GATE AG 2010 • Q28 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transformation of t³e⁴ᵗ is

Options:

  • (A) 4!/
  • (B) 3!/
  • (C) 3!/
  • (D) 4!/

Official Answer Key:

B

Step-by-Step Solution & Explanation

Standard transform: L{tⁿe^(at)} = n!/(s−a)^(n+1). Here n=3, a=4: L{t³e⁴ᵗ} = 3!/(s−4)⁴.

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