Engineering Mathematics-II Unit 2 – Laplace Transform: AKTU previous year questions
14 AKTU questions from Unit 2 (Laplace Transform) asked in 2023–2025, tagged by marks, year and topic. In short: about 15 marks of every paper come from this unit; the most asked topic is Laplace Transform Fundamentals (6 times); 11 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 2 previous year questions
- Find Laplace Transform of f(t) = sin 2t cos 3t. (2 marks, 2025, Laplace Transform Fundamentals)
- Find inverse Laplace Transform of F(s) = (s−1)/(s²+3s+2). (2 marks, 2025, Inverse Laplace Transform)
- Solve the following differential equations using Laplace Transform: d³y/dt³ + 2d²y/dt² − dy/dt − 2y = 0; y(0) = 1, y'(0) = y''(0) = 2 (7 marks, 2025, Applications of Laplace Transform)
- Find the Laplace Transform of the following function: ∫₀ᵗ (eᵗ sin t / t) dt. (7 marks, 2025, Laplace Transform Fundamentals)
- Use convolution theorem to evaluate L⁻¹[ p² / (p²+4)(p²+9) ] (7 marks, 2025, Inverse Laplace Transform)
- Find the Laplace Transform of t⁴e^(2t) (2 marks, 2024, Laplace Transform Fundamentals)
- Using convolution theorem, find the Inverse Laplace Transform of 1 / [(s²+a²)(s²+b²)] (7 marks, 2024, Inverse Laplace Transform)
- Find L{ (1 − cos t) / t² } using properties of Laplace Transform. (7 marks, 2024, Laplace Transform Fundamentals)
- Using Laplace Transform, solve: y'' + 3y' + 2y = e^(−t), y(0) = 0, y'(0) = 1 (7 marks, 2024, Applications of Laplace Transform)
- Explain the first shifting property of the Laplace transform with example. (2 marks, 2023, Laplace Transform Fundamentals)
- Find the inverse Laplace transform of F(s) = 1 / (s² + 2s + 2). (2 marks, 2023, Inverse Laplace Transform)
- Find the Laplace transform of the function f(x) = x³ sin x. Hence, prove that ∫₀^∞ e^(−x) x³ sin x dx = 0. (7 marks, 2023, Laplace Transform Fundamentals)
Most asked Unit 2 topics
- Laplace Transform Fundamentals – asked 6 times
- Inverse Laplace Transform – asked 5 times
- Applications of Laplace Transform – asked 3 times
Unit 2 question pattern
- 2-mark questions: 5 asked in 2023–2025
- 7-mark questions: 9 asked in 2023–2025
- About 15 marks from Unit 2 in every paper
- 11 questions were asked again in a later year
Unit 2 questions year by year
- 2025: 5 Unit 2 questions asked (25 marks across that year's papers)
- 2024: 4 Unit 2 questions asked (23 marks across that year's papers)
- 2023: 5 Unit 2 questions asked (25 marks across that year's papers)