September 25, 2023

# Laplace Transform Mcq : Free 100+ MCQ

“Master Laplace Transforms with 120 Multiple-Choice Questions and Answers: Test your knowledge of Laplace transforms with a comprehensive set of laplace transform mcq covering various aspects, from basic principles to advanced applications. Boost your understanding of this essential mathematical tool for solving complex differential equations.”

## Laplace Transform Mcq

### Laplace Transform Mcq 1 to 10

MCQ.1 What is the Laplace transform of a constant ‘a’?
A) a
B) 1/a
C) s/a
D) e^(as)

MCQ.2 Which of the following is not a property of Laplace transforms?
A) Linearity
B) Time-shift property
C) Convolution property
D) Differentiation property

MCQ.3 The Laplace transform of a unit impulse function δ(t) is:
A) 1
B) e^(-s)
C) 1/s
D) ∞

MCQ.4 What is the Laplace transform of sin(at)?
A) a/s
B) s/a
C) 1/(s^2 + a^2)
D) 1/a

MCQ.5 The Laplace transform of e^(at) is:
A) a/s
B) 1/s
C) s/a
D) 1/(s – a)

MCQ.6 Which Laplace transform property is used to solve linear constant coefficient differential equations?
A) Linearity
B) Convolution
C) Differentiation
D) Shifting

MCQ.7 The Laplace transform of t^n, where n is a positive integer, is:
A) n/s
B) s^n
C) n!
D) 1/(s^n)

MCQ.8 What is the Laplace transform of a periodic function?
A) Periodic
B) Impulse
C) Not well-defined
D) Zero

MCQ.9 The Laplace transform of a unit step function u(t) is:
A) 1/s
B) s
C) 1/(s^2)
D) 1/(s-1)

MCQ.10 The Laplace transform of a derivative, dx/dt, is equal to:
A) sX(s)
B) X(s)/s
C) X(s) – X(0)
D) X(0)/s

### Laplace Transform Mcq 11 to 20

MCQ.11 What is the Laplace transform of the product of two functions, f(t) and g(t)?
A) L[f(t)] * L[g(t)]
B) L[f(t) * g(t)]
C) L[f(t)] + L[g(t)]
D) L[f(t)] / L[g(t)]

MCQ.12 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f(at)?
A) F(as)
B) F(s/a)
C) F(s-a)
D) F(s)/a

MCQ.13 Which Laplace transform property allows you to evaluate the Laplace transform of the convolution of two functions?
A) Linearity
B) Shifting
C) Differentiation
D) Convolution

MCQ.14 The Laplace transform of a periodic function can be represented as a sum of:
A) Exponentials
B) Sines and cosines
C) Impulses
D) Polynomials

MCQ.15 What is the Laplace transform of a unit ramp function u(t)?
A) 1
B) 1/s^2
C) 1/s^3
D) 1/s^4

MCQ.16 The Laplace transform of the delta function δ(t-a) is:
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.17 Which property of Laplace transforms is used to find the Laplace transform of a shifted function?
A) Linearity
B) Shifting
C) Differentiation
D) Convolution

MCQ.18 The Laplace transform of a constant times a function is equal to:
A) The constant times the Laplace transform of the function
B) The Laplace transform of the constant times the Laplace transform of the function
C) The Laplace transform of the derivative of the function
D) The Laplace transform of the integral of the function
Answer: A) The constant times the Laplace transform of the function

MCQ.19 The Laplace transform of a second derivative, d²x/dt², is equal to:
A) s²X(s) – s
B) s²X(s) – s + X(0) – X'(0)
C) s²X(s)
D) s²X(s) – X(0)

MCQ.20 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f'(t) (the derivative of f(t))?
A) sF(s)
B) F(s) – f(0)
C) F'(s)
D) sF(s) – f(0)

### Laplace Transform Mcq 21 to 30

MCQ.21 The Laplace transform of a convolution of two functions f(t) and g(t) is equal to:
A) F(s) * G(s)
B) F(s) / G(s)
C) F(s) + G(s)
D) F(s) – G(s)

MCQ.22 The Laplace transform of a delta function δ(t) shifted to t = a is:
A) 1
B) e^(-as)
C) 1/s
D) δ(t-a)

MCQ.23 What is the Laplace transform of a function that has a finite duration, say from t = 0 to t = T?
A) It cannot be computed with Laplace transform
B) F(s) * (1 – e^(-Ts))
C) F(s) * (1 – e^(-sT))
D) F(s) * e^(-sT)
Answer: C) F(s) * (1 – e^(-sT))

MCQ.24 The Laplace transform of a constant times an impulse function δ(t) at t = a is:
A) 1
B) 1/a
C) ae^(-as)
D) δ(t-a)

MCQ.25 The Laplace transform of a periodic function with period T can be computed using the Laplace transform of one period. What is the result?
A) 1
B) T
C) 1/s
D) It depends on the specific periodic function

MCQ.26 What is the Laplace transform of a derivative, dx/dt, if the initial condition x(0) is known?
A) sX(s) – x(0)
B) sX(s)
C) X(s) – x(0)
D) X(s)

MCQ.27 If the Laplace transform of f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

MCQ.28 What is the Laplace transform of the convolution of two functions f(t) and g(t) when it’s given that the Laplace transforms of f(t) and g(t) are F(s) and G(s), respectively?
A) F(s) * G(s)
B) F(s) / G(s)
C) F(s) + G(s)
D) F(s) – G(s)

MCQ.29 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f(t – a), where ‘a’ is a constant?
A) e^(-as) * F(s)
B) F(s – a)
C) e^(as) * F(s)
D) F(s)/a

MCQ.30 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

### Laplace Transform Mcq 31 to 40

MCQ.31 The Laplace transform of a function f(t) is F(s). What is the Laplace transform of f(at), where ‘a’ is a constant?
A) F(s)
B) F(as)
C) F(s/a)
D) aF(s)

MCQ.32 The Laplace transform of a periodic function can be computed using the Laplace transform of one period, which is equal to:
A) 1
B) The period
C) 1/s
D) It depends on the specific periodic function

MCQ.33 What is the Laplace transform of the unit step function u(t-a)?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.34 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.35 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.36 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.37 The Laplace transform of a constant ‘a’ times the unit step function u(t) is:
A) a/s
B) a
C) 1/s
D) 0

MCQ.38 What is the Laplace transform of a function f(t) that is zero for t < 0?
A) F(s)
B) F(s) * e^(-s0)
C) 0
D) F(s) * e^(st)

MCQ.39 The Laplace transform of the function f(t) = t^n, where n is a non-negative integer, is:
A) n/s
B) s^n
C) n!
D) 1/(s^n+1)

MCQ.40 What is the Laplace transform of the Dirac delta function δ(t)?
A) 1
B) 0
C) ∞
D) Not defined

### Laplace Transform Mcq 41 to 50

MCQ.41 The Laplace transform of the function f(t) = e^(-at) is:
A) 1/(s – a)
B) 1/(s + a)
C) 1/(s² – a²)
D) 1/(s² + a²)

MCQ.42 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

MCQ.43 The Laplace transform of the derivative of a function, d/dt[f(t)], is equal to:
A) sF(s) – f(0)
B) sF(s)
C) F(s) – f(0)
D) F(s)

MCQ.44 What is the Laplace transform of the unit step function u(t-a)?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.45 If the Laplace transform of f(t) is F(s), what is the Laplace transform of f(at), where ‘a’ is a constant?
A) F(s)
B) F(as)
C) F(s/a)
D) aF(s)

MCQ.46 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.47 The Laplace transform of a constant ‘a’ times the unit step function u(t) is:
A) a/s
B) a
C) 1/s
D) 0

MCQ.48 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.49 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.50 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

### Laplace Transform Mcq 51 to 60

MCQ.51 The Laplace transform of a function f(t) = t^n, where n is a non-negative integer, is:
A) n/s
B) s^n
C) n!
D) 1/(s^n+1)

MCQ.52 What is the Laplace transform of the Dirac delta function δ(t)?
A) 1
B) 0
C) ∞
D) Not defined

MCQ.53 The Laplace transform of the function f(t) = e^(-at) is:
A) 1/(s – a)
B) 1/(s + a)
C) 1/(s² – a²)
D) 1/(s² + a²)

MCQ.54 The Laplace transform of a function f(t) = t^n, where n is a non-negative integer, is:
A) n/s
B) s^n
C) n!
D) 1/(s^n+1)

MCQ.55 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.56 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

MCQ.57 The Laplace transform of a derivative, dx/dt, is equal to:
A) sX(s) – x(0)
B) sX(s)
C) X(s) – x(0)
D) X(s)

MCQ.58 The Laplace transform of the unit step function u(t-a) is:
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.59 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.60 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

### Laplace Transform Mcq 61 to 70

MCQ.61 The Laplace transform of a constant ‘a’ times the unit step function u(t) is:
A) a/s
B) a
C) 1/s
D) 0

MCQ.62 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.63 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.64 The Laplace transform of a periodic function can be computed using the Laplace transform of one period, which is equal to:
A) 1
B) The period
C) 1/s
D) It depends on the specific periodic function

MCQ.65 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f(at), where ‘a’ is a constant?
A) F(s)
B) F(as)
C) F(s/a)
D) aF(s)

MCQ.66 What is the Laplace transform of the function f(t) = 1?
A) 1
B) s
C) 1/s
D) e^(-s)

MCQ.67 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”'(t) (the third derivative of f(t))?
A) s³F(s)
B) F”'(s)
C) s³F(s) – s²f(0) – sf'(0) – f”(0)
D) s³F(s) – s²f(0) – sf'(0)

MCQ.68 The Laplace transform of a constant ‘a’ is:
A) 1/a
B) s/a
C) a/s
D) e^(as)

MCQ.69 What is the Laplace transform of the impulse function δ(t-a), where ‘a’ is a constant?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.70 The Laplace transform of a periodic function can be computed using the Laplace transform of one period, which is equal to:
A) 1
B) The period
C) 1/s
D) It depends on the specific periodic function

### Laplace Transform Mcq 71 to 80

MCQ.71 What is the Laplace transform of a constant times the unit step function u(t-a)?
A) 1
B) e^(-as)
C) a/s
D) e^(as)

MCQ.72 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f'(t) (the derivative of f(t))?
A) sF(s)
B) F'(s)
C) sF(s) – f(0)
D) F(s) – f(0)

MCQ.73 The Laplace transform of the function f(t) = t is:
A) 1/s²
B) 1/s³
C) 1/s² – 1/s
D) 1/s³ – 1/s²

MCQ.74 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.75 The Laplace transform of the unit step function u(t) is:
A) 1/s
B) s
C) 1/(s^2)
D) 1/(s-1)

MCQ.76 What is the Laplace transform of the unit impulse function δ(t) shifted to t = a?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.77 The Laplace transform of a constant times the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.78 The Laplace transform of the derivative of a function, dx/dt, is equal to:
A) sX(s) – x(0)
B) sX(s)
C) X(s) – x(0)
D) X(s)

MCQ.79 What is the Laplace transform of sin(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.80 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

### Laplace Transform Mcq 81 to 90

MCQ.81 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.82 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.83 The Laplace transform of a constant ‘a’ times the unit step function u(t) is:
A) a/s
B) a
C) 1/s
D) 0

MCQ.84 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.85 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.86 The Laplace transform of a periodic function can be computed using the Laplace transform of one period, which is equal to:
A) 1
B) The period
C) 1/s
D) It depends on the specific periodic function

MCQ.87 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f(at), where ‘a’ is a constant?
A) F(s)
B) F(as)
C) F(s/a)
D) aF(s)

MCQ.88 The Laplace transform of a constant times the unit step function u(t-a) is:
A) 1
B) e^(-as)
C) a/s
D) e^(as)

MCQ.89 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.90 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

### Laplace Transform Mcq 91 to 100

MCQ.91 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.92 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

MCQ.93 The Laplace transform of a constant ‘a’ times the impulse function δ(t) is:
A) a
B) 0
C) ∞
D) Not defined

MCQ.94 What is the Laplace transform of sin(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.95 The Laplace transform of a constant times the unit step function u(t-a) is:
A) 1
B) e^(-as)
C) a/s
D) e^(as)

MCQ.96 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f'(t) (the derivative of f(t))?
A) sF(s)
B) F'(s)
C) sF(s) – f(0)
D) F(s) – f(0)

MCQ.97 The Laplace transform of the function f(t) = t is:
A) 1/s²
B) 1/s³
C) 1/s² – 1/s
D) 1/s³ – 1/s²

MCQ.98 The Laplace transform of a constant ‘a’ times the unit impulse function δ(t) is:
A) a
B) 0
C) ∞
D) Not defined

MCQ.99 What is the Laplace transform of the impulse function δ(t-a), where ‘a’ is a constant?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.100 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”'(t) (the third derivative of f(t))?
A) s³F(s)
B) F”'(s)
C) s³F(s) – s²f(0) – sf'(0) – f”(0)
D) s³F(s) – s²f(0) – sf'(0)

### Laplace Transform Mcq 101 to 110

MCQ.101 The Laplace transform of a constant ‘a’ is:
A) 1/a
B) s/a
C) a/s
D) e^(as)

MCQ.102 What is the Laplace transform of the unit impulse function δ(t-a), where ‘a’ is a constant?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.103 The Laplace transform of a periodic function can be computed using the Laplace transform of one period, which is equal to:
A) 1
B) The period
C) 1/s
D) It depends on the specific periodic function

MCQ.104 What is the Laplace transform of a constant times the unit step function u(t-a)?
A) 1
B) e^(-as)
C) a/s
D) e^(as)

MCQ.105 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f'(t) (the derivative of f(t))?
A) sF(s)
B) F'(s)
C) sF(s) – f(0)
D) F(s) – f(0)

MCQ.106 The Laplace transform of the function f(t) = t is:
A) 1/s²
B) 1/s³
C) 1/s² – 1/s
D) 1/s³ – 1/s²

MCQ.107 The Laplace transform of a function that has a finite duration from t = a to t = b is:
A) F(s) * (e^(-as) – e^(-bs))
B) F(s) * (1 – e^(-s(b-a)))
C) F(s) * (e^(-s(b-a)) – e^(-sa))
D) F(s) * (e^(-s(b-a)))
Answer: B) F(s) * (1 – e^(-s(b-a)))

MCQ.108 The Laplace transform of the unit step function u(t) is:
A) 1/s
B) s
C) 1/(s^2)
D) 1/(s-1)

MCQ.109 What is the Laplace transform of the unit impulse function δ(t) shifted to t = a?
A) e^(-as)
B) e^(as)
C) 1/(s-a)
D) 1/(s+a)

MCQ.110 The Laplace transform of a constant times the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

### Laplace Transform Mcq 111 to 120

MCQ.111 The Laplace transform of the derivative of a function, dx/dt, is equal to:
A) sX(s) – x(0)
B) sX(s)
C) X(s) – x(0)
D) X(s)

MCQ.112 What is the Laplace transform of sin(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.113 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f”(t) (the second derivative of f(t))?
A) s²F(s)
B) F”(s)
C) s²F(s) – sf(0) – f'(0)
D) s²F(s) – sf(0)

MCQ.114 The Laplace transform of a constant ‘a’ times the impulse function δ(t) is:
A) a
B) 0
C) ∞
D) Not defined

MCQ.115 What is the Laplace transform of the integral of a function, ∫[0 to t] f(u) du?
A) 1/s * F(s)
B) s * F(s)
C) F(s) / s
D) F(s)

MCQ.116 The Laplace transform of the impulse function δ(t) is:
A) 1
B) 0
C) ∞
D) Not defined

MCQ.117 What is the Laplace transform of cos(ωt), where ω is a constant?
A) ω/s
B) s/ω
C) 1/(s² + ω²)
D) s²/ω

MCQ.118 If the Laplace transform of a function f(t) is F(s), what is the Laplace transform of f'(t) (the derivative of f(t))?
A) sF(s)
B) F'(s)
C) sF(s) – f(0)
D) F(s) – f(0)

MCQ.119 The Laplace transform of the function f(t) = t is:
A) 1/s²
B) 1/s³
C) 1/s² – 1/s
D) 1/s³ – 1/s²

MCQ.120 The Laplace transform of a constant ‘a’ times the unit impulse function δ(t) is:
A) a
B) 0
C) ∞
D) Not defined

I hope you find these laplace transform mcq helpful for practicing Laplace transforms. If you have any more questions or need further assistance, please feel free to ask!

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#### Abhijeet Bendale

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