Region of Convergence MCQ’s

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

1. The impulse response h (t) of a LTI system is given by h (t) = exp (-2t) u (t) where, u (t) denotes the unit step function. The output of this system to the sinusoidal input x(t) = 2 cos(2t) for all t, is _____________
a) 0
b) 2-0.25 cos(2t-0.125π)
c) 2-0.5 cos(2t-0.125π)
d) 2-0.5 cos(2t-0.25π)

2. The ROC of u(n) = _k^nC is __________
a) | z | > 1
b) | z | < 1
c) -1 < | z | < 1
d) -1 < | z |

3. The impulse response h (t) of a LTI system is given by h (t) = exp (-2t) u (t) where, u (t) denotes the unit step function. The frequency response H(ω) is ____________
a) \frac{1}{1+j2ω}
b) \frac{sin⁡ω}{ω}
c) \frac{1}{2+jω}
d) \frac{jω}{2+jω}

4. The Radius of convergence of f(n) = 5n/n!, n≥0 is __________
a) -2<|z|<2
b) Z-plane
c) | z |<2
d) |z| = 2

5. The system under consideration is an RC low-pass filter with R = 1 kΩ and C = 1 µF. Let H (f) denotes the frequency response of the RC, low-pass filter. Let t1(f) be the group delay function of the given RC low-pass filter and f2 = 100 Hz. Then tg(f2) in ms is ___________
a) 0.717
b) 7.17
c) 71.7
d) 4.505

6. Given that X(s) is the Laplace transform of the signal cos 2t u (t). The signal X(3s) corresponds is _______________
a) cos(\frac{2}{3} t) u (t)
b) \frac{1}{3} cos(\frac{2}{3} t) u (t)
c) cos⁡6t u(t)
d) \frac{1}{3} cos⁡6t u(t)

7. The ROC of u(n) = 4n, for n<0; 2n, for n≥0 is ___________
a) 0<z<1
b) z<4
c) 2<z
d) 2<z<4

8. Given that X(s) is the Laplace transform of the signal cos 2t u (t). The time signal corresponding to (s+1) X(s) is _________________
a) (cos 2t – 2 sin 2t) u (t)
b) (cos 2t + \frac{sin⁡2t}{2}) u (t)
c) (cos 2t + 2 sin 2t) u (t)
d) (cos 2t – \frac{sin⁡2t}{2}) u (t)

9. The value of the radius of convergence of f(n) = 2n, n<0 is ____________
a) 0<| z |<1
b) -2<| z |
c) | z |<2
d) z-plane

10. For the system, y (t) = u{x (t)} which of the following holds true?
a) System is Linear, time-invariant, causal and stable
b) System is time-invariant, causal and stable
c) System is causal and stable
d) System is stable

11. For the circuit given below, if the frequency of the source is 50 Hz, then a value of to which results in a transient free response is _________________

a) 0
b) 1.78 ms
c) 7.23 ms
d) 9.21 ms

12. The impulse response of a LTI system which is continuous is H (t) = e-|t|. The system is ___________
a) Causal and stable
b) Causal but not stable
c) Stable but not causal
d) Neither causal nor stable

13. Given, R = 10 Ω, L = 100 mH and C = 10 μF. Selectivity is ____________

a) 10
b) 1.2
c) 0.15
d) 0.1

14. A series RC circuit excited by voltage V is __________
a) A memory less system
b) A causal system
c) A dynamic system
d) Static system

15. The steady state value of F (t), if it is known that F(s) = \frac{b}{s(s+1)(s+a)}, where a>0, is ________________
a) \frac{b}{a}
b) \frac{a}{b}
c) 1
d) Cannot be determined

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