Engineering Maths · all questions

Transform Theory
practice.

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Q21

Open question

Laplace transform of sin ht is

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Q22

Open question

Laplace transform of cos (ωt) is

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Q23

Open question

The Laplace transform of a function f(t) is

\frac{1}{s ^{2} ( s + 1 )} .

The function f(t) is

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Q24

Open question

The inverse Laplace transform of

H (s) = \frac{s + 3}{s ^{2} + 2 s + 1}

for t ≥ 0 is

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Q25

Open question

Let

{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - \pi ,\,\,{\text{if}}}&{ - \pi < {\text{x}} \leqslant {\text{0}}} \\ {\pi ,\,\,{\text{if}}}&{0 < {\text{x}} \leqslant \pi } \end{array}} \right.

be a periodic function of period 2π. The coefficient of sin5x in the Fourier series expansion of f(x) in the interval [-π, π] is

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Q26

Open question

Given the Fourier series in (-π, π) for f(x) = x cosx, the value of a₀ will be

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Q27

Open question

Laplace transform of the function f(t) is given by

F (s) = L {f (t)} = \int_{0}^{\infty} f (t) e^{- st} dt .

Laplace transform of the function shown below is given by
Transform Theory mcq question image

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Q28

Open question

If L defines the Laplace Transform of a function, L [sin (at)] will be equal to

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Q29

Open question

The Fourier series expansion of the saw-toothed waveform f(x) = x in (-π, π) of period 2π gives the series,

1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + ....

The sum is equal to

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Q30

Open question

Laplace transform of 8t³

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Q31

Open question

The inverse Laplace transform of the function

F (s) = \frac{1}{s ( s + 1 )}

is given by

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Q32

Open question

Laplace transform analysis gives

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Q33

Open question

Inverse Laplace transform of the function

\frac{s}{s ^{2} + 3 s + 2},

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Q34

Open question

Which of the following is the advantage of using Laplace transform techniques?

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Q35

Open question

The initial value theorem does not hold good for which of the following functions?

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Q36

Open question

Find the inverse Laplace transform of

F (s) = \frac{s ^{2} + 2 s - 2}{s ( s + 4 ) ( s - 5 )}

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Q37

Open question

Give transfer function

H (s) = \frac{s + 2}{s ^{2} + s + 4},

under steady state condition, the sinusoidal input and output are, respectively x(t) = cos 2t, y(t) = cos(2t +

ϕ

), then angle

ϕ

will be

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Q38

Open question

Which of the following correctly defines Laplace transform of a function in the time domain?

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Q39

Open question

The Laplace transform of

I (t)

is given by

I (s) = \frac{5}{s ( s ^{2} + 2 )} .

t \to \infty

the value of

I (t)

tends to

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Q40

Open question

Given that

F (s)

is the one-side Laplace transform of

f (t),

the Laplace transform of

\int_{0}^{t} f (τ) d τ

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Transform Theorypractice.

Transform Theory
practice.