Laplace Transform MCQ Questions | Inverse Laplace Transform MCQ | Laplace Transform Analysis Gives MCQ

1. If the Laplace transform of function f(t) is given by s+3/(s+1)(s+2), then f(0) is

a. 32

b. 12

c. 0

d. 1

2. Which of the following Laplace domain behaviors is correct for inductance?

a. L

b. s/L

c. 1/sL

d. sL

3. What is the linearity property of the Laplace transform?
a. A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s)

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

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

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

4. The unit step is not defined at point t =?
a. 0
b. 1
c. 2
d. 3

5. In ∂/∂x(uⁿ), where un is constant, is equal to

a. nu^n-1∂/_∂x

b. nu^n-1∂/_∂x

c. nuⁿ∂u⁄_∂x

d. 0

6. What is the Frequency Shifting Property of Laplace Transform?

a. es0t f(t)) ⟷ F(s – s0)

b. es0t f(t)) ⟷ F(s + s0)

c. es0t f(t)) ⟷ F(s * s0)

d. es0t f(t)) ⟷ F(s0)

7. The total period of the function shown in the figure is 4 sec, and the amplitude is 10. Find the function of f1 at (t) from an initial value of t = 0 to 1 of a unit step function.

a. 10t [u (t) – u (t + 1)]
b. 10t [u (t) + u (t – 1)]
c. 10t [u (t) + u (t + 1)]
d. 10t {u (t) – u (t – 1)}

8. M(x,y)∂²x+N(x,y)∂=0 is

a. Homogeneous ODE

b. Nonhomogeneous ODE

c. Partial ODE

d. nonlinear ODE

9. Laplace Transform of Unit Step Function is:

a. 1

b. s

c. 1/s

d. 2s

10. Laplace Transform of function e^-at is:

a. 1/s

b. -1/s

c. 1/(s+a)

d. 1/(s-a)

11. Find the function f (t) in terms of the unit step function in the graph below.

a. 4t [u (t) – u (t + 5)]
b. 4t [u (t) + u (t + 5)]
c. 4t [u (t) – u (t – 5)]
d. 4t [u (t) + u (t – 5)]

12. The Laplace transform of a function f (t) is?

a. (int_0^{infty}) f(t) e^-st
b. (int_{-infty}^0) f(t) e^-st
c. (int_0^{infty}) f(t) e^st
d. (int_{-infty}^0) f(t) e^st

13. Laplace transform is an integral transform that converts a function of a real variable to a function of a complex variable:

a. True

b. False

14. Transformation in which a function in one space is transformed to another space by a process of Integration that involves kernel is termed as

a. differential transform

b. integral transform

c. algebraic transform

d. rational transform

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15. The Inverse Laplace transform of (1/s+1) is:

a. e-t

b. et

c. 1

d. e1

16. Laplace transform changes the ____ domain function to the _____ domain function.

a. time, time
b. time, frequency
c. frequency, time
d. frequency, frequency

17. What is the Integration of Laplace Transform?

a. t∫0 f(λ) dλ ⟷ s F(s)

b. t∫0 f(λ) dλ ⟷ F(s)

c. t∫0 f(λ) dλ ⟷ 1⁄s F(s)

d. t∫0 f(λ) dλ ⟷ s F(s)

18. Laplace transform is an

a. differential transform

b. algebraic transform

c. integral transform

d. rational transform

19. Laplace transform of function f(t)=1.5sin(3t-π/2) is

a. 1.5/(s²+9)

b. 1.5s/(s²+9)

c. −1.5s/(s²+9)

d. s−1.5s/(s²+9)

20. Laplace Transform of Function sin ωt is:

a. 1/( s² + ω² )

b. 1/( s² – ω² )

c. ω/( s² + ω² )

d. ω/( s² – ω² )

21. In the bilateral Laplace transform, what is the lower limit?

a. 0
b. 1
c. ∞
d. – ∞

22. Vector field or direction field is also known as

a. slope field

b. universal field

c. exponential field

d. electrical field

23. Laplace transform if cos⁡(at)u(t) is?

a. s ⁄ a²+s²
b. a ⁄ a²+s²
c. s² ⁄ a²+s²
d. a² ⁄ a²+s²

24. What is the Multiplication by Time of Laplace Transform?

a. T f(t) ⟷ (−d F(s)⁄ds)

b. T f(t) ⟷ d F(s)⁄ds)

c. T f(t) ⟷ F(s)⁄ds)

d. T f(t) ⟷ (−t F(s)⁄ds)

25. The unit step is not defined at t =?

a. 0
b. 1
c. 2
d. 3

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26. (a,b] or [a,b) represents

a. infinite interval

b. closed interval

c. half-open interval

d. open interval

27. The total period of the function shown in the figure is 4 sec, and the amplitude is 10. Find the f1 (t) function from the initial value t = 0 to 1 in terms of a unit step function.

a. 10t [u (t) – u (t + 1)]
b. 10t [u (t) + u (t – 1)]
c. 10t [u (t) + u (t + 1)]
d. 10t {u (t) – u (t – 1)}

28. Value of ∫∞−∞etSin(t)dt = ?

a) 0.50
b) 0.25
c) 0.17
d) 0.12

29. Find the value of ∫∞0tsin(t)cos(t).

a. s ⁄ s²+2²
b. a ⁄ a²+s⁴
c. 1
d. 0

30. Find the function f₂ (t) from the time t = 1 to 3 sec.

a. (-10t+20) [u (t-1) +u (t-3)]
b. (-10t+20) [u (t-1) – u (t-3)]
c. (-10t-20) [u (t-1) + u (t-3)]
d. (-10t-20) [u (t-1) – u (t-3)]

31. The elementary functions are not closed under

a. Parenthesis

b. Integration

c. Differentiation

d. Brackets

32. Solution ‘y’ for y”-y-6y=0 by Laplace transform when y(0)=11 and y'(0)=28 is

a. e^-2t+e^3t

b. 10e^-2t+e^3t

c. e^-2t+10e^3t

d. e^-2t+10e^-3t

33. What is the Complex Shift Property of Laplace Transform?

a. f(t) e−at ⟷ F(s + a)

b. f(t) e−at ⟷ F(s – a)

c. f(t) e−at ⟷ F(s * a)

d. f(t) eat ⟷ F(s + a)

34. find the expression f (t) in the graph below.

a. 2t
b. 3t
c. 4t
d. 5t

35. Value of ∫∞−∞etSin(t)Cos(t)dt = ?

a. 0.5
b. 0.75
c. 0.2
d. 0.71

 36. An equation containing derivatives of one or more unknown functions concerning one or more independent variables is said to be a

a. integral equation

b. differential equation

c. algebraic equation

d. logical equation

37. If birth rate U_b and death rate U_d of the number of bacteria is proportional to the number of bacteria present and Ub>Ud, then at t=0, the number of bacteria

a. moves randomly

b. grows exponentially

c. decays exponentially

d. stays stable

38. A tool to graphically obtain the solutions to a first-order differential equation is

a. slope field

b. universal field

c. exponential field

d. electrical field

39. In derivative equation, ‘F(x,y,y^‘, …,yⁿ)=0′ y^‘ is

a. first derivative

b. second derivative

c. n-1 derivative

d. nth derivative

40. Value of ∫∞−∞etlog(1+t)dt = ?

a. Sum of infinite integers
b. Sum of infinite factorials
c. Sum of squares of Integers
d. Sum of square of factorials

41. Ä in Newton’s dot notation represents

a. ∂²A⁄∂t²

b. ∂A/∂ t²

c. ∂A/∂t

d. ^∂2A

42. In derivative equation, ‘F(x,y,y^‘, …,yⁿ)=0′ first derivative is represented as

a. y^‘=∂y/∂x

b. y^‘=∂x/∂y

c. y^‘=∂y x ∂x

d. y^‘=∂/∂x

43. What is the Laplace Transform of 1?

a. s

b. o

c. 1/s

d. π

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

a. sF(s) * f(0)s

b. F(s) + f(0)s

c. F(s) – f(0)

d. F(0)

45. Division is the inverse of

a. multiplication

b. Differentiation

c. Integration

d. exponential

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

a. as/(s2+a2)

b. a/(s2+a2)

c. s/(s2+a2)

d. 1/(s2+a2)

47. The standard form of second order equation y”+y-6y=0 is

a. y”=6y’

b. y”=6y-y

c. y”=6y+y

d. y”=y-6y

48. Derivative equation F(x,y,y^‘, …,yⁿ)=0 has order

a. 1

b. 2

c. n-1

d. n

49 Transfer function may be defined as ____________

a. Ratio of out to input
b. Ratio of place transform of obtaining the output to a given input
c. Ratio of Laplace transform of obtained output to given input with zero initial value
d. None of the mentioned

50. Poles of any transfer function are defined as the roots of the equation of the transfer function’s denominator.

a. True
b. False

51. Inverse Laplace transform of F(s)=(0.2s+1.8)/(s²+3.24) is

a. 0.2cos1.8t

b. 0.2sin1.8t

c. 0.2cos1.8t+0.2sin1.8t

d. 0.2cos1.8t+sin1.8t

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

a. F(s+c)

b. 1

c. F(s-c)

d. 0

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

a. Bilateral transform

b. Inverse Laplace transform

c. Laplace transform

d. All the above