Laplace transform concepts are essential in engineering mathematics, control systems, and signal processing. If you are preparing for competitive exams like GATE, ESE, or university semester tests, practicing high-quality Laplace transform mcq questions can significantly improve your conceptual clarity and problem-solving speed. These multiple-choice questions help you revise important properties such as linearity, shifting theorem, convolution, region of convergence (ROC), and stability analysis. In this article, you will find carefully designed technical-level questions that strengthen your fundamentals while also preparing you for real exam patterns. Practice consistently and analyse each solution to master the topic effectively.
60 Laplace Transform MCQs for Competitive Exams
- The Laplace transform of t5t^5t5 is:
A) 5!s6\frac{5!}{s^6}s65!
B) 5!s5\frac{5!}{s^5}s55!
C) 1s6\frac{1}{s^6}s61
D) 120s5\frac{120}{s^5}s5120
Answer: A
- The Laplace transform of e−4te^{-4t}e−4t is:
A) 1s−4\frac{1}{s-4}s−41
B) 1s+4\frac{1}{s+4}s+41
C) ss+4\frac{s}{s+4}s+4s
D) 4s\frac{4}{s}s4
Answer: B
- The Laplace transform of te−2tt e^{-2t}te−2t is:
A) 1(s+2)2\frac{1}{(s+2)^2}(s+2)21
B) 1(s−2)2\frac{1}{(s-2)^2}(s−2)21
C) 2(s+2)2\frac{2}{(s+2)^2}(s+2)22
D) 1s2+4\frac{1}{s^2+4}s2+41
Answer: A
- The inverse Laplace of 2s2+9\frac{2}{s^2+9}s2+92 is:
A) sin(3t)\sin(3t)sin(3t)
B) 23sin(3t)\frac{2}{3}\sin(3t)32sin(3t)
C) 2cos(3t)2\cos(3t)2cos(3t)
D) 13sin(3t)\frac{1}{3}\sin(3t)31sin(3t)
Answer: B
- The Laplace transform of cos(4t)\cos(4t)cos(4t) is:
A) ss2+16\frac{s}{s^2+16}s2+16s
B) 4s2+16\frac{4}{s^2+16}s2+164
C) ss2−16\frac{s}{s^2-16}s2−16s
D) 4s2−16\frac{4}{s^2-16}s2−164
Answer: A
- If L{f(t)}=F(s)L\{f(t)\}=F(s)L{f(t)}=F(s), then L{t2f(t)}L\{t^2 f(t)\}L{t2f(t)} equals:
A) d2ds2F(s)\frac{d^2}{ds^2}F(s)ds2d2F(s)
B) (−1)2d2ds2F(s)(-1)^2 \frac{d^2}{ds^2}F(s)(−1)2ds2d2F(s)
C) −d2ds2F(s)-\frac{d^2}{ds^2}F(s)−ds2d2F(s)
D) s2F(s)s^2F(s)s2F(s)
Answer: B
- The Laplace transform of δ(t−a)\delta(t-a)δ(t−a) is:
A) 1
B) e−ase^{-as}e−as
C) 1s\frac{1}{s}s1
D) se−ass e^{-as}se−as
Answer: B
- The Laplace transform of d3f(t)dt3\frac{d^3f(t)}{dt^3}dt3d3f(t) is:
A) s3F(s)s^3F(s)s3F(s)
B) s3F(s)−s2f(0)−sf′(0)−f′′(0)s^3F(s)-s^2f(0)-sf'(0)-f”(0)s3F(s)−s2f(0)−sf′(0)−f′′(0)
C) sF(s)sF(s)sF(s)
D) F(s)/s3F(s)/s^3F(s)/s3
Answer: B
- The final value theorem is applicable if:
A) All poles are in LHP except possibly at origin
B) Any pole location
C) Poles in RHP
D) Imaginary axis poles
Answer: A
- The Laplace transform of sinh(5t)\sinh(5t)sinh(5t) is:
A) 5s2−25\frac{5}{s^2-25}s2−255
B) ss2−25\frac{s}{s^2-25}s2−25s
C) 5s2+25\frac{5}{s^2+25}s2+255
D) ss2+25\frac{s}{s^2+25}s2+25s
Answer: A
- If F(s)=1(s+1)(s+3)F(s)=\frac{1}{(s+1)(s+3)}F(s)=(s+1)(s+3)1, the inverse Laplace contains:
A) Two exponentials
B) Sinusoidal term
C) Polynomial
D) Impulse
Answer: A
- The Laplace transform of u(t)u(t)u(t) is:
A) 1
B) 1s\frac{1}{s}s1
C) 0
D) sss
Answer: B
- The convolution integral limits are:
A) 0 to t
B) 0 to ∞
C) −∞ to ∞
D) t to ∞
Answer: A
- The Laplace transform of e2tcos(3t)e^{2t}\cos(3t)e2tcos(3t) is:
A) s−2(s−2)2+9\frac{s-2}{(s-2)^2+9}(s−2)2+9s−2
B) s+2(s+2)2+9\frac{s+2}{(s+2)^2+9}(s+2)2+9s+2
C) 3(s−2)2+9\frac{3}{(s-2)^2+9}(s−2)2+93
D) 3(s+2)2+9\frac{3}{(s+2)^2+9}(s+2)2+93
Answer: A
- The region of convergence excludes:
A) Zeros
B) Poles
C) Constants
D) Coefficients
Answer: B
- Laplace transform converts differentiation into:
A) Division by s
B) Multiplication by s
C) Integration
D) Convolution
Answer: B
- If all poles are simple and in LHP, system is:
A) Unstable
B) Stable
C) Marginally stable
D) Non-causal
Answer: B
- The Laplace transform of constant A is:
A) A
B) As\frac{A}{s}sA
C) AsAsAs
D) 0
Answer: B
- Inverse Laplace of 1s3\frac{1}{s^3}s31 is:
A) t
B) t22\frac{t^2}{2}2t2
C) t2t^2t2
D) t36\frac{t^3}{6}6t3
Answer: B
- Laplace transform of cosh(at)\cosh(at)cosh(at) denominator is:
A) s2+a2s^2+a^2s2+a2
B) s2−a2s^2-a^2s2−a2
C) s−as-as−a
D) s+as+as+a
Answer: B
- If F(s)=ss2+1F(s)=\frac{s}{s^2+1}F(s)=s2+1s, inverse Laplace is:
A) sin t
B) cos t
C) e^t
D) t
Answer: B
- The Laplace transform of tsin(at)t\sin(at)tsin(at) equals:
A) 2as(s2+a2)2\frac{2as}{(s^2+a^2)^2}(s2+a2)22as
B) as2+a2\frac{a}{s^2+a^2}s2+a2a
C) ss2+a2\frac{s}{s^2+a^2}s2+a2s
D) 1s2+a2\frac{1}{s^2+a^2}s2+a21
Answer: A
- The scaling property states:
A) L{f(at)}=1aF(s/a)L\{f(at)\}=\frac{1}{a}F(s/a)L{f(at)}=a1F(s/a)
B) L{f(at)}=aF(as)L\{f(at)\}=aF(as)L{f(at)}=aF(as)
C) L{f(at)}=F(as)L\{f(at)\}=F(as)L{f(at)}=F(as)
D) None
Answer: A
- Laplace transform of zero function is:
A) 1
B) s
C) 0
D) Undefined
Answer: C
- Bilateral Laplace transform integrates over:
A) 0 to ∞
B) −∞ to ∞
C) 0 to T
D) 1 to ∞
Answer: B
- The Laplace transform of t4e−tt^4 e^{-t}t4e−t is:
A) 24(s+1)5\frac{24}{(s+1)^5}(s+1)524
B) 24(s−1)5\frac{24}{(s-1)^5}(s−1)524
C) 1(s+1)4\frac{1}{(s+1)^4}(s+1)41
D) 4!(s−1)4\frac{4!}{(s-1)^4}(s−1)44!
Answer: A
- The Laplace transform of δ(t)\delta(t)δ(t) is:
A) 1
B) 0
C) s
D) 1s\frac{1}{s}s1
Answer: A
- The region of convergence (ROC) of a causal system lies:
A) To the right of the rightmost pole
B) To the left of the leftmost pole
C) Between poles
D) On the imaginary axis
Answer: A
- The inverse Laplace of 1s+5\frac{1}{s+5}s+51 is:
A) e−5te^{-5t}e−5t
B) e5te^{5t}e5t
C) 5e−t5e^{-t}5e−t
D) t
Answer: A
- If L{f(t)}=F(s)L\{f(t)\}=F(s)L{f(t)}=F(s), then L{eatf(t)}L\{e^{at}f(t)\}L{eatf(t)} equals:
A) F(s−a)F(s-a)F(s−a)
B) F(s+a)F(s+a)F(s+a)
C) sF(s)sF(s)sF(s)
D) F(s)a\frac{F(s)}{a}aF(s)
Answer: A
- The Laplace transform of t2t^2t2 is:
A) 2s3\frac{2}{s^3}s32
B) 2!s3\frac{2!}{s^3}s32!
C) 1s3\frac{1}{s^3}s31
D) Both A and B
Answer: D
- In control systems, poles primarily determine:
A) Stability
B) Input
C) Time variable
D) Gain only
Answer: A
- The Laplace transform of cos(0)\cos(0)cos(0) is:
A) 1s\frac{1}{s}s1
B) 0
C) s
D) 1
Answer: A
- The Laplace transform of 1−e−at1 – e^{-at}1−e−at is:
A) as(s+a)\frac{a}{s(s+a)}s(s+a)a
B) 1s\frac{1}{s}s1
C) 1s+a\frac{1}{s+a}s+a1
D) ss+a\frac{s}{s+a}s+as
Answer: A
- The Laplace transform of f′(t)f'(t)f′(t) is:
A) sF(s)−f(0)sF(s) – f(0)sF(s)−f(0)
B) sF(s)sF(s)sF(s)
C) F(s)s\frac{F(s)}{s}sF(s)
D) None
Answer: A
- Stability of an LTI system requires poles in:
A) Left Half Plane (LHP)
B) Right Half Plane (RHP)
C) Imaginary axis only
D) Origin
Answer: A
- The Laplace transform of t3t^3t3 is:
A) 6s4\frac{6}{s^4}s46
B) 3s4\frac{3}{s^4}s43
C) 1s4\frac{1}{s^4}s41
D) 24s4\frac{24}{s^4}s424
Answer: A
- The inverse Laplace of ss2+4\frac{s}{s^2+4}s2+4s is:
A) cos(2t)\cos(2t)cos(2t)
B) sin(2t)\sin(2t)sin(2t)
C) e2te^{2t}e2t
D) t
Answer: A
- The final value theorem is given by:
A) lims→0sF(s)\lim_{s \to 0} sF(s)lims→0sF(s)
B) lims→∞sF(s)\lim_{s \to \infty} sF(s)lims→∞sF(s)
C) limF(s)\lim F(s)limF(s)
D) None
Answer: A
- The Laplace transform of u(t−a)u(t-a)u(t−a) includes factor:
A) e−ase^{-as}e−as
B) ease^{as}eas
C) s
D) 1s\frac{1}{s}s1
Answer: A
- The denominator of L{e−at}L\{e^{-at}\}L{e−at} is:
A) s+as+as+a
B) s−as-as−a
C) s2+a2s^2+a^2s2+a2
D) s2−a2s^2-a^2s2−a2
Answer: A
- Convolution in time domain corresponds to:
A) Product in s-domain
B) Sum in s-domain
C) Division in s-domain
D) None
Answer: A
- The Laplace transform variable is:
A) s
B) t
C) z
D) ω
Answer: A
- The Laplace transform of sin(0)\sin(0)sin(0) is:
A) 0
B) 1
C) s
D) 1s\frac{1}{s}s1
Answer: A
- Inverse Laplace transform commonly uses:
A) Partial fraction expansion
B) Taylor series only
C) Fourier transform
D) None
Answer: A
- The region of convergence (ROC) never includes:
A) Poles
B) Zeros
C) Constants
D) Coefficients
Answer: A
- The Laplace transform of teatt e^{at}teat is:
A) 1(s−a)2\frac{1}{(s-a)^2}(s−a)21
B) 1(s+a)2\frac{1}{(s+a)^2}(s+a)21
C) s(s−a)2\frac{s}{(s-a)^2}(s−a)2s
D) None
Answer: A
- The Laplace transform of 1 is:
A) 1s\frac{1}{s}s1
B) s
C) 0
D) 1
Answer: A
- The inverse Laplace of 1s\frac{1}{s}s1 is:
A) 1
B) t
C) 0
D) ete^tet
Answer: A
- The Laplace transform of cosh(0)\cosh(0)cosh(0) is:
A) 1s\frac{1}{s}s1
B) 1
C) 0
D) s
Answer: A
- The Laplace transform of f(t)t\frac{f(t)}{t}tf(t) involves:
A) Integration of F(s)F(s)F(s)
B) Differentiation
C) Multiplication
D) None
Answer: A
- The transfer function is defined as:
A) Output/Input
B) Input/Output
C) Time/Frequency
D) None
Answer: A
- Poles on imaginary axis imply:
A) Marginal stability
B) Stability
C) Instability
D) None
Answer: A
- The general form of L{tn}L\{t^n\}L{tn} is:
A) n!sn+1\frac{n!}{s^{n+1}}sn+1n!
B) nsn\frac{n}{s^n}snn
C) 1sn\frac{1}{s^n}sn1
D) None
Answer: A
- Laplace transform simplifies solving:
A) Ordinary Differential Equations (ODEs)
B) Geometry problems
C) Statistical problems
D) Algebra only
Answer: A
- The Laplace transform of δ(t−a)\delta(t-a)δ(t−a) is:
A) e−ase^{-as}e−as
B) ease^{as}eas
C) 1s\frac{1}{s}s1
D) s
Answer: A
- The ROC depends on:
A) Pole location
B) Zeros
C) Constant term
D) None
Answer: A
- Bilateral Laplace transform includes:
A) Negative time
B) Positive time only
C) Periodic time only
D) None
Answer: A
- The Laplace transform of 0 is:
A) 0
B) 1
C) s
D) ∞
Answer: A
- Laplace transform converts time-domain into:
A) s-domain
B) Frequency domain only
C) Spatial domain
D) None
Answer: A
Conclusion
Practicing technical-level Laplace transform MCQ questions sharpens your conceptual clarity and exam performance. When you consistently solve problems on properties like linearity, time shifting, frequency shifting, convolution, ROC, and stability, you build a strong mathematical foundation. This directly helps you in competitive exams such as GATE, ESE, and university engineering papers.
Instead of memorizing formulas blindly, focus on understanding why each result works. Analyze pole locations, apply theorems correctly, and revise standard transforms regularly. With disciplined practice and careful error analysis, you will improve speed, accuracy, and confidence. Mastering Laplace transform becomes easier when you combine theory with continuous problem-solving.
