1
GATE EE 2015 Set 2
+1
-0.3
The Laplace transform of f(t)=$$2\sqrt{t/\mathrm\pi}$$ is $$s^{-3/2}$$. The Laplace transform of g(t)=$$\sqrt{1/\mathrm{πt}}$$ is
A
$$\left(3s^{-5/2}\right)/2$$
B
$$s^{-1/2}$$
C
$$s^{1/2}$$
D
$$s^{3/2}$$
2
GATE EE 2013
+1
-0.3
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A
All the poles of the system must lie on the left side of the j$$\mathrm\omega$$ axis
B
Zeros of the system can lie anywhere in the s-plane
C
All the poles must lie within $$\left|s\right|=1$$
D
All the roots of the characteristic equation must be located on the left side of the j$$\mathrm\omega$$ axis
3
GATE EE 2012
+1
-0.3
The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is
A
$$-\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
B
$$-\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
C
$$\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
D
$$\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
4
GATE EE 2002
+1
-0.3
Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is
A
$$\underset{s\rightarrow0}{L\mathrm{im}\;}Y\left(s\right)$$
B
$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}Y\left(s\right)$$
C
$$\underset{s\rightarrow0}{L\mathrm{im}\;}sY\left(s\right)$$
D
$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}sY\left(s\right)$$
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