# Properties of ROC MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of ROC”.

1. If H(f) = \frac{y(t)}{x(t)}, then for this to be true x(t) is ___________
a) exp(\frac{j2nf}{t})
b) exp(-\frac{j2nf}{t})
c) exp(j2nft)
d) exp(-j2nft)

2. The z-transform of –u(-n-1) is ___________
a) \frac{1}{1-z}
b) \frac{z}{1-z}
c) \frac{1}{1-z^{-1}}
d) \frac{z}{1-z^{-1}}

3. Given a system function H(s) = \frac{1}{s+3}. Let us consider a signal sin 2t. Then the steady state response is ___________
a) \frac{1}{8}
b) Infinite
c) 0
d) 8

4. The value of z(ak u[-k]) is _______________
a) \frac{z}{z-a}
b) \frac{z}{a-z}
c) \frac{z^2}{z-a}
d) \frac{a}{a-z}

5. Given 2 signals (-3)k u(k) and u (k-1). These two signals are superimposed. This superimposed signal is _______________
a) \frac{z}{z+3} + \frac{1}{z-1}
b) \frac{z}{z+3} – \frac{1}{z-1}
c) \frac{z}{z-3} + \frac{1}{z-1}
d) \frac{z}{z+3} + \frac{1}{z+1}

6. The value of z{[k-1] u(k)} is _______________
a) \frac{z(z+2)}{(z-1)^2}
b) \frac{2z-z^2}{(z-1)^2}
c) \frac{z^2}{(z-1)^2}
d) \frac{z(z-2)}{(z+1)^2}

7. If a system has N different poles, then the system can have ______________
a) N ROC’s
b) (N-1) ROC’s
c) (N+1) ROC’s
d) 2N ROC’s

8. X1(z) = 2z + 1 + z-1 and X2(z) = z + 1 + 2z-1 is ________________
a) Even signal
b) Odd signal
c) In time power signal
d) In time energy signal

9. The area under Gaussian pulse \int_{-∞}^∞ e^{{-π}^{{t}^2}} \,dt is ___________
a) Unity
b) Infinity
c) Pulse
d) Zero

10. The spectral density of white noise is ____________
a) Exponential
b) Uniform
c) Poisson
d) Gaussian

11. A current I given by I = – 8 + 6\sqrt{2} (sin (ωt + 30°)) A is passed through three meters. The respective readings (in ampere) will be?
a) 8, 6 and 10
b) 8, 6 and 8
c) – 8, 10 and 10
d) -8, 2 and 2

12. The system x(k) = 7(\frac{1}{3})k u(-k-1)-6(\frac{1}{2})k u(k) is ___________
a) Causal
b) Anti-causal
c) Non-causal
d) Cannot be determined

13. In the circuit given below, the value of ZL for maximum power to be transferred is _____________

a) R
b) R + jωL
c) R – jωL
d) jωL

14. The CDF for a certain random variable is given as F(x) = {0, -∞<x≤0; kx2, 0<x≤10; 100k, 10<x<∞;} The value of k is __________
a) 100
b) 50
c) 1/50
d) 1/100

15. For a stable system which of the following is correct?
a) |z| < 1
b) |z| = 1
c) |z| > 1
d) |z| ≠ 1

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