1
GATE EE 2024
MCQ (Single Correct Answer)
+1
-0.33

If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal $x(t) = e^{t^2}[u(t-1)-u(t-10)]$ is

A

$-\infty < \text{Re}(s) < \infty$

B

$\text{Re}(s) \ge 10$

C

$\text{Re}(s) \le 1$

D

$1 \le \text{Re}(s) \le 10$

2
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+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
$$s^{3/2}$$
3
GATE EE 2013
MCQ (Single Correct Answer)
+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
4
GATE EE 2012
MCQ (Single Correct Answer)
+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
$$\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
GATE EE Subjects
EXAM MAP