Laplace Transform MCQs

Practice Laplace Transform MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Network TheoryLaplace Transform

The Laplace transform of a unit step u(t) is?

A1
B1/s
Cs
D1/s^2

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Correct Answer: B. 1/s

Explanation: The unilateral or ordinary Laplace transform of the unit step for t>=0 is 1/s.

Reference: Standard network theory: laplace transform

Question 2

Network TheoryLaplace Transform

The Laplace transform of e^(-at)u(t) is?

A1/(s-a)
B1/(s+a)
Cs/(s+a)
Da/(s+a)

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Correct Answer: B. 1/(s+a)

Explanation: L{e^(-at)} = 1/(s+a), for the appropriate region of convergence.

Reference: Standard network theory: laplace transform

Question 3

Network TheoryLaplace Transform

The Laplace transform of sin(omega t)u(t) is?

As/(s^2+omega^2)
Bomega/(s^2+omega^2)
C1/(s+omega)
Domega/s^2

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Correct Answer: B. omega/(s^2+omega^2)

Explanation: The standard transform is L{sin(omega t)}=omega/(s^2+omega^2).

Reference: Standard network theory: laplace transform

Question 4

Network TheoryLaplace Transform

The initial-value theorem for a function f(t) is commonly written, when applicable, as f(0+) =?

Alim s->0 sF(s)
Blim s->infinity sF(s)
Clim s->infinity F(s)/s
DF(0)

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Correct Answer: B. lim s->infinity sF(s)

Explanation: The initial-value theorem gives f(0+) = lim as s approaches infinity of sF(s), subject to its applicability conditions.

Reference: Standard network theory: laplace transform

Question 5

Network TheoryLaplace Transform

The final-value theorem is commonly written, when applicable, as f(infinity) =?

Alim s->0 sF(s)
Blim s->infinity sF(s)
Clim s->0 F(s)/s
DF(infinity) directly

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Correct Answer: A. lim s->0 sF(s)

Explanation: The final-value theorem gives lim t->infinity f(t)=lim s->0 sF(s), provided the required pole conditions are satisfied.

Reference: Standard network theory: laplace transform

Question 6

Network TheoryLaplace Transform

For F(s)=10/[s(s+2)], the final value of f(t), assuming the final-value theorem applies, is?

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Correct Answer: C. 5

Explanation: lim s->0 sF(s)=lim s->0 10/(s+2)=5.

Reference: Standard network theory: laplace transform

Question 7

Network TheoryLaplace Transform

The inverse Laplace transform of 1/(s+4) is?

Ae^(-4t)u(t)
Be^(4t)u(t)
C4e^(-t)u(t)
Dsin(4t)u(t)

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Correct Answer: A. e^(-4t)u(t)

Explanation: The standard pair is 1/(s+a) ↔ e^(-at)u(t).

Reference: Standard network theory: laplace transform

Question 8

Signals & SystemsLaplace Transform

The ROC of a bilateral Laplace transform can contain a pole of X(s)?

AAlways
BNever
COnly for causal signals
DOnly at s=0

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Correct Answer: B. Never

Explanation: The Laplace-transform integral does not converge at a pole, so poles are excluded from the ROC.

Reference: Standard signals and systems: laplace transform

Question 9

Signals & SystemsLaplace Transform

For a causal rational LTI system, the ROC of H(s) lies?

ATo the right of the rightmost pole
BTo the left of the leftmost pole
COnly between every pair of poles
DExactly on the jω-axis

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Correct Answer: A. To the right of the rightmost pole

Explanation: A causal rational impulse response is right-sided, so its ROC is to the right of the rightmost pole.

Reference: Standard signals and systems: laplace transform

Question 10

Signals & SystemsLaplace Transform

A causal rational continuous-time LTI system is BIBO stable if all its poles lie?

AStrictly in the left half of the s-plane
BStrictly in the right half-plane
COnly on the jω-axis
DAt the origin only

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Correct Answer: A. Strictly in the left half of the s-plane

Explanation: For a causal rational system, BIBO stability requires the jω-axis to lie in the ROC, which means all poles must be strictly in the left half-plane.

Reference: Standard signals and systems: laplace transform

Question 11

Signals & SystemsLaplace Transform

The bilateral Laplace transform of x(t) is?

A∫x(t)e^(-st)dt over all time
B∫x(t)e^(st)dt from 0 to 1
Cx(t)/s
Ddx(t)/dt only

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Correct Answer: A. ∫x(t)e^(-st)dt over all time

Explanation: The bilateral Laplace transform is X(s)=∫ from -∞ to ∞ x(t)e^(-st)dt.

Reference: Standard signals and systems: laplace transform

Question 12

Signals & SystemsLaplace Transform

The Laplace transform of e^(-at)u(t), with the appropriate ROC, is?

A1/(s-a)
B1/(s+a)
Cs/(s+a)
Da/(s²+a²)

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Correct Answer: B. 1/(s+a)

Explanation: For a right-sided exponential e^(-at)u(t), X(s)=1/(s+a) with ROC Re{s}>-a.

Reference: Standard signals and systems: laplace transform

Question 13

Signals & SystemsLaplace Transform

For x(t)=e^(-2t)u(t), the ROC of its bilateral Laplace transform is?

ARe{s}>-2
BRe{s}<-2
CRe{s}=0 only
DAll s including the pole

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Correct Answer: A. Re{s}>-2

Explanation: A right-sided exponential has ROC to the right of its pole at s=-2.

Reference: Standard signals and systems: laplace transform

Question 14

Signals & SystemsLaplace Transform

For x(t)=-e^(-2t)u(-t), whose transform is 1/(s+2), the ROC is?

ARe{s}>-2
BRe{s}<-2
CRe{s}>2
DAll s

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Correct Answer: B. Re{s}<-2

Explanation: The left-sided version has the same algebraic transform but an ROC to the left of the pole: Re{s}<-2.

Reference: Standard signals and systems: laplace transform

Question 15

Network TheoryLaplace Transform

The unilateral Laplace transform of the unit impulse delta(t) is?

A0
B1
C1/s
Ds

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Correct Answer: B. 1

Explanation: The unilateral Laplace transform of a unit impulse at t=0 is 1 under the standard engineering convention.

Reference: Standard network theory: impulse transform

Question 16

Network TheoryLaplace Transform

The Laplace transform of t for t>=0 is?

A1/s
B1/s^2
Cs
Ds^2

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Correct Answer: B. 1/s^2

Explanation: Using L{t^n}=n!/s^(n+1), for n=1 the transform is 1/s^2.

Reference: Standard network theory: transform of ramp

Question 17

Network TheoryLaplace Transform

The initial-value theorem for a function f(t) with suitable transform F(s) gives f(0+) as?

Alim s->0 of sF(s)
Blim s->infinity of sF(s)
Clim s->0 of F(s)/s
Dlim s->infinity of F(s)/s

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Correct Answer: B. lim s->infinity of sF(s)

Explanation: Under the theorem's applicability conditions, f(0+)=lim as s approaches infinity of sF(s).

Reference: Standard network theory: initial-value theorem

Question 18

Network TheoryLaplace Transform

If F(s)=5/[s(s+5)], the initial value f(0+) obtained using the initial-value theorem is?

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Correct Answer: A. 0

Explanation: f(0+)=lim s->infinity sF(s)=lim 5/(s+5)=0.

Reference: Standard network theory: initial-value theorem numerical

Question 19

Network TheoryLaplace Transform

The final-value theorem gives f(infinity), when applicable, as?

Alim s->infinity sF(s)
Blim s->0 sF(s)
Clim s->0 F(s)/s
Dlim s->infinity F(s)

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Correct Answer: B. lim s->0 sF(s)

Explanation: If the required pole conditions are satisfied, f(infinity)=lim as s approaches zero of sF(s).

Reference: Standard network theory: final-value theorem

Question 20

Network TheoryLaplace Transform

The final-value theorem is not valid for a response whose sF(s) has?

AAll poles strictly in the left-half plane
BA pole in the right-half plane
CNo finite poles
DOnly negative real poles

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Correct Answer: B. A pole in the right-half plane

Explanation: A right-half-plane pole produces a growing mode, so the response does not approach a finite final value and the final-value theorem cannot be used in its standard form.

Reference: Standard network theory: final-value theorem applicability

Question 21

Network TheoryLaplace Transform

The inverse Laplace transform of 1/[(s+2)(s+3)] is?

Ae^(-2t)+e^(-3t)
Be^(-2t)-e^(-3t)
C2e^(-2t)-3e^(-3t)
De^(-5t)

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Correct Answer: B. e^(-2t)-e^(-3t)

Explanation: Partial fractions give 1/(s+2)-1/(s+3), hence f(t)=e^(-2t)-e^(-3t) for t>=0.

Reference: Standard network theory: partial fractions numerical