# Difference Equations MCQ’s

This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Difference Equations”.

1. Difference equation is used in :
a) Discrete time analysis
b) Continuous time analysis
c) Digital analysis
d) None of the mentioned

2. Difference equation in discrete systems is similar to the _____________ in continuous systems.
a) Difference equation
b) Differential equation
d) None of the mentioned

3. Difference equation model results in:
a) Sampled-data systems
b) Numerical analysis of continuous time systems
c) Continuous time feedback systems
d) Both a and b

4. Difference equation solution yields at the sampling instants only:
a) True
b) False

5. Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.
Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is false

6. If X(z) =(z+z-3)/(z+z-1), then x(n) series has:
a) Alternate 0s
b) Alternate 1s
c) Alternate 2s
d) Alternate -1s

7. Difference equation technique for higher order systems is used in:
a) Laplace transform
b) Fourier transform
c) Z-transform
d) None of the mentioned

8. The poles of a digital filter with linear phase response can lie
a) Only at z =0
b) Only on the unit circle
c) Only inside the unit circle but not at z =0
d) On the left side of Real (z) =0 line

9. Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.
Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true bit R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true

10. Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.
Reason (R): For a rational system, ROC is bounded by poles
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true bit R is NOT the correct explanation of A
c) A is true but R is false
d) A is false but R is true