Allied & ICAR Exam Bank • ALLIED_2719 MSQ • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

Which of the following Laplace transforms are CORRECT?

Options:

  • (A) $\mathcal{L}\{1\} = \frac{1}{s}$ for $s > 0$
  • (B) $\mathcal{L}\{\delta(t)\} = 1$ (Dirac delta)
  • (C) $\mathcal{L}\{u(t - a)\} = \frac{e^{-as}}{s}$ (Heaviside step)
  • (D) $\mathcal{L}\{t f(t)\} = -\frac{d}{ds} F(s)$

Answer Key:

A, B, C, D

Step-by-Step Solution & Explanation

All four properties are canonical Laplace transform pairs.
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