GATE AG 2020 • Q37 MCQ • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

For f(t) = 4cos2t + 6e⁻⁸ᵗ, find F(s) = L{f(t)}.

Options:

  • (A) 4s/(s²+4) + 6/(s+8)
  • (B) 4s/(s²−4) + 6/(s−8)
  • (C) 8/(s²+4) + 6/(s+8)
  • (D) 8/(s²−4) + 6/(s−8)

Official Answer Key:

A

Step-by-Step Solution & Explanation

L{cos2t}=s/(s²+4), so L{4cos2t}=4s/(s²+4). L{e⁻⁸ᵗ}=1/(s+8), so L{6e⁻⁸ᵗ}=6/(s+8). F(s)=4s/(s²+4)+6/(s+8), matching option (A). The examiners issued “marks to all” for this question, likely due to an error/ambiguity in the printed options.

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test