# 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) = x2(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{sin⁡πt}{π} [u (t+1) – u(t-1)]
b) \frac{sin⁡πt}{π} u(t-1)
c) \frac{sin⁡πt}{π} u(t+1)
d) \frac{sin⁡πt}{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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