List of practice Questions

Let \[ f(t)= \begin{cases} \sin t, & 0\le t\le \pi,\\ 0, & t>\pi. \end{cases} \] The Laplace transform of \(f(t)\) is
The Laplace transform of \[ \int_{0}^{t} p\sin(t-p)\,dp \] is
The Laplace transform of \[ \int_{0}^{t} p\sin(t-p)\,dp \] is
Laplace transform of $\int_0^t u^2 \sin(t - u) \, du$ is:
\( \mathcal{L}\{ \sin(t-3)u(t-3) \ = \)}
Laplace transform of $\int_0^t u^2 \sin(t - u) \, du$ is:
\( \mathcal{L}\{ \sin(t-3)u(t-3) \ = \)}
The inverse Laplace transform of $F(s) = \frac{s^2 - 3s + 4}{s^3}$ is _______}
What does the Laplace transform do the differential equation of an RLC circuit?
If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is
If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is
The inverse Laplace transform of $\frac{s+3}{s^2 - 4s + 13}$ is:}

Match List-I (Time domain function) with List-II (Laplace transform).

If $a = cos\theta + i \cdot sin\theta$ then $1+a^{2}$ is:
For $6x^2 - 12y^2 = -36$ hyperbola, the lengths of conjugate axis and latus-rectum, respectively, are:
The solution of Laplace’s equation satisfies which condition?
The Fourier transform of a real-valued time signal has
A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ is
The Laplace transform of \( \cos\sqrt{t} \) is:

If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is

Let \(y(t)\) be the solution of the differential equation \(y''+4y=0\), \(y(0)=1\), \(y'(0)=-6\), then the Laplace transformation \(Y(s)\) of the solution is equal to
Which of the options correctly represents the Laplace inverse of \( \dfrac{2}{s^3} \)?
If the Laplace transform of a function \( f(t) \) is given by \[ \frac{2s + 1}{(s + 1)(s + 2)} \] then \( f(0) \) is equal to ______
If the Laplace transform of a function \( f(t) \) is given by \( \frac{2s + 1}{(s + 1)(s + 2)} \), then \( f(0) \) is equal to ...........
The Laplace transform of \( e^{-2t} \cos(\sqrt{2} t) \) is .......