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GATE 2017-2018 :: GATE ECE

1. The current ib through the base of a silicon npn transistor is 1 + 0.1 cos(10000 Ï€ t) mA. At 300 K, the rÏ€ in the small signal model of the transistor is

2.  A. 250 â„¦ B. 27.5 â„¦ C. 25 â„¦ D. 22.5 â„¦

3. 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

4.  A. 6000/Ï€, 0 B. 6400/Ï€, 0 C. 6400/Ï€, 20/(Ï€ √2) D. 6000/Ï€, 20/(Ï€ √2)

5. 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
6.  A. 1750 B. 2625 C. 4000 D. 5250

7. 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
8.  A. 1.2 GHz and left circular B. 4 Hz and left circular C. 1.2 GHz and right circular D. 4 Hz and right circular

9. Consider the given circuit.

In this circuit, the race around
10.  A. does not occur B. occurs when CLK = 0 C. occurs when CLK = 1 and A = B = 1 D. occurs when CLK = 1 and A = B = 0

11. 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
12.  A. 4 B. 6 C. 8 D. 10

13. The i-v characteristics of the diode in the circuit given below are

The current in the circuit is
14.  A. 10 mA B. 9.3 mA C. 6.67 mA D. 6.2 mA

15. In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

16.  A. zero B. a step function C. an exponentially decaying function D. an impulse function

17. The average power delivered to an impedance (4 - j3) â„¦ by a current 5cos(100Ï€ t + 100) A is
18.  A. 44.2 W B. 50 W C. 62.5 W D. 125 W

19. The unilateral Laplace transform of f(t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is
20.  A. - s/(s2 + s + 1)2 B. - (2s + 1)/(s2 + s + 1)2 C. s/(s2 + s + 1)2 D. (2s + 1)/(s2 + s + 1)2