Allied & ICAR Exam Bank • ALLIED_0073 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = t^2$ is $\frac{k}{s^3}$. The value of $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

$\mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}}$. For $n = 2$: $\frac{2!}{s^3} = \frac{2}{s^3} \implies k = 2$.
← Previous (ALLIED_0072) Next (ALLIED_0074) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test