GATE Electrical Engineering Test 1 Online Questions Answers

1. Square roots of –i, where i = √–1, are

2. In the circuit shown below what is the output voltage (V_out) in Volts if a silicon transistor Q and an ideal op-amp are used?

3.

4. A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at 1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is

5. The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature voltage. If L_a = 0.1 mH, R_a = 1Ω, neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated torque at the rated speed and the rated field current is

6. A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at

7. The impulse response of a system is h(t) = tu(t). For an input u(t – 1), the output is

8. In the feedback network shown below, if the feedback factor k is increased, then the

9. The curl of the gradient of the scalar field defined by V = 2x²y + 3y²z + 4z²x is

10. A continuous random variable X has a probability density function f(x) = e⁻^x, 0 < x < ∞. Then P{X > 1} is

11. Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10μs. It is given that L = (100/π) μF. Assuming latching and holding currents of the Thyristor are both zero and the initial charge on C is zero, T conducts for

12. A function y = 5x² + 10x is defined over an open interval x = (1, 2). At least at one point in this interval, dy/dx is exactly

13. For a power system network with n nodes, Z₃₃ of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is 1.3 <–10° per unit. If a capacitor having reactance of – j3.5 per unit is now added to the network between node 3 and the reference node, the current drawn by the capacitor per unit is

14. The PEAK-TO-PEAK source current ripple in Amps is

15. The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_WZ1 = 100V is applied across WX to get an open circuit voltage V_YZ1 across YZ. Next, an ac voltage V_YZ2 = 100V is applied across WX. Then. V_YZ1/V_WX1, V_WX2/V_YZ2 are respectively,

16. The angle δ in the swing equation of a synchronous generator is the

17. Leakage flux in an induction motor is

18. The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is

19. A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of E = 6a_x + 8 a_y kV/mm. The relative permittivity of the dielectric material is equal to 2. The value of constant ε₀ is 8.85 x 10⁻¹² F/m. the energy stored in the dielectric in Joules is energy stored in the dielectric in Joules is

20. The flux density at a point in space is given by B = 4xa_x + 2kya_y + 8a_z Wb/m². The value of constant k must be equal to

21. In the circuit shown below the op-amps are ideal. Then V_out in Volts is

22. A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is

23. A source v_s(t) = V cos100πt has as internal impedance of (4 + j3)Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

24. Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is

25. Which one of the following statements is NOTY TRUE for a continuous time causal and stable LTI system?

26. In the circuit shown below, Q₁ has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If V_cc is + 5V, X and Y are digital signals with 0V as logic 0 and V_cc as logic 1, then the Boolean expression for Z is

27. Two systems with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

28. The impulse response of a continuous time system is given by h(t) = δ (t – 1) + δ(t – 3). The value of the step response at t = 2 is

29. For a periodic signal v(t) = 30 sin 100t + 10 cos 300t + 6 sin (500t + π/4), the fundamental frequency in rad/s is

30. Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

31. The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is

32. Given a vector field F = y²xa_x – yza_y – x²a_z, the line integral ∫F · dI evaluated along a segment on the x-axis from x = 1 to x = 2 is

33. The transfer function V₂(s)/V₁(s) of the circuit shown below is

34. A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 10 < – 150° A and if the voltage at the load terminals is 100 < 60° V, then the

35. Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V₁ and V₂, as indicated. The correct relation among the voltmeter readings is

36. When the Newton-Raphson method is applied to solve the equation f(x) = x³ + 2 x – 1 = 0, the solution at the end of the first iteration with the initial guess value as x₀ = 1.2 is

37. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

38. Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

39. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is

40. The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20 log|G(s)|) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G(s) is