GATE Electronics and Communication Test 3 Online Question Answers

1. A transmission line with a characteristics impedance of 100Ω is used to match a 50Ω section to a 200Ω section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately:

2. The vector of direction A is radially outward from the origin, with |A| = kr where r = x + y + z and k is a constant. The value of n for which ∇.A = 0 is

3. Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is:

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

5. The current shown is a:

6. The transfer function of a compensator is given as:
G_C(s) = s+a/a+b
G_C(s) = s+a/a+b compensator if

7. The radiation pattern of an antenna in spherical co-ordinates is given by
F(θ) = cosθ; 0 ≤ θ ≤ π/2
The directivity of antenna is

8. The unilateral Laplace transform of f(t) is 1/s² + s +1. The unilateral Laplace transform of tf(t) is.

9. The fourier transformer of a signal h(t) is H(jω) = (2 cosω) (sin 2ω)/ω. The value of h(0) is:

10. The average power delivered to an impedance (4 - j3)Ω by a current 5 cos (100πt + 100)A is

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

12. Given that
A = [-5      -3] and I = [1    0],  the value of A³ is:
2        0                  0    1

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

14. The impedance looking into nodes 1 and 2 in the given circuit is:

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 source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increase the probability of the first symbol by a small amount ε. After encoding, the entropy of the source

17. In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally sized. The device M1is in the linear region if:

18. With initial condition x(1) = 0.5, the solution of the differential equation t dx/dt is

19. A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permitivity 10.89. Given μ₀ = 4π x 10^-7 H/m, ε = 10^-9/36π F/m, the  characteristics impedance of the cable is

20. In the circuit shown

21. The output Y of a 2-bit comparator  is logic 1 whenever the 2 bit input A greater than the 2-bit input B. The number of combinations for which the output is logic 1, is:

22. In a baseband communications link, frequencies up to 3500 Hzare used for signalling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signalling rate in symbols per second is:

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

24. If V_A - V_B = 6V, then V_C - V_D is :

25. The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by E  = 10(â_y + jâ_z) e^-j25x. The frequency and polarization of the wave, respectively, are

26. The input x(t) and output y(t) of a system are related as y(t) = ∫^t_-∞ x(τ)cos(3τ)dτ. The system is:

27. In the circuit shown below, the current through the inductor is

28. The 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:

29. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is:

30. A plane wave propagating in air with E = (8â_x + 6â_y - 5â_z) i^{(ωt + 3x – 4y)} V/m is incident on a perfectly conducting slab positioned at x ≤ 0. The E field of the reflected wave is:

31. If x[n] = (1/3)^|n| - (1/2)ⁿ u[n], then the region of convergence (ROC) of its Z transformer in the Z-plane will be:

32. The current i_b through the base of a silicon npn transistor is 1 + 0.1 cos (1000πt) mA. At 300 K, the r_π in the small signal model of the transistor is:

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

The current in the circuit is:

34. The voltage gain A of the current circuit shown below is:

35. The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is

36. The feedback system shown below oscillates at 2 rad/s when

37. The maximum value of f(x) = x³ - 9x² + 24x + 5 in the interval [1, 6] is:

38. 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:

39. The signal m(t) as shown in applied both to a phase modulator (with k_p as the phase constant) and a frequency modulator (with k_r as the frequency constant) having the same carrier frequency

The ratio k_p/k_f (in rad /Hz) for the phase maximum phase deviation is:

40. The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is
H_z = 3 cos (2.094 x 10²x) cos(2.618x10²y) cos(6.283x10¹⁰t - βz)

The phase velocity V_p of the wave inside the waveguide satisfies