1
GATE EE 2011
+2
-0.6
Let the Laplace transform of a function f(t) which exists for t > 0 be F1(s) and the Laplace transform of its delayed version f(1 - $$\tau$$) be F2(s). Let F1*(s) be the complex conjugate of F1(s) with the Laplace variable set as $$s=\sigma\;+\;j\omega$$. If G(s) =$$\frac{F_2\left(s\right).F_1^\ast\left(s\right)}{\left|F_1\left(s\right)\right|^2}$$ , then the inverse Laplace transform of G(s) is
A
An ideal impulse $$\delta\left(t\right)$$
B
An ideal delayed impulse $$\delta\left(t-\tau\right)$$
C
An ideal step function u(t)
D
An ideal delayed step function $$u\left(t-\tau\right)$$
2
GATE EE 2008
+2
-0.6
A function y(t) satisfies the following differential equation:$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\left(t\right)$$\$ where $$\delta\left(t\right)$$ is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form
A
et
B
e-t
C
etu(t)
D
e-tu(t)
3
GATE EE 2005
+2
-0.6
The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches
A
3
B
5
C
17/2
D
$$\infty$$
4
GATE EE 2005
+2
-0.6
For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$\rightarrow\infty$$ ?
A
0
B
5/2
C
5
D
10
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