100+ Laplace transform Multiple Choice Questions with Answers

This article lists 100 Laplace transform MCQs for engineering students. All the Laplace transform Questions & Answers given below include a hint and a link wherever possible to the relevant topic. This is helpful for users who are preparing for their exams, or interviews, or professionals who would like to brush up on the fundamentals of Laplace transform.

A Laplace transform is a mathematical form that converts real type variable function to complex type variable function. These functions are represented in the s-domain or a complex frequency-type domain. There is a number of conversion formulas in the Laplace transform where the integral of Laplace transform is L{f}(s) = Integration (0àinfinity) = f(t) e ^-st dt.

Where f(t) is the time domain function, f(s) is the frequency domain function where “s” is given as sigma + jw. Laplace transform can be of different types such as bilateral Laplace transform, and Inverse Laplace transform.

A Laplace transform where the limit values are extended on both sides is called a bilateral Laplace transform. A Laplace transform where the inverse operation is performed on the Laplace function is inverse Laplace function. Any function that involves in Laplace function deals with a probability value.

The advantages of the Laplace transform include it represents ODE to simpler terms and changes the convolution type operators to multiplication operators. The disadvantages include it solves only known value constants and solving only complex equations and not simple ones. Laplace transform is used in fields such as optics, system modeling, and nuclear physics.

1).What is the linearity property of Laplace transform?

A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s)

A f1(t) + B f2(t) ⟷ A F1(s) - B F2(s)

A f1(t) + B f2(t) ⟷ A F1(s) * B F2(s)

A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s) A F1(s)

2).What is the Frequency Shifting Property of Laplace Transform?

es0t f(t)) ⟷ F(s - s0)

es0t f(t)) ⟷ F(s + s0)

es0t f(t)) ⟷ F(s * s0)

es0t f(t)) ⟷ F(s0)

3). What is the Integration of Laplace Transform?

t∫0 f(λ) dλ ⟷ s F(s)

t∫0 f(λ) dλ ⟷ F(s)

t∫0 f(λ) dλ ⟷ 1⁄s F(s)

4). What is the Multiplication by Time of Laplace Transform?

T f(t) ⟷ (−d F(s)⁄ds)

T f(t) ⟷ d F(s)⁄ds)

T f(t) ⟷ F(s)⁄ds)

T f(t) ⟷ (−t F(s)⁄ds)

5). What is the Complex Shift Property of Laplace Transform?

f(t) e−at ⟷ F(s + a)

f(t) e−at ⟷ F(s - a)

f(t) e−at ⟷ F(s * a)

f(t) eat ⟷ F(s + a)

6). What is the Time Reversal Property of Laplace Transform?

f (-t) ⟷ F(-s)

f (-t) ⟷ F(s)

7). What is the Time Scaling Property of Laplace Transform?

f (t⁄a) ⟷ F(as)

f (t⁄a) ⟷ s F(as)

f (t⁄a) ⟷ a F(as)

f (t⁄a) ⟷ s

8). What is the standard notation of Laplace transform?

L(f; s) = F(s)

L(f; s) /F(s)

L(f; s) * F(s)

L(f; s)

9). What is the Laplace Transform of 1 is?

1/s

10). What is the Laplace Transform of f'(t) is?

sF(s) * f(0)

sF(s) + f(0)

sF(s) - f(0)

F(0)

11). What is the Laplace Transform of sin(at) is?

as/(s2+a2)

a/(s2+a2)

s/(s2+a2)

1/(s2+a2)

12). What is the Laplace Transform of t sin(at) is?

as/(s2+a2)2

2as/(s2+a2)

2as/(s2+a2)2

as/(s2+a2)

13). What is the Laplace Transform of sin(at +b) is?

(s sin(b)+ a cos(b)/(s2+a2)

(s sin(b)+ a cos(b)

s/(s2+a2)

(s sin(b)+ a cos(b)/(s+a)

14). What is the Laplace Transform of sinh(at) is?

1/(s2-a2)

2a/(s2-a2)

s/(s2-a2)

a/(s2-a2)

15). What is the Laplace Transform of eat sin(bt) is?

2b/((s-a)2+b2)

b/((s-a)2+b2)

ab/((s-a)2+b2)

1/((s-a)2+b2)

16). What is the Laplace Transform of ect f(t) is?

F(s+c)

F(s-c)

17). What is the Laplace Transform of eat is?

1/(s - a)

1/(s + a)

1/(s a)

s/(a)

18). What is the Laplace Transform of cos(at) is?

as/(s2+a2)

2s/(s2+a2)

a/(s2+a2)

s/(s2+a2)

19). What is the Laplace Transform of t cos(at) is?

(s2+a2)/(s2+a2)

(s2-a2)/(s2+a2)2

(s2+a2)/(s2-a2)2

(s2-a2)/(s2-a2)

20). What is the Laplace Transform of cos(at + b) is?

(s cos(b)+a sin(b)/(s2-a2)

(s cos(b)-a sin(b)/(s2-a2)

(s cos(b)+a sin(b)/(s2+a2)

(s cos(b)-a sin(b)/(s2+a2)

21). What is the Laplace Transform of cosh(at) is?

1/(s2-a2)

s/(s2+a2)

s/(s2-a2)

a/(s2-a2)

22). What is the Laplace Transform of e(at)cos((bt) is?

(s+a)/((s-a)2+b2)

(s-a)/((s-a)2-b2)

(s+a)/((s-a)2-b2)

(s-a)/((s-a)2+b2)

23). What is the Laplace Transform of f’’(t) is?

s2F(s) − sf(0) − f'(0)

s2F(s) − sf(0) + f'(0)

s2F(s) + sf(0) − f'(0)

s2F(s)sf(0) − f'(0)

24). What is the Laplace Transform of √(t) is?

√π/2s(3.2)

√π/2s(3/2)

√π/2s(2)

√π/2s(3)

25). A two-sided Laplace transforms with extending limits of integrations is _______?

Bilateral transform

Inverse Laplace transform

Laplace transform

All the above

Laplace Transform MCQs for Exams

26). What is the Laplace transform of random variable X will be?

L{f}(S) = E[e+sX]

L{f}(S) = E[sX]

L{f}(S) = E[e*sX]

L{f}(S) = E[e-sX]

27). Laplace Transform for simplifying the complicated differential equations by adding __________?

Polynomials

Random Variable

Integers

All The above

28). Laplace transform is deployed in technical activities like?

System Modelling

Digital Signal Processing

Electrical Circuit Analysis

All The above

29). Major application of Laplace transform is in_____?

Telecommunications

Signals

Both a and b

Motor

30). What is the Inverse transform of the function F(s)?

f(t) = 1/L+1{F(t)}

f(t) = L-1{F(s)}

f(s) = -L-1{F(s)}

f(s) = 1/L-1{F(s)}

31). If the two Laplace transform, say F(s) and G(s), then what will be the Inverse Laplace transform?

L-1{aF(s)+bG(s)} = a L-1{F(s)} + bL-1 {G(s)}

L-1{aF(s)+bG(s)} = a L-1{F(s)} + L-1 {G(s)}

L-1{aF(s)+bG(s)} = a L-1{F(s)} - bL-1 {G(s)}

L-1{aF(s)+bG(s)} = L-1{F(s)} - bL-1 {G(s)}

32). What is the Inverse Laplace transform of 1 is ?

1/s

33). What is the Laplace transform of sin(at)−at cos(at) is ?

2a3/(s2-a2)2

2a3/(s2+a2)2

2a3/(s2+a2)

a3/(s2-a2)2

34). What is the Laplace transform of sin(at) + at cos(at) is ?

2as2/(s2+a2)2

2as2/(s2-a2)2

-2as/(s2+a2)2

as2/(s2+a2)2

35). What is the Laplace transform of cos(at)−at sin(at) is?

(s2+a2)/(s2-a2)2

2s(s2−a2)/(s2+a2)2

(s2−a2)/(s2+a2)2

s(s2−a2)/(s2+a2)2

36). What is the Laplace transform of cos(at)−at sin(at) is?

s(s2−3a2)/(s2+a2)2

s(s2+3a2)/(s2+a2)2

s(s2−2a2)/(s2+a2)2

s(s2-a2)/(s2+a2)2

37). What is the Laplace transform of eat sinh(bt)?

b/(s−a)2 + b2

-b/(s−a)2 + b2

b/(s−a)2−b2

b/(s+a)2+b2

38). What is the Laplace transform of eat cosh(bt)?

s-a/(s−a)2+b2

s-a/(s−a)2−b2

s+a/(s−a)2−b2

s-a/(s+a)2−b2

39). Laplace transform plays a important role in ?

Control Systems

Electrical Machines

Switch Gear

All the above

40). What is the Integration of Laplace transform?

t∫0 f(λ) dλ ⟷ 1⁄s

t∫0 f(λ) dλ ⟷ 1⁄s F(s)

t∫0 f(λ) dλ ⟷ F(s)

t∫0 f(λ) dλ ⟷ s F(s)

41). What is the Nth Derivative property of Laplace transform?

(dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi +1 (0−)

(dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi − 1 (0)

(dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi − 1 (0−)

(dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn + i fi − 1 (0)

42). What is the Inverse Laplace transform of 1/s?

∞

43). What is the Inverse Laplace transform of 1/s , L-1(1/sn)?

tn/n!, n=1,2,3….

tn/(n+1)!, n=1,2,3,…

tn/(n-1)!, n=1,2,3...

44). What is the Inverse Laplace transform of (1/s2+a2)?

sinat

(1/a) sinat

cosat

45). What is the Inverse Laplace transform of (1/s-a)?

eat

e-at

46). What is the Inverse Laplace transform of (s/s2+a2)?

cos at

sin at

cosec at

sec at

47). What is the Inverse Laplace transform of (1/(s-a)2+b2)

(1/b) eat sin bt

b eat sin bt

eat sin bt

48). What is the Inverse Laplace transform of (s-a /(s-a)2+b2)

eat

eat sin bt

cos bt

eat cos bt

49). Inverse Laplace transform is ____ type?

Linear

Non-Linear

Constant

Both a and b

50). The Inverse Laplace transform of 1 is _____ type of function?

Delta function

Unit function

Both a and b

Star

Laplace Transform MCQs for Interviews

51). Laplace transform purpose is?

To represent complex differential equation in to simple polynomial

To convert derivate into a multiple domain variable

To covert polynomials to differential equation using inverse Laplace transform

All the above

52). Laplace transform used in converting ____ functions?

To convert time domain to frequency domain

To convert frequency domain into time domain

Both a and b

To convert from frequency to mid frequency

53). In which of the following field does laplace equation is used along with three-dimensional problem solving?

Electrostatics

Magnetostatics

Moment Magento Force

All the above

54). In which of the following field laplace equation used along with 2D _______?

Fluid Flow

Electric Flow

Ferromagnetic

All The Above

55). What is the Laplace transform of δ(t)?

∞

56). Find the Laplace transform of e-at u(t) and its ROC?

1/(s-a) , Re{s}>a

1/(s+a) , Re{s}>-a

(s+a) , Re{s}>a

1/(s-a) , Re{s}>-a

57). Find the Laplace transform of u(t) and its ROC?

. 1/s , σ<0

1/s , σ>0

58). Find the inverse Laplace transform of F(s) = k/(s-a) (k and a are constants) is?

k eat

k/s eat

s eat

1/s e

59). Frequency domain is also called?

S-domain

P-domain

S-plane

Both a and c

60). What is the Value of ∫_(-∞)^∞ [e^t Sin(t)]dt?

0.50

0.25

0.17

0.12

61). What is the value of ∫_(-∞)^∞[e^t log(1+t) ]dt?

Sum of infinite integers

Sum of infinite factorials

62). What is the Laplace transform of y(t) = e^t.t. Sint(t) cos(t)?

(2(s+1))/[(s-1)^2+4]^2

(4(s-1))/[(s-1)^2+4]^2

(4(s+1))/[(s-1)^2+4]^2

(2(s-1))/[(s-1)^2+4]^2

63). What is the Laplace transform of L(cat) is ?

1/(s-2log⁡(c))

1/(s+2log⁡(c))

1/(2slog⁡(c))

-1/(s+2log⁡(c))

64). What is the Laplace transform of d/(dt ) (sint/t)?

s×cot-1 s-1

s×tan-1 s-1

s×sin-1 s-1

s×cos-1 s-1

65). What is the Laplace transform of (sinh⁡(at))/(t )?

1/(3 ) 1/(2 ) log⁡( (s-a)/(s+a))

1/(2 ) log⁡( (s-a)/(s+a))

1/(3 ) 1/(2 ) log⁡( sa/(s+a))

1/(2 ) log⁡( (s+a)/(s-a))

66). What is the mathematical representation of Inverse Laplace transform is _________?

f(t)=L-1{F(s)}

f(t)=L-1{F(x)}

f(t)=L-1{F(t)}

f(s)=L-1{F(t)}

67). A system is said to be stable if ?

Poles lies at the left of the imaginary axis

Poles lies at the right of imaginary axis

Zeros lies at the left of the imaginary axis

Zeros lies at the right of the imaginary axis

68). What is the Initial value theorem?

lim┬(t→0^+ )⁡〖x(t)〗 = lim┬(s→infinite)⁡s x(s)

lim┬(t→0^+ )⁡〖x(t)〗 = x(s)

lim┬(t→0^+ )⁡〖x(t)〗 = lim┬(s→0)⁡s x(s)

lim┬(t→0^- )⁡〖x(t)〗 = lim┬(s→0)⁡s x(s)

69). If x(t) =δ(t) then Laplace transform of X(S) and Roc ?

δ(t)1 and Roc is imaginary axis

δ(t)1 and Roc is infinite

δ(t)1 and Roc is zero

70). If Laplace transform of x(s) is rational then ROC?

ROC does not contain any pole

ROC does contain pole

ROC is infinite

All the above

71). If x(t) is Right sided signal then ROC of its Laplace transform of X(s) will be?

Right to the Right most of pole

Left side of pole

Imaginary axis

Left to the Left most pole in S-plane

72). If x(t) is Right sided signal then ROC of its Laplace transform of X(s) will be?

Right to the Right most of pole

Left side of pole

Imaginary axis

Left to the Left most pole in S-plane

73). If x(t) is Double sided signal then ROC of its Laplace transform of X(s) will be ?

Right to the Right most of pole

Between the poles but does not contain any pole

Imaginary axis

Left to the Left most pole in S-plane

74). Frequency domain involves in?

Maths

Signals

Physics

Both a and b

75). What is the Laplace transform of the signal x(t) = (dδ(t))/dt?

1/s

Laplace Transform MCQs for Students

76). What is the Laplace transform of x(t) = 1/(√Πt)?

S ^-1⁄2

S^-1

S^-2

S^1⁄2

77). Frequency is expressed as ?

Hertz

Seconds

Ohms

Watts

78). Which of the following is the advantage of frequency domain?

Solves linear differential equation

Converts in to other domain

Solves complex equations

All the above

79). What is The Unilateral Laplace transform?

Different inputs and Same output

Same inputs and Different outputs

Same inputs and Same outputs

Different inputs and Different outputs

80). What is The Bilateral Laplace transform?

Different inputs and same output

Same inputs and different outputs

Same inputs and Same outputs

Different inputs and different outputs

81). What is Laplace transform?

A mathematical method for solving differential equations

A technique for finding the frequency response of a system

A method for solving integral equations

A technique for solving partial differential equations

82). What is the Laplace transform of the unit step function?

1/s

1-e^(-s)

1/s^2

83). What is the inverse Laplace transform of 1/s^2?

t^2

e^-t

84). What is the Laplace transform of e^(-at)u(t)?

1/(s+a)

e^(-as)

s/(s+a)

a/(s+a)

85).What is the Laplace transform of a periodic function?

Converges to a complex function

Converges to a real function

Does not converge

Converges to a constant function

86). What is the Laplace transform of a impulse function?

Converges to 1

Converges to 0

Converges to a complex function

Does not converge

87). Laplace transform can be used for what kind of equation?

Linear differential equation

Nonlinear differential equation

Linear algebraic equation

All of the above

88). What is the Laplace transform of a derivative of a function?

sL(x(t)) - x(0)

L(x'(t))

L(x(t))/s

-L(x(t))/s

89). What is the Laplace transform of a integral of a function?

L(∫x(t)dt)

1/s L(x(t))

L(x(t))/s

-L(x(t))/s

90). What is the Laplace transform of a convolution of two functions?

L(x(t))*L(y(t))

L(x(t)y(t))

L(x(t))+L(y(t))

L(x(t))/L(y(t))

91). What is the Laplace transform of a cosine function?

(s^2 + 1)/(s^2 + 2s cos(w)+ 1)

(s^2 + 1)/(s^2 + 2s + 1)

(s^2 + 1)/(s^2 - 2s cos(w) + 1)

(s^2 + 1)/(s^2 - 2s + 1)

92). What is the Laplace transform of a sine function?

(s^2 - 1)/(s^2 + 2s sin(w) + 1)

(s^2 - 1)/(s^2 + 2s + 1)

(s^2 - 1)/(s^2 - 2s sin(w) + 1)

(s^2 - 1)/(s^2 - 2s + 1)

93).What is the Laplace transform of a impulse function?

1/s^2

1/s

94).What is the Laplace transform of a function that is zero for tT?

(1 - e^(-sT))/s

e^(-sT)

1 - e^(-sT)

1 - e^(-sT))/s^2

95). What is the Laplace transform of a function that is zero for t>T?

(1 - e^(-sT))/s

e^(-sT)

1 - e^(-sT)

1 +e^(-sT)

96). What is the Laplace transform of a function that is zero for t<T?

e^(-sT)

(1 - e^(-sT))/s

1 - e^(-sT)

(1 - e^(-sT))/s^2

97). What is the Laplace transform of a function that is zero for t<0?

1/s

e^(-sT)

98). What is the Laplace transform of a function that is zero for t>0?

1/s

e^(-sT)

99). What is the Laplace transform of a function that is zero for t≠0?

1/s

e^(-sT)

100). What is the Laplace transform of a function that is zero for t=0?

1/s

e^(-sT)