Test: Laplace Transform- 2


10 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Laplace Transform- 2


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Attempt Test: Laplace Transform- 2 | 10 questions in 30 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for GATE Exam | Download free PDF with solutions
QUESTION: 1

Consider the function f(t) having Laplace transform,the final value of f(t) would be

Solution:


L-1[F(S)] = sin ω0t
f(t) - sin ω0t
So, - 1 < f(∞) <1

QUESTION: 2

The transfer function H(S) of a stable system is

the impulse response is

Solution:


System is stable
⇒ 

QUESTION: 3

If L[f(t)] = then f(0+) and f(∞) are given by

Solution:
QUESTION: 4

Find the laplace transform of time function shown in figure.

Solution:


Taking laplace,

QUESTION: 5

Consider the following signal:

the laplace transform of above system is

Solution:
QUESTION: 6

Consider a signal x(t) having laplace transform given by,

The time domain signal x(t) is equal to

Solution:
QUESTION: 7

Given that:

then, L[h(t)] is

Solution:

Convolution in time domain is multiplication in s-domain.
∴ 

QUESTION: 8

A causal LTI system is described by the difference equation, 2y[n] = αy[n- 2] - 2x[n] + βx[n - 1]. The system is stable only if,

Solution:


Taking z-transform



For system to bs stable, β can be of any value.

⇒ 
For system to be stable all poles should be inside unity circle.

QUESTION: 9

Match List-I (Function in time domain) with List-II (Corresponding Laplace Transform F(S)) and select the correct answer using the codes given below the lists:
List-I
A. 
B.
C.
D.
List-II
1.
2. 
3. 
4. 
Codes:

Solution:
QUESTION: 10

The lapiace transform of 

Solution:

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