of G(s) is

35. The two vectors [1, 1, 1] and [1, a , a²], where

a = (– 1/2 + j √3/2), are

36. A zero mean random signal is uniformly distributed between limits –a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is

37. The input voltage given to a converter is

v_i = 100√2 sin (100πt) V

The current drawn by the converter is

i_i = 10√2 sin (100πt – π/3) + 5√2 sin 300πt + π/4 2√sin (500πt – π/6)A

The active power drawn by the converter is

38. In the circuit given below, the value of R required for the transfer of maximum power to the load having a resistance of 3Ω is

39. A 220 V, DC shunt motor is operating at a speed of 1440 rmp. The armature resistance is 1.0 Ω and armature current is 10A. of the excitation of the machine is reduced by 10%, the extra resistance to be put in the armature circuit to maintain the same speed and torque will be

40. A 4—point starter is used to start and control the speed of a