# GATE-2012 ECE Q34 (signals)

Question 34 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

## Solution

Let us Laplace transform to find  and later

,  where with real numbers  and .

Using integration by parts,

.

Rearranging,

.

Extending this to find the Laplace Transform of the second derivative of the function,

.

Coming back to the problem,

Taking Laplace transform,

.

To find the inverse Laplace transform, let us revisit the Laplace transform for some simple functions.

For , the Laplace transform is,
.

.

Also from the earlier discussion in this post,

Applying the above equations to find the inverse Laplace transform

.

Taking the differential,

.

Plugging in  ,

Based on the above, the right choice is (D) 1

## References

 GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf

 Wiki entry on Laplace transform of function’s derivative