## Introduction to Systems MCQ

Introduction to Systems MCQ, Multiple Choice Questions on Systems, Signal & Systems MCQ, Engineering MCQ, Causal System MCQ, Non-Causal System MCQ, Discrete-Time System MCQ, Linear System MCQ, Non-Linear System MCQ

### Multiple Choice Questions

Q.1. Consider the following statements regarding a discrete system with the out-put input relationship y(n)=x(n)+3. The system

- is linear
- is causal
- have bounded input for bounded output
- is non-realisable

- 1, 2, and 3 are correct
- 2 and 3 are correct
- 1 and 2 are correct
- 1, 3 and 4 are correct

**Answer: **2 and 3 are correct

Q.2. Which are of the following system is nonlinear?

- y(t)=2x(t-1)-3x(t-2)+x(t-3)
- y(t)=5x(t)
- y(t)=2x(t-1)-x(t-2)+x(t-4)
- y(t)=2x(t)+3.6

**Answer:** y(t)=2x(t)+3.6

Q.3. Which are of the following systems are invertible?

- y(n)=nx(n)
- y(n)=x(n)x(n-1)
- y(n)=\frac{\mathrm{d} x(t)}{\mathrm{d} x}
- y(n)=x(1-n)

**Answer:** y(n)=x(1-n)

Q.4. Which are of the following pairs is NOT correctly matched?

- unstable system \frac{\mathrm{d}y }{\mathrm{d} x}-0.1y(t)=x(t)
- Nonlinear system \frac{\mathrm{d}y }{\mathrm{d} x}+2t^{2}y(t)=x(t)
- Noncausal system y(t)=x(t+2)
- Nondynamic system y(t)=3x^{2}(t)

**Answer:** Nonlinear system \frac{\mathrm{d}y }{\mathrm{d} x}+2t^{2}y(t)=x(t)

Q.5. The discrete-time equation y(n+1)+0.5ny(n)=0.5x(n+1) is not attributable to a

- memory less system
- time-varying system
- linear system
- causal system

**Answer:** memory less system

Q.6. A continuous-lime system is governed by the equation 3y^{3}(t)+2y^{2}(t)+y(t)=x^{2}(t)+x(t), The system is

- linear and dynamic
- linear and non-dynamic
- non-linear and dynamic
- non-linear and non-dynamic

**Answer:** non-linear and non-dynamic

Q.7. Which one of the following systems is a causal system

- y(t)=\sin [u(t+3)]
- y(t)=5u(t) +3u(t-1)
- y(t)=5u(t) +3u(t+1)
- y(t)=\sin [u(t-3)]+\sin [u(t+3)]

**Answer:** y(t)=5u(t) +3u(t-1)

Q.8. Which one of the following is the response *y(t)* of a causal LTI system described by H(s)=\frac{s+1}{s^{2}+2s+2}, for a given input x(t)=e^{-t}u(t)

- y(t)=e^{-t}\sin tu(t)
- y(t)=e^{-(t-1)}\sin (t-1)u(t-1)
- y(t)=\sin (t-1)u(t-1)
- y(t)=e^{-t}\cos tu(t)

**Answer:** y(t)=e^{-t}\sin tu(t)

Q.9. The discrete time system described by y(n)=x(n^{2}) is

- causal, linear and time variant
- causal, linear and time variant
- non-causal, linear and time invariant
- non-causal, linear and time-variant

**Answer:** non-causal, linear and time-variant

Q.10. The system y(n)=x(Mn), -\infty < n< \infty where *M* is a positive constant is

- shift variant
- shift invariant
- non-causal
- causal

**Answer:** shift variant & non-causal

Q.11. The system y(n+2)+y(n+1)=x(n+2) is

- causal and memory less
- causal and has memory
- is causal
- is non-causal

**Answer:** causal and has memory

Q.12. For the systems shown below which of the systems are linear?

- \frac{\mathrm{d}y }{\mathrm{d} x}+2y(t)=f(t)\frac{\mathrm{d} f}{\mathrm{d} x}
- \frac{\mathrm{d}y }{\mathrm{d} x}+y^{2}(t)=f(t)
- \frac{\mathrm{d}y }{\mathrm{d} x}+2y(t)=f(t)
- \frac{\mathrm{d}y }{\mathrm{d} x}+2ty(t)=f(t)

**Answer:** \frac{\mathrm{d}y }{\mathrm{d} x}+2y(t)=f(t) & \frac{\mathrm{d}y }{\mathrm{d} x}+2ty(t)=f(t)

Q.13. Which of the following systems is time-invariant?

- y(t)=x(2t)
- y(t)=x(t)+x(t-1)
- y(t)=x(t/2)
- y(t)=x(-t)

**Answer:** y(t)=x(t)+x(t-1)

Q.14. The system y(t)=x(3t-6) is

- linear, time variant
- linear, time invariant
- nonlinear, time variant
- nonlinear, time invariant

**Answer:** linear, time variant

Q.15. The system y(n)=x(n)x(n-1) is

- dynamic and linear
- dynamic, nonlinear
- causal and time invariant
- noncausal, time variant
**Answer:**dynamic and nonlinear & causal and time invariant

Q.16. Which of the following systems is invertible?

- y(t)=\int_{-\infty }^{t}x(t)d\tau
- y(t)=x(2t-3)
- y(t)=\cos [x(t)]
- y(t)=x^{n}(t) n integer

**Answer:** y(t)=\int_{-\infty }^{t}x(t)d\tau & y(t)=x(2t-3)

Q.17. The system y(t)=e^{x(t)} is

- Stable, causal
- noncausal, stable
- unstable, causal
- unstable noncausal

**Answer:** Stable, causal

Q.18. The system y(n)=\cos [x(n)] is

- stable, linear, time variant
- stable, nonlinear, time invariant
- unstable, nonlinear, time variant
- unstable, linear, time invariant

**Answer:** stable, nonlinear, time invariant

Q.19. Which of the following system are BIBO stable?

- y(n)=\sum_{k=-\infty }^{\infty }x(k)
- y(n)=a^{x(n)}
- y(n)=\left|x(n) \right|
- y(n)=log_{10}[x(n)]

**Answer:** y(n)=a^{x(n)}, y(n)=\left|x(n) \right| & y(n)=log_{10}[x(n)]

Q.20. If *x(t)* is the input and *y(t)* is zero-state response to *y(t)* then the system y(t)=\int_{-\infty }^{t}tx(\lambda )d\lambda is

- causal, static
- causal, dynamic
- noncausal, dynamic
- non-causal, static

**Answer:** causal, dynamic