This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Laplace Transform by Properties – 1”.

1. Laplace of function f(t) is given by

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Explanation: Laplace of function f(t) is given by

2. Laplace transform any function changes it domain to s-domain.

a) True

b) False

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Explanation: Laplace of function f(t) is given by ,hence it changes domain of function from one domain to s-domain.

3. Laplace transform if sin(at)u(t) is

a) s ⁄ a^{2}+s^{2}

b) a ⁄ a^{2}+s^{2}

c) s^{2} ⁄ a^{2}+s^{2}

d) a^{2} ⁄ a^{2}+s^{2}

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4. Laplace transform if cos(at)u(t) is

a) s ⁄ a^{2}+s^{2}

b) a ⁄ a^{2}+s^{2}

c) s^{2} ⁄ a^{2}+s^{2}

d) a^{2} ⁄ a^{2}+s^{2}

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5. Find the laplace transform of e^{t} Sin(t).

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6. Laplace transform of t^{2} sin(2t)

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7. Find the laplace transform of t^{5⁄2}

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8. Value of ∫_{-∞}^{∞}e^{t} Sin(t)Cos(t)dt = ?

a) 0.5

b) 0.75

c) 0.2

d) 0.71

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Explanation: L(Sin(2t) = ∫

_{-∞}

^{∞}e

^{-st}Sin(2t)dt = 2/(s

^{2}+ 4)

Putting s=-1

∫

_{-∞}

^{∞}e

^{t}Sin(2t)dt = 0.4

hence,

∫

_{-∞}

^{∞}e

^{-st}Sin(t)Cos(t)dt = 0.2.

9. Value of ∫_{-∞}^{∞}e^{t} Sin(t) dt = ?

a) 0.50

b) 0.25

c) 0.17

d) 0.12

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Explanation: L(Sin(2t) = ∫

_{-∞}

^{∞}e

^{-st}Sin(t)dt = 1/(s

^{2}+ 1)

Putting s = -1

∫

_{-∞}

^{∞}e

^{t}Sin(t)dt = 0.5.

10. Value of ∫_{-∞}^{∞}e^{t} log(1+t)dt = ?

a) Sum of infinite integers

b) Sum of infinite factorials

c) Sum of squares of Integers

d) Sum of square of factorials

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11. Find the laplace transform of y(t)=e^{t}.t.Sin(t)Cos(t)

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12. Find the value of ∫_{0}^{∞} tSin(t)Cos(t)

a) s ⁄ s^{2}+2^{2}

b) a ⁄ a^{2}+s^{4}

c) 1

d) 0

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13. Find the laplace transform of y(t)=e^{|t-1|} u(t).

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**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__.