Q1:

An absolutely integrable signal x(t) is known to have Laplace transform with only one pole at s = 2 then x(t) is

Q2:

A causal LTI system with impulse response h(t) has following properties .

1.Output is $\frac{1}{6}{e}^{2t}$ for all t when input is $x\left(t\right)=e^{2t}$

2.The h(t) satisfies following differential equation $\frac{d}{dt}h\left(t\right)+2\text{ h(t)}=e^{-4t}u(t)+k\text{ u(t)}\text{.what will be the value of k}\text{.}$

Q3:

$Ifg(t)\to G\left(s\right)=\frac{s+2}{(s^2+4)}\text{ then f(t)=g(2t) }\text{. find f}\left(s\right)$

Q4:

Consider the system described by y'(t) + 2y(t) = x(t) + x'(t) .Find the impulse response of the system

Q5:

The Laplace transform of $e^{-b\left|t\right|}$ exist , if and only  if _____ and the Laplace transform is

Q6:

$LetX\left(s\right)=\frac{3s+5}{s^2+10s+21}$. be the Laplace transform of a signal x(t). Then x$\left(o^{+}\right)$is

Q7:

A signal $x_1(t)$with Laplace transform $X_1\left(S\right)$has R.O.C $\sigma$> - 6 and single $x_2$(t) with Laplace transform $X_2(s)$ had R.O.C as $\sigma$>3. What is the R.O.C of Y(s).

$y\left(t\right)=x_1\left(t+3\right) \times \text{}\text{}{x}_2\left(-t+2\right)$

Q8:

Function u(t+1)$\ast$r (t-2) is given by

Q9:

The Laplace transform of a function f(t) is $F\left(s\right)=\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)};$at $t\to \infty$ f(t) is equal to

Q10:

Find Laplace transform of $x\left(t\right)=sgn\left(t\right).$ 

Q11:

The value at $t=\infty$ for the given  $F\left(s\right)=\frac{s+2}{s\left(s-2\right)}\text{ is}$

Q12:

An absolutely integrable signal x(t) is known to have Laplace transform with only one pole at $s=2$ then x(t) is

Q13:

If inverse Laplace transform of $\frac{2s+5}{s^2+5s+6}$is $e^{-2t}u(t)-e^{-3t}u(-t)$than ROC will be

Q14:

Let Y(s) be the Laplace transform of the function y(t) than the final value of the function is:-

Q15:

A rectangular current pulse of duration T and magnitude I has the Laplace transform