# Properties of Systems – 5 MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Systems – 5″.

1. For the system y (t) = ∑_{k=-∞}^n x(k), which of the following holds true?

a) Invertible

b) Non-Invertible

c) Invertible as well as Non-Invertible in its respective domains

d) Cannot be determined

2. 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

3. For the system y (t) = x^{2}(t), which of the following holds true?

a) Invertible

b) Non-Invertible

c) Invertible as well as Non-Invertible in its respective domains

d) Cannot be determined

4. For the system, y (t) = x (t-5) – x (3-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 Linear, time-invariant and stable

d) System is Linear, time-invariant and causal

5. For the system, y (t) = cos 2πt 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 Linear, causal and stable

d) System is Linear, time-invariant and stable

6. For the system, t\frac{dy (t)}{dt} – 8 y (t) = x (t), which of the following holds true?

a) System is Linear, time-invariant, causal and stable

b) System is Linear, time-invariant and causal

c) System is time-invariant, causal and stable

d) System is Linear, causal and stable

7. For the system, y (t) = x (\frac{t}{2}), which of the following holds true?

a) System is Linear, time-invariant, causal and stable

b) System is Linear and time-invariant

c) System is Linear and causal

d) System is Linear and stable

8. For the system, y (t) = |x (t)|, which of the following holds true?

a) System is Linear, time-invariant, causal and stable

b) System is Linear, time-invariant and causal

c) System is Linear, time-invariant and stable

d) System is Linear, causal and stable

9. For the system, y (t) = \int_{-∞}^{t+3} x(t) \,dt, which of the following holds true?

a) System is Linear, time-invariant and causal

b) System is time-invariant and causal

c) System is Linear and time-invariant

d) System is Linear and stable

10. The impulse response of a continuous time LTI system 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

11. The impulse response of a continuous time LTI system is H (t) = e^{-t} u (t-2). The system is __________

a) Causal and stable

b) Causal but not stable

c) Stable but not causal

d) Neither causal nor stable

12. The impulse response of a continuous time LTI system is H (t) = (2e^{-2t} -e^{\frac{t-100}{100}}) \,u (t). The system is ____________

a) Causal and stable

b) Causal but not stable

c) Stable but not causal

d) Neither causal nor stable

13. The impulse response of a continuous time LTI system is H (t) = e^{-t} u (3-t). The system is __________

a) Causal and stable

b) Causal but not stable

c) Stable but not causal

d) Neither causal nor stable

14. The continuous time convolution integral y(t) = cos πt [u (t+1) – u (t-1) * u(t)] is __________

a) \frac{sinπt}{π} [u (t+1) – u(t-1)]

b) \frac{sinπt}{π} u(t-1)

c) \frac{sinπt}{π} u(t+1)

d) \frac{sinπt}{π} u(t)

15. The continuous time convolution integral y(t) = e-3tu(t) * u(t+3) is ___________

a) \frac{1}{3}[1 – e^{-3(t+3)}] u(t+3)

b) \frac{1}{3}[1 – e^{-3(t+3)}] u(t)

c) \frac{1}{3}[1 – e^{-3t}] u(t)

d) \frac{1}{3}[1 – e^{-3t}] u(t+3)

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