# Introduction to Systems MCQ

## 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

Introduction to Signals 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

1. is linear
2. is causal
3. have bounded input for bounded output
4. 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

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

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

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

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

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

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

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

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