🧪 Gate MCQ Quiz Hub

1. The impulse response of a system is h(t) = t u(t) . For an input u(t -1) , the output is
t2/2 u(t)
t(t - 1)/2 u(t - 1)
(t - 1)2/2 u(t - 1)
(t2 - 1)/2 u(t - 1)

2. Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
All the poles of the system must lie on the left side of the jω axis.
Zeros of the system can lie anywhere in the s-plane.
All the poles must lie within |s| = 1
All the roots of the characteristic equation must be located on the left side of the jω

3. 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
product of h1 (t) and h2 (t)
sum of h1 (t) and h2 (t)
convolution of h1 (t) and h2 (t)
subtraction of of h2 (t) and h1 (t)

4. A source vs (t) = V cos 100 πt has an 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
3
4
5
7

5. A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 10∠-150oA and if the voltage at the load terminals is 100∠60o V, then the
load absorbs real power and delivers reactive power.
load absorbs real power and absorbs reactive power.
load delivers real power and delivers reactive power
load delivers real power and absorbs reactive power.

6. A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a short-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
50.0% of the rated current
64.0% of the rated current
80.0% of the rated current
88.8% of the rated current.

7. The flux density at a point in space is given by B = 4 xax + 2kyay + 8 az Wb/m2. The value of constant k must be equal to
-2
-50.
+0.5
+2

8. A continuous random variable X has a probability density function f(x) = e-x , 0 < x < ∞. Then P{X > 1} is
0.368
0.5
0.632
1.0

9. The curl of the gradient of the scalar field defined by V = 2x2y + 3y2z + 4z2x is
4xyax + 6yzay + 8zxaz
4ax + 6ay + 8az
(4xy + 4z2)ax + (2x2 + 6yz)ay + (3y2 + 8zx)az
0

10. 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 A.
an AND gate
an OR gate
an XOR gate
a NAND gate

11. 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 A.
an AND gate
an OR gate
an XOR gate
a NAND gate

12. For a periodic signal v(t) = 30 sin100t + 10 cos 300t + 6 sin (500t + π / 4) , the fundamental frequency in rad/s is
100
300
500
1500

13. 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
5
12
15
20

14. The angle δ in the swing equation of a synchronous generator is the
angle betweeangle between stator voltage and currentn stator voltage and current
angular displacement of the rotor with respect to the stator
angular displacement of the stator mmf with respect to a synchronously rotating axis
angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.

15. Leakage flux in an induction motor is
flux that leaks through the machine
flux that links both stator and rotor windings
flux that links none of the windings
flux that links the stator winding or the rotor winding but not both

16. 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 ∠-10o 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
0.325∠-100o
0.325∠80o
0.371∠-100o
0.433∠80o

17. A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of E = 6ax + 8ay kV/mm. The relative permitivity of the dielectric material is equal to 2. The value of constant εo is 8.85 * 10-12 F/m. The energy stored in the dielectric in Joules is
8.85 * 10-11
8.85 * 10-5
88.5
885

18. 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
0
1
2
3

19. 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
q1 R1 + q2 R2
q1/R1 + q2/R2
(q1 R1 + q2 R2)/(R1 + R2)
q1 R2 + q2 R1

20. 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
100
98
52
48

21. A function y = 5x2 +10 x is defined over an open interval x = (1, 2) . At least at one point in this interval, dy/dx is exactly
20
25
30
35

22. When the Newton-Raphson method is applied to solve the equation f (x) = x3 + 2x -1= 0, the solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
"“0.82
0.49
0.705
1.69

23. They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel?
make out
call out
dig out
fall out

24. In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was
40
43
46
49

25. Complete the sentence: Dare _______________ mistakes.
commitB. to commit
to commit
committed
committing

26. Choose the grammatically CORRECT sentence:
Two and two add four.
Two and two become four
Two and two are four
Two and two make four.

27. Choose the grammatically CORRECT sentence:
Two and two add four.
Two and two become four
Two and two are four
Two and two make four.

28. Statement: You can always give me a ring whenever you need. Which one of the following is the best inference from the above statement?
Because I have a nice caller tune.
Because I have a better telephone facility.
Because a friend in need is a friend indeed
Because you need not pay towards the telephone bills when you give me a ring.

29. What is the chance that a leap year, selected at random, will contain 53 Saturdays?
2/7
3/7
1/7
5/7

30. Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement?
The emergence of nationalism in colonial India led to our Independence.
Nationalism in India emerged in the context of colonialism.
Nationalism in India is homogeneous.
Nationalism in India is heterogeneous.

31. The set of values of p for which the roots of the equation 3x2+2x+p(p“1) = 0 are of opposite sign is
("“∞, 0)
(0, 1)
(0, ∞)
(0, ∞)

32. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is A. 30B. 36C. 40D.
64
36
40
24

33. Find the sum to n terms of the series 10+84+ 734 + .....
[9(9n + 1)]/10 + 1
[9(9n - 1)]/8 + 1
[9(9n - 1)]/8 + n
[9(9n - 1)]/8 + n2