# Definition of the Laplace Transform MCQ’s

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Definition of the Laplace Transform”.

1. Laplace transform changes the ____ domain function to the _____ domain function.

a) time, time

b) time, frequency

c) frequency, time

d) frequency, frequency

2. In the bilateral Laplace transform, the lower limit is?

a) 0

b) 1

c) ∞

d) – ∞

3. The Laplace transform of a function f (t) is?

a) ∫∞0 f(t) e^{-st}

b) ∫0−∞ f(t) e^{-st}

c) ∫∞0 f(t) e^{st}

d) ∫0−∞ f(t) e^{st}

4. The unit step is not defined at t =?

a) 0

b) 1

c) 2

d) 3

5. Find the function f_{2} (t) from the time t = 1 to 3 sec.

a) (-10t+20) [u (t-1) +u (t-3)]b) (-10t+20) [u (t-1) – u (t-3)]c) (-10t-20) [u (t-1) + u (t-3)]d) (-10t-20) [u (t-1) – u (t-3)]

6. Find the expression of f (t) in the graph shown below.

a) 10t [u (t) – u (t – 1)] – (-10t+20) [u (t-1) – u (t-3)] + (20t – 40) [u (t-3) – u (t-4)]b) 10t [u (t) – u (t – 1)] – (-10t+20) [u (t-1) – u (t-3)] – (20t – 40) [u (t-3) – u (t-4)]c) 10t [u (t) – u (t – 1)] + (-10t+20) [u (t-1) – u (t-3)] + (20t – 40) [u (t-3) – u (t-4)]d) 10t [u (t) – u (t – 1)] + (-10t+20) [u (t-1) – u (t-3)] – (20t – 40) [u (t-3) – u (t-4)]

7. The total period of the function shown in the figure is 4 sec and the amplitude is 10. Find the function f_{1} (t) from t = 0 to 1 in terms of unit step function.

a) 10t [u (t) – u (t + 1)]b) 10t [u (t) + u (t – 1)]c) 10t [u (t) + u (t + 1)]d) 10t [u (t) – u (t – 1)]

8. Find the function f_{3} (t) from the time t = 3 to 4 sec.

a) (20t – 40) [u (t-3) – u (t-4)]b) (20t + 40) [u (t-3) – u (t-4)]c) (20t + 40) [u (t-3) + u (t-4)]d) (20t – 40) [u (t-3) + u (t-4)]

9. In the graph shown below, find the expression f (t).

a) 2t

b) 3t

c) 4t

d) 5t

10. Find the function f (t) in terms of unit step function in the graph shown below.

a) 4t [u (t) – u (t + 5)]b) 4t [u (t) + u (t + 5)]c) 4t [u (t) – u (t – 5)]d) 4t [u (t) + u (t – 5)]