GATE AG 2024 • Q12 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

Laplace transform of a function f(t) = t⁴ as a function of ‘s’ is __________.

Options:

  • (A) 120/s⁵
  • (B) 24/s⁵
  • (C) 120/s⁴
  • (D) 24/s⁴

Official Answer Key:

B

Step-by-Step Solution & Explanation

The standard transform pair is: L{tⁿ} = n!/s^(n+1) For n = 4: L{t⁴} = 4!/s⁵ = (4 × 3 × 2 × 1)/s⁵ = 24/s⁵ Traps: (A) uses 5! = 120 instead of 4!; (C) and (D) use the wrong power of s (n instead of n + 1).

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