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# Test: Laplace Transform- 2

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

Test: Laplace Transform- 2 for GATE 2022 is part of GATE ECE (Electronics) 2023 Mock Test Series preparation. The Test: Laplace Transform- 2 questions and answers have been prepared according to the GATE exam syllabus.The Test: Laplace Transform- 2 MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Laplace Transform- 2 below.
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Test: Laplace Transform- 2 - Question 1

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

Detailed Solution for Test: Laplace Transform- 2 - Question 1

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

Test: Laplace Transform- 2 - Question 2

### The transfer function H(S) of a stable system is the impulse response is

Detailed Solution for Test: Laplace Transform- 2 - Question 2

System is stable
⇒

Test: Laplace Transform- 2 - Question 3

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

Test: Laplace Transform- 2 - Question 4

Find the laplace transform of time function shown in figure.

Detailed Solution for Test: Laplace Transform- 2 - Question 4

Taking laplace,

Test: Laplace Transform- 2 - Question 5

Consider the following signal:

the laplace transform of above system is

Test: Laplace Transform- 2 - Question 6

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

The time domain signal x(t) is equal to

Test: Laplace Transform- 2 - Question 7

Given that:

then, L[h(t)] is

Detailed Solution for Test: Laplace Transform- 2 - Question 7

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

Test: Laplace Transform- 2 - 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,

Detailed Solution for Test: Laplace Transform- 2 - Question 8

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.

Test: Laplace Transform- 2 - 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:

Test: Laplace Transform- 2 - Question 10

The lapiace transform of

Detailed Solution for Test: Laplace Transform- 2 - Question 10

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## GATE ECE (Electronics) 2023 Mock Test Series

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