Gate MCQ Quiz Hub

1. The current ib through the base of a silicon npn transistor is 1 + 0.1 cos(10000 π t) mA. At 300 K, the rπ in the small signal model of the transistor is
250 Ω
27.5 Ω
25 Ω
22.5 Ω

2. The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X2(t)] and E[X(t)] , respectively, are
6000/Ï€, 0
6400/Ï€, 0
6400/Ï€, 20/(Ï€ √2)
6000/Ï€, 20/(Ï€ √2)

3. In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is
1720
2625
4000
5250

4. The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by . The frequency and polarization of the wave, respectively, are
1.2 GHz and left circular
4 Hz and left circular
1.2 GHz and right circular
4 Hz and right circular

5. The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is
4
6
8
10

6. The average power delivered to an impedance (4 - j3) Ω by a current 5cos(100π t + 100) A is
44.2 W
50 W
62.5 W
125 W

7. The unilateral Laplace transform of f(t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is
- s/(s2 + s + 1)2
- (2s + 1)/(s2 + s + 1)2
s/(s2 + s + 1)2
(2s + 1)/(s2 + s + 1)2

8. With initial condition x(1) = 0.5 , the solution of the differential equation, t dx/dt + x = t is
x = t - 1/2
x = t2 - 1/2
x = t2/2
x = t/2

9. A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount ε and decreases that of the second by ε . After encoding, the entropy of the source
increases
remains the same
increases only if N = 2
decreases

10. The radiation pattern of an antenna in spherical co-ordinates is given by F(θ) = cos4 θ; 0 ≤ θ ≤ π /2 The directivity of the antenna is
10 dB
12.6 dB
11.5 dB
18 dB

11. If x[n] = (1/3)|n| - (1/ 2)n u[n], then the region of convergence (ROC) of its Z-transform in the Z-plane will be
1/3 < |z| < 3
1/3 < |z| < 1/2
1/2 < |z| < 3
1/3 < |z|

12. A system with transfer function G(s) = [(s2 + 9)(s + 2)] / [(s + 1)(s + 3)(s + 4)] is excited by sin(w t) . The steady-state output of the system is zero at
w = 1 rad/s
w = 2 rad/s
w = 3 rad/s
w = 4 rad/s

13. Two independent random variables X and Y are uniformly distributed in the interval [“1, 1]. The probability that max[X, Y] is less than 1 2 is
3/4
9/16
1/4
2/3

14. If x = √-1 , then the value of xx is
e-Ï€/2
eπ/2
x
1

15. The source of a silicon (ni = 1010 per cm3) n-channel MOS transistor has an area of 1 sq μm and a depth of 1 μm. If the dopant density in the source is 1019/cm3, the number of holes in the source region with the above volume is approximately
107
100
10
0

16. A BPSK scheme operating over an AWGN channel with noise power spectral density of N0 / 2 , uses equiprobable signals s1(t) = √2E/T sin(wc t) and s2(t) = -√2E/T sin(wc t) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45o with respect to the received signal, the probability of error in the resulting system is
Q(√2E/N0)
Q(√E/N0)
Q(√E/2N0)
Q(√E/4N0)

17. A transmission line with a characteristic impedance of 100 Ω is used to match a 50 Ω section to a 200 Ω section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately
82.5 cm
1.05 m
1.58 m
1.75 m

18. The input x(t) and output y(t) of a system are related as y(t) = . The system is
time-invariant and stable
stable and not time-invariant
time-invariant and not stable
not time-invariant and not stable

19. The Fourier transform of a signal h(t) is H(jw) = (2cosw)(sin2w) /w . The value of h(0) is
1/4
1/2
1
2

20. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
1/3
1/2
2/3
3/4

21. A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0) = 9/10, then the probability of error for an optimum receiver will be
7/80
63/80
9/10
1/10

22. Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
0
1/2
1
3/2

23. The maximum value of f(x) = x3 - 9x2 +24x + 5 in the interval [1, 6] is
21
25
41
46

24. An infinitely long uniform solid wire of radius a carries a uniform dc current of density j. The magnetic field at a distance r from the center of the wire is proportional to
r for r < a and 1/r2 for r > a
0 for r < a and 1/r for r > a
r for r < a and 1/r for r > a
0 for r < a and 1/r2 for r > a

25. The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). Gc (s) is a lead compensator if
a =1, b = 2
a = 3, b = 2
a = "“3, b = "“1
a = 3, b = 1

26. The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). The phase of the above lead compensator is maximum at
√2 rad/s
√3 rad/s
√6 rad/s
1/√3 rad/s

27. If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =
2.23
4.33
11.37
27.64

28. One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow.
requested that
should be given
the driving test
instead of tomorrow

29. A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is
1/4
1/16
7/16
9/16