PYQs Based Test - 13 : Laplace Transforms

The Laplace transform of $f\left(t\right)=2\sqrt{\frac{t}{\pi }}$ is $s^{-\frac{3}{2}}$. The Laplace transform of $g\left(t\right)=\sqrt{\frac{1}{\pi t}}$ is

The solution of $\frac{d^{2}y}{d{t}^2}-y=1,$ which additionally satisfies ${y|}_{t=0}={\frac{dy}{dt}|}_{t=0}=0$ in the Laplace s-domain is

If the Laplace transform of y(t) is given by $Y\left(s\right)=L\left(y\left(t\right)\right)=\frac{5}{2\left(s-1\right)}-\frac{2}{s-2}+\frac{1}{2\left(s-3\right)}$, then y(0) + y'(0) = _________.

Let z(t) = x(t) y(t), where “ ” denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct).

If the Laplace transform of function f(t) is given by $\frac{s+3}{(s+1)(s+2)}$, then f(0) is