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21.  Total electric field intensity is given as (V/m). The maximum value of will occur; if and only if 

Answer: Option B Explanation: To find value of y at which E will be maximum, differentiable E_{T} with respect to y and set it equal to zero. 
22.  The effective length of an 1/2 antenna (Given R_{r} = 73 Ω and (A_{e})_{max} = 0.34λ^{2} and η = 120p) is __________ . 

Answer: Option B Explanation:
= l_{e} = 0.5133λ. 
23.  Find Z_{11}, 

Answer: Option C Explanation:
Z_{11}(s) = Z_{1}(s) + Z_{2}(s) = 1 Ω. 
24.  Consider a Binary Symmetric Channel (BSC) with probability of error being p. To transmit a bit, say 1, we transmit a sequence of three 1 s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is 

Answer: Option A Explanation: Probability of error = P Thus probability of no error = (1  P) Now probability that transmitted bit, received in error = all bits are with error + one bit is with error = P^{3} + 3C_{1}P^{2} (1  P) = P^{3} + 3P^{2} (1  P). 
25.  Consider the sequence x(n) whose fourier transform X(e^{jω}) is depicted for  p ≤ ω ≤ p as shown in figure


Answer: Option B Explanation: Accordingly, we note first that periodicity in the time domain implies that the Fourier transform is zero, except possibly for impulses located at various integer multiples of the fundamental frequency. This is not true for X(e^{jω}). We conclude, then, that x[n] is not periodic. Next, from the symmetry properties for Fourier Transforms, we know that a real valued sequence must have a Fourier transform of even magnitude and a phase function that is odd. This is true for the given X(e^{jω}) and ∠X(e^{jω}). We thus conclude that x[n] is real. Third, if x[n] is an even function, then, by the symmetry properties for real signals, X(e^{jω}) must be real and even. However, since X(e^{jω}) = X(e^{jω}) e^{j2ω}, X(e^{jω}) is not a realvalued function. Consequently, x[n] is not even. Finally, to test for the finiteenergy property, we may use Parseval's relation, X(e^{jω})^{2} dω It is clear that integrating X(e^{jω})^{2} from  p to p will yield a finite quantity. We conclude that x[n] has finite energy. 