Question Bank • QB_SUB_EM_0147 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = e^{3t}$ for $s > 3$ is:

Options:

  • (A) $\frac{1}{s - 3}$
  • (B) $\frac{1}{s + 3}$
  • (C) $\frac{3}{s^2 + 3^2}$
  • (D) $\frac{s}{s^2 - 3^2}$

Answer Key:

A

Step-by-Step Solution & Explanation

$\mathcal{L}\{e^{at}\} = \int_0^\infty e^{-st} e^{at}\, dt = \int_0^\infty e^{-(s-a)t}\, dt = \frac{1}{s - a}$ Here $a = 3$, so $\mathcal{L}\{e^{3t}\} = \frac{1}{s - 3}$.
← Previous (QB_EM_ADV_010) Next (QB_EM_ADV_061) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test