What is the Laplace transform of impulse input having magnitude 'X'?

Answer: Option A

The correct answer is A: X.
Here's why:
An impulse function (also called a Dirac delta function) is a signal that is infinitely short and has an area of 1.
When the impulse has a magnitude of 'X', it means its area is 'X' instead of 1.
The Laplace transform is a mathematical tool used to convert time-domain functions (like signals) into the frequency domain.
A key property of the Laplace transform is that the Laplace transform of the unit impulse function (magnitude 1) is 1.
Since our impulse has a magnitude of 'X', we can think of it as 'X' times the unit impulse function.
The Laplace transform is a linear operator, meaning the Laplace transform of X * f(t) is X * F(s), where F(s) is the Laplace transform of f(t).
Therefore, the Laplace transform of an impulse with magnitude 'X' is X * 1 = X.