Question 21. The radiation pattern of an antenna in spherical co-ordinates is given byF(θ) = cos4 θ; 0 ≤ θ ≤ π /2The directivity of the antenna is

Question 22. 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

Question 23. A system with transfer functionG(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

Question 24. In the sum of products function f (X, Y, Z) = Σ(2, 3, 4, 5) , the prime implicants are

Question 25. 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

Question 26. 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

Question 27. If x = √-1 , then the value of xx is

Question 28. 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

Question 29. 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

Question 30. The Fourier transform of a signal h(t) is H(jw) = (2cosw)(sin2w) /w . The value of h(0) is