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
GATE EE Subjects
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics
Digital Electronics
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