This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Laplace Transform by Properties – 3”.

1. Time domain function of ^{s} ⁄_{ a2 + s2} is given by

a) Cos(at)

b) Sin(at)

c) Cos(at)Sin(at)

d) None of the above

View Answer

Explanation: L[Cos(at)] =

^{s}⁄

_{ a2 + s2}

L^{-1} [^{s} ⁄_{ a2 + s2} ] = Cos(at).

2. Inverse Laplace transform of 1/(s+1)(s-1)(s+2) is

a) –^{1}⁄_{2} e^{t} + ^{1}⁄_{6} e^{-t} + ^{1}⁄_{3} e^{2t}

b) –^{1}⁄_{2} e^{-t} + ^{1}⁄_{6} e^{t} + ^{1}⁄_{3} e^{-2t}

c) ^{1}⁄_{2} e^{-t} – ^{1}⁄_{6} e^{t} – ^{1}⁄_{3} e^{-2}

d) –^{1}⁄_{2} e^{-t} + ^{1}⁄_{6} e^{-t} + ^{1}⁄_{3} e^{-2}

View Answer

3. Inverse laplace transform of 1/(s-1)^{2} (s+5) is

a) ^{1}⁄_{6} e^{ – t} – ^{1}⁄_{36} e^{t} + ^{1}⁄_{36} e^{-5t}

b) ^{1}⁄_{6} e^{t}t – ^{1}⁄_{36} e^{t} + ^{1}⁄_{36} e^{-5t}

c) ^{1}⁄_{6} e^{-t}t^{2} – ^{1}⁄_{36} e^{-t} + ^{1}⁄_{36} e^{5t}

d) ^{1}⁄_{6} e^{-t} t-^{1}⁄_{36} e^{-t} + ^{1}⁄_{36} e^{5t}

View Answer

4. Find the inverse lapalce transform of

a) ^{1}⁄_{12} e^{t} – ^{1}⁄_{13} Cos(-t) – ^{1}⁄_{12} Sin(-t) – ^{1}⁄_{156} e^{-5t}

b) ^{1}⁄_{12} e^{-t} – ^{1}⁄_{13} Cos(t) – ^{1}⁄_{12} Sin(t) – ^{1}⁄_{156} e^{5t}

c) ^{1}⁄_{12} e^{t} – ^{1}⁄_{13} Cos(t) – ^{1}⁄_{12} Sin(t) – ^{1}⁄_{156} e^{-5t}

d) ^{1}⁄_{12} e^{t} + ^{1}⁄_{13} Cos(t) + ^{1}⁄_{12} Sin(t) + ^{1}⁄_{156} e^{-5t}

View Answer

5. Find the inverse laplace transform of ^{s}⁄_{(s2 + 4)2}

a) ^{1}⁄_{4} sin(2t)

b) ^{t2}⁄_{4} sin(2t)

c) ^{t}⁄_{4} sin(2t)

d) ^{t}⁄_{4} sin(2t^{2})

View Answer

6. Final value theorem states that

View Answer

7. Initial value theorem states that

View Answer

8. Find the value of x(∞) if

a) 5

b) 4

c) ^{12}⁄_{20}

d) 2

View Answer

9. Find the value of x(0) if

a) 5

b) 4

c) ^{12}⁄_{20}

d) 2

View Answer

10. Find the inverse lapace of

a) ^{1}⁄_{3} e^{t} [Cos(t) – Cos(2t)].

b) ^{1}⁄_{3} e^{-t} [Cos(t) + Cos(2t)].

c) ^{1}⁄_{3} e^{t} [Cos(t) + Cos(2t)].

d) ^{1}⁄_{3} e^{-t} [Cos(t) – Cos(2t)].

View Answer

11. Find the inverse laplace transform of

a) -e^{-t + 1} + e^{t – 1}

b)-e^{-t + 1} – e^{t + 1}

c) -e^{-t + 1} + e^{t + 1}

d)-e^{-t + 1} – e^{t – 1}

View Answer

12. Find the inverse lapalce transform of ^{1}⁄_{s(s-1)(s2+1)}

a) ^{1}⁄_{2} e^{-t} + ^{1}⁄_{2} Sin(-t) – ^{1}⁄_{2} Cos(-t)

b) ^{1}⁄_{2} e^{t} + ^{1}⁄_{2} Sin(t) – ^{1}⁄_{2} Cos(t)

c) ^{1}⁄_{2} e^{t} + ^{1}⁄_{2} Sin(t) + ^{1}⁄_{2} Cos(t)

d) ^{1}⁄_{2} e^{t} – ^{1}⁄_{2} Sin(t) – ^{1}⁄_{2} Cos(t)

View Answer

**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

To practice all areas of Engineering Mathematics, __here is complete set of 1000+ Multiple Choice Questions and Answers__.