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# Laplace transform mcqs ## Laplace Transform MCQs A Laplace transform mcqs is a mathematical formula that changes a variable function from an actual type to a complex type. The s- domain or a complex frequency-type domain is used to represent these functions. The Laplace transform has a variety of conversion formulae, where the integral is Lf(s) = Integration (0àinfinity) = f(t) e-st dt.

The frequency domain function is denoted as f(s), where “s” is defined as sigma + jw, and f(t) is the time domain function. The bilateral Laplace and Inverse Laplace transform are examples of distinct forms of Laplace transform mcqs.

1. Find the ROC and Laplace transform of e-at u(t).
a) s ⁄ a2+s2
b) a ⁄ a2+s2
c) s2⁄ a2+s2
d) a2⁄ a2+s2

2. In what context is the ROC defined or stated for signals that include both causal and anti-causal terms?
a. Greater than the largest pole
b. Less than the smallest pole
c. Between two poles
d. Cannot be defined

3. For the time-domain signal equation e-at cos t.u(t), what should the laplace transform value be?
a) 1 / s + a with ROC σ > – a
b) ω / (s + a) 2+ ω2with 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. The Laplace transform of a function is 1/8 s1​Eeas. The function is

a) Esin ωt

b) Eeat

c) Eu(t − a)

d) E cos ωt

5. Shifting the signal in time corresponds to the ______ according to the Laplace Transform’s time-shifting feature.

a) Time-domain multiplication via e-st0

b) Frequency domain e-st0 multiplication.

c) Time-domain multiplication by est0

d) Frequency domain multiplication by est0

6. According to the Energy Spectral Density’s (ESD) characteristic, which of the following transform pairs is/are produced between the auto-correlation function and the energy spectral density?

a) Laplace Transform
b. Z-transform
c. Fourier Transform
d. All of the above

7. When a step function is integral, it is

A ramp function

An impulse function

Modified ramp function

A sinusoidal function

8. Which statement, if any, from the list below, is true?

The correlation function’s value increases as the similarity level between two signals increases.

The degree of similarity between two signals decreases as the correlation function value increases.

The degree of similarity between two signals increases as the correlation function’s value decreases.

d) The degree of similarity between two signals decreases as the correlation function’s value decreases.
Only C
b. Only B
c. A & D
d. B & C

9. What characteristic does the auto-correlation function of a complex-valued signal display?
a. Commutative property
b. Distributive property
c. Conjugate property
d. Associative property

10. For the solution of linear constant coefficient differential equations with ________, the unilateral Laplace transform is suitable.
a. Zero initial condition
b. Non-zero initial condition
c. Zero final condition
d. Non-zero final condition

11. The solution of the differential equation, for t > 0, y”(t) + 2y'(t) + y(t) = 0 with initial conditions y(0) = 0 and y'(0) = 1, is (u(t) denotes the unit step function),

text u(t)

(b)(e-1 – te-t) u(t)

(-e-t + te-t) u(t)

(d)e-t u(t)

12. What should be the location of poles corresponding to ROC for bilateral Inverse Laplace Transform, especially for determining the nature of the 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

## Conclusion

Laplace transform mcqs: The Laplace transform is a key technique to analyze systems and solve differential equations. Anyone working with complicated mathematical issues has to be able to master its ideas and characteristics. You may evaluate your knowledge of the Laplace transform mcqs by answering and determining where you still need to improve. To solidify your understanding, don’t forget to go over the right answers and justifications. You’ll soon master using the Laplace transform to resolve problems in the real world if you keep practicing. if you want to play another quiz NEET MCQs Question

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