Laplace Transform – Conceptual MCQs
Reference: Chapter 6, Advanced Engineering Mathematics (10th Edition) by Erwin Kreyszig
1. 1. What is the Laplace Transform of f(t) = 1?
A) 1/s^2
B) 1/s
C) s
D) e^(-s)
✅Answer: B
2. 2. What is the Laplace Transform of f(t) = t?
A) 1/s^2
B) s
C) 1/s
D) t^2
✅Answer: A
3. 3. The Laplace Transform of e^(at) is:
A) 1/(s-a)
B) 1/(s+a)
C) 1/s^2
D) s
✅Answer: A
4. 4. What is L{sin(at)}?
A) s/(s^2 + a^2)
B) a/(s^2 + a^2)
C) 1/(s-a)
D) 1/(s^2 + a^2)
✅Answer: B
5. 5. What is the Laplace Transform of cos(at)?
A) s/(s^2 + a^2)
B) a/(s^2 + a^2)
C) 1/(s-a)
D) 1/s^2
✅Answer: A
6. 6. The Laplace Transform of δ(t - a) is:
A) e^(-as)
B) δ(t - a)
C) 1/s
D) s e^(-as)
✅Answer: A
7. 7. What is L^-1 {1/(s^2 + 4)}?
A) cos(2t)
B) sin(2t)
C) e^(2t)
D) 0.5 sin(2t)
✅Answer: B
8. 8. The Laplace Transform of f'(t) is:
A) sF(s) + f(0)
B) sF(s) - f(0)
C) d/ds F(s)
D) F(s) + s
✅Answer: B
9. 9. What does the Final Value Theorem state?
A) lim s→∞ F(s)
B) lim s→0 sF(s)
C) lim t→∞ f(t) = F(0)
D) lim t→∞ f(t) = 1/s
✅Answer: B
10. 10. What is the Laplace Transform of u(t - a)?
A) e^(-as)
B) 1/s
C) e^(-as)/s
D) 1/(s - a)
✅Answer: C