This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Existence and Laplace Transform of Elementary Functions – 1”.

1. If f(t) = 1, then its Laplace Transform is given by

a) s

b) ^{1}⁄_{s}

c) 1

d) Does not exist

View Answer

Explanation: The Laplace Transform of a functions is given by

put f(t) = 1

On simplifying, we get

^{1}⁄

_{s}.

2. If f(t) = t^{n} where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by

a) n!

b) t^{n+1}

c) n! ⁄ s^{n+1}

d) Does not exist

View Answer

Explanation:The Laplace Transform of a functions is given by

f(t) = t

^{n}

On simplifying, we get n! ⁄ s

^{n+1}.

3. If f(t)=√t, then its Laplace Transform is given by

a) ^{1}⁄_{2}

b) ^{1}⁄_{s}

c) √π ⁄ 2√s

d) Does not exist

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t)=√t

On Solving, we get √π ⁄ 2√s.

4. If f(t) = sin(at), then its Laplace Transform is given by

a) cos(at)

b) 1 ⁄ a^{sin(at)}

c) Indeterminate

d) a ⁄ s^{2}+a^{2}

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = sin(at)

On solving, we get a ⁄ s

^{2}+a

^{2}.

5. If f(t) = tsin(at) then its Laplace Transform is given by

a) 2as ⁄ (s^{2}+a^{2})^{2}

b) a ⁄ s^{2}+a^{2}

c) Indeterminate

d) √π ⁄ 2√s

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = tsin(at)

On Solving, we get 2as ⁄ (s

^{2}+a

^{2})

^{2}.

6. If f(t) = e^{at}, its Laplace Transform is given by

a) a ⁄ s^{2}+a^{2}

b) √π ⁄ 2√s

c) 1 ⁄ s-a

d) Does not exist

View Answer

Explanation: The Laplace Transform of a functions is given by

Put f(t) = e

^{at}

On solving the above integral, we obtain 1 ⁄ s-a.

7. If f(t) = t^{p} where p > – 1, its Laplace Transform is given by

a) √π ⁄ 2√s

b) f(t) = tsin(at)

c) γ(p+1) ⁄ s^{p+1}

d) Does not exist

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = t

^{p}

On Solving, we get γ(p+1) ⁄ s

^{p+1}.

8. If f(t) = cos(at), its Laplace transform is given by

a) s ⁄ s^{2}+a^{2}

b) a ⁄ s^{2}+a^{2}

c) √π ⁄ 2√s

d) Does not exist

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = cos(at)

On solving the above integral, we get s ⁄ s

^{2}+a

^{2}.

9. If f(t) = tcos(at), its Laplace transform is given by

a) 1 ⁄ s-a

b) s^{2} – a^{2} ⁄ (s^{2}+a^{2})^{2}

c) Indeterminate

d) s^{2}at

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = tcos(at)

On solving the above integral, using suitable rules of integration we get the answer s

^{2}– a

^{2}⁄ (s

^{2}+a

^{2})

^{2}.

10. If f(t) = sin(at) – atcos(at), then its Laplace transform is given by

a) Indeterminate form is encountered

b) a^{3} ⁄ (s^{2} + a^{2})^{2}

c) 2a^{3} ⁄ (s^{2} – a^{2})^{2}

d) 2a^{3} ⁄ (s^{2} + a^{2})^{2}

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = sin(at) – atcos(at)

On solving the above integral, we obtain the answer2 a

^{3}⁄ (s

^{2}+ a

^{2})

^{2}.

11. If f(t) = sin(at) – atcos(at), then its Laplace transform is given by

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = sin(at) – atcos(at)

On solving, we obtain 2as

^{2}⁄ (s

^{2}+a

^{2})

^{2}

12. If f(t) = cos(at) – atsin(at), then its Laplace transform is given by

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = cos(at) – atsin(at)

On solving, we obtain a

^{3}⁄ (s

^{2}+ a

^{2})

^{2}.

13. If f(t) = cos(at) + atsin(at), its Laplace transform is given by

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = cos(at) + atsin(at) to solve the problem.

14. If f(t) = sin(at + b), its Laplace transform is given by

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = sin(at + b) to solve the problem.

15. If f(t) = cos(at + b) , its Laplace transform is given by

View Answer

Explanation:The Laplace Transform of a functions is given by

Put f(t) = cos(at + b) to solve the problem.

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