Question Bank • QB_EM_ADV_062 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The inverse Laplace transform $\mathcal{L}^{-1}\left\{ \frac{1}{s(s + 1)} \right\}$ is:

Options:

  • (A) $1 - e^{-t}$
  • (B) $1 + e^{-t}$
  • (C) $e^{-t} - 1$
  • (D) $t e^{-t}$

Answer Key:

A

Step-by-Step Solution & Explanation

Decomposing into partial fractions: $\frac{1}{s(s+1)} = \frac{1}{s} - \frac{1}{s+1}$ Taking inverse Laplace transforms term by term: $\mathcal{L}^{-1}\left\{ \frac{1}{s} \right\} - \mathcal{L}^{-1}\left\{ \frac{1}{s+1} \right\} = 1 - e^{-t}$
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