Laplace Transform - MCQs with answers

Laplace Transform - MCQs with answers

1. A Laplace Transform exists when ______

A. The function is piece-wise continuous
B. The function is of exponential order
C. The function is piecewise discrete
D. The function is of differential order

a. A & B
b. C & D
c. A & D
d. B & C

2. Where is the ROC defined or specified for the signals containing causal as well as anti-causal terms?

a. Greater than the largest pole
b. Less than the smallest pole
c. Between two poles
d. Cannot be defined

3. What should be the value of laplace transform for the time-domain signal equation e-at cos ωt.u(t)?

a. 1 / s + a with ROC σ > - a

b. ω / (s + a) 2 + ω2 with ROC σ > - a

c. s + a / (s + a)2 + ω2 with ROC σ > - a

d. Aω / s2 + ω2 with ROC σ > 0

ANSWER: c. s + a / (s + a)2 + ω2 with ROC σ > - a

4. According to the time-shifting property of Laplace Transform, shifting the signal in time domain corresponds to the ______

a. Multiplication by e-st0 in the time domain

b. Multiplication by e-st0 in the frequency domain

c. Multiplication by est0 in the time domain

d. Multiplication by est0 in the frequency domain

ANSWER: b. Multiplication by e-st0 in the frequency domain

5. Which result is generated/ obtained by the addition of a step to a ramp function ?

a. Step Function shifted by an amount equal to ramp
b. Ramp Function shifted by an amount equal to step
c. Ramp function of zero slope
d. Step function of zero slope

ANSWER: b. Ramp Function shifted by an amount equal to step

6. Unilateral Laplace Transform is applicable for the determination of linear constant coefficient differential equations with ________

a. Zero initial condition
b. Non-zero initial condition
c. Zero final condition
d. Non-zero final condition

7. What should be location of poles corresponding to ROC for bilateral Inverse Laplace Transform especially for determining the nature of time domain signal?

a. On L.H.S of ROC
b. On R.H.S of ROC
c. On both sides of ROC
d. None of the above

ANSWER: c. On both sides of ROC

8. Generally, the convolution process associated with the Laplace Transform in time domain results into________
a. Simple multiplication in complex frequency domain
b. Simple division in complex frequency domain
c. Simple multiplication in complex time domain
d. Simple division in complex time domain

ANSWER: a. Simple multiplication in complex frequency domain

9. An impulse response of the system at initially rest condition is basically a response to its input & hence also regarded as,

a. Black's function
b. Red's function
c. Green's function
d. None of the above

10. When is the system said to be causal as well as stable in accordance to pole/zero of ROC specified by system transfer function?

a. Only if all the poles of system transfer function lie in left-half of S-plane

b. Only if all the poles of system transfer function lie in right-half of S-plane

c. Only if all the poles of system transfer function lie at the centre of S-plane

d. None of the above