1.Given a continuous-time periodic signal
 Let a_k and ω₀, be the coefficients and fundamental frequency of the Fourier series of f(t) respectively. Then which of the following statements is correct?
(A)
(B)
(C)
(D)a₀＜5,ω₀＜2,a₅＞0.
(E) None of the above statements are correct.

2.Consider a discrete signal x(n) = cos(2nr / N), where integer N is the fundamental period. Let a be the coefficients of the discrete-time Fourier series of x(n). Then which of the following statements is correct? (A) a1=-1/2,a2=1/2. (B) a1=a2=j/2 (C) (D) (E) None of the above statements are correct.

3.Consider an LTI system whose impulse response is G(jω)=1/(a+ jω), a ＞ 0. Suppose that there is an input signal X(jω)=1/(a+ jω). Assume that the output signal is y(t)= , where u(t) is a unit-step signal. Then which of the following statements is correct? (A)β+y=-a (B) βy=-a (C) β-y=t+a (D) βy=at (E) None of the above statements are correct.

4.Consider the following three systems, where [n] or x(t) is the system input, y[n] or y(t) denotes the system output, and I.Which of the following statements is correct? (A) I is time-invariant, II is linear, Ill is causal. (B) I is memoryless, II is causal, III is nonlincar. (C) I is stable, II is linear, III is memoryless. (D) I is causal, II is memoryless, III is linear. (E) None of the above statements are correct.

5. Let z =1- . Assume that , whereθ denotes the principal argument. Then which of the following statements is correct? (A) r =2,θ =π/5 (B)(C)(D) (E) None of the above statements are correct.

6.Which one of the following functions, where z = x+ jy is a complex variable, is analytic? (A) f(2)=, where =x-jy. (B) f(z) = xy+jx (C)f(z)=x2ーjy2 (D) f(z)=x2+y2+j2xy (E) None of the above statements are correct.

7.Let z be a complex number. Which of the following statements is correct? (A) Log(z1/z2) = Log(z1)+ Log(z2), where Log(z) is the principal value of the complex logarithm. (B) cos(j) is not a real value.(C) , n=0,±1,±2,......(D) z2+2z-ez=,where exp(2)=ez. (E) None of the above statements are correct.

8. Let f(z)=z/(z2+9), and C be a circle|z - j2|=4 in counterclockwise direction. The evaluation of. Then which of the following statements is correct? (A) a＜0,β＞0 (B) a ＞0,β＞0 (C)a=0,1＜β＜4 (D) a＞0, -3＜β＜4 (E) None of the above statements are correct.

9. Let f(z)=, and C be the right-hand half of the circle|z|=2 form z = j2 to z =-j2. Compute the value of S. f(z)dz =a+ jB. Then which of the following statements is correct? (A) a=0,-15＜β＜0 (B) a＞0,0＜β＜15 (C)-12＜a+β＜l2 (D)-2＜aβ＜-12 (E) None of the above statements are correct

10. The Laurent series of is Which of the following statements is correct? (A) aβ=1/6 (B) aβ=1/12 (C) a+β=5/6 (D)a+β=1/3 (E) None of the above statements are correct. 

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