Transform Theory MCQs Question and Answer in Engineering Maths Page-4 section-1

31.
The inverse Laplace transform of the function $${\text{F}}\left( {\text{s}} \right) = \frac{1}{{{\text{s}}\left( {{\text{s}} + 1} \right)}}$$ is given by

A. f(t) = sin t

B. f(t) = e^-t sin t

C. f(t) = e^-t

D. f(t) = 1 - e^-t

Answer & Solution Discuss in Board Save for Later

32.
Laplace transform analysis gives

A. Time domain response only

B. Frequency domain response only

C. Both A and B

D. None of the above

Answer & Solution Discuss in Board Save for Later

33.
Inverse Laplace transform of the function $$\frac{s}{{{s^2} + 3s + 2}},$$ is

A. $$ - {e^{ - t}} + 2{e^{ - 2t}}$$

B. $${e^{ - t}} - 2{e^{ - 2t}}$$

C. $${e^{ - t}} + 2{e^{ - 2t}}$$

D. $$2{e^{ - t}} + {e^{ - 2t}}$$

Answer & Solution Discuss in Board Save for Later

34.
Which of the following is the advantage of using Laplace transform techniques?

A. Permits use of simple algebra

B. Converts functions in the $$t$$-domain into $$s$$-domain

C. Initial conditions are automatically taken care of

D. All of the above

Answer & Solution Discuss in Board Save for Later

35.
The initial value theorem does not hold good for which of the following functions?

A. Ramp function

B. Delta function

C. Step function

D. Hyperbolic function

Answer & Solution Discuss in Board Save for Later

36.
Find the inverse Laplace transform of $$F\left( s \right) = \frac{{{s^2} + 2s - 2}}{{s\left( {s + 4} \right)\left( {s - 5} \right)}}$$

A. $$\left( {\frac{1}{{10}} + \frac{1}{6}{e^{ - 4t}} + \frac{{11}}{{15}}{e^{5t}}} \right)u\left( t \right)$$

B. $$\left( {\frac{1}{{10}} + \frac{1}{6}{e^{6t}} + \frac{{10}}{{15}}{e^{5t}}} \right)u\left( t \right)$$

C. $$\left( {1 + \frac{1}{6}{e^{ - 4t}} + \frac{{10}}{{15}}{e^{5t}}} \right)u\left( t \right)$$

D. $$\left( {\frac{1}{{10}} - \frac{1}{6}{e^{4t}} + \frac{{10}}{{15}}{e^{ - 5t}}} \right)u\left( t \right)$$

Answer & Solution Discuss in Board Save for Later

37.
Give transfer function $$H\left( s \right) = \frac{{s + 2}}{{{s^2} + s + 4}},$$ under steady state condition, the sinusoidal input and output are, respectively x(t) = cos 2t, y(t) = cos(2t + $$\phi $$), then angle $$\phi $$ will be

A. 45°

B. 0°

C. -45°

D. -90°

Answer & Solution Discuss in Board Save for Later

38.
Which of the following correctly defines Laplace transform of a function in the time domain?

A. $$L\left\{ {f\left( t \right)} \right\} = \int_{{0^ - }}^\infty {f\left( t \right){e^{ - st}}dt} $$

B. $$L\left\{ {f\left( t \right)} \right\} = \int_{{0^ - }}^\infty {f\left( t \right){e^{ + st}}dt} $$

C. $$L\left\{ {f\left( t \right)} \right\} = \int_{{0^ - }}^\infty {f{{\left( t \right)}^{ - st}}{e^{ - st}}dt} $$

D. $$L\left\{ {f\left( t \right)} \right\} = \int_{{0^ - }}^\infty {f\left( s \right){e^{ - st}}dt} $$

Answer & Solution Discuss in Board Save for Later

39.
The Laplace transform of $$I\left( t \right)$$ is given by $$I\left( s \right) = \frac{5}{{s\left( {{s^2} + 2} \right)}}.$$ As $$t \to \infty $$ the value of $$I\left( t \right)$$ tends to

A. 0

B. 1

C. $$\frac{5}{2}$$

D. $$\infty $$

Answer & Solution Discuss in Board Save for Later

40.
Given that $$F\left( s \right)$$ is the one-side Laplace transform of $$f\left( t \right),$$ the Laplace transform of $$\int_0^t {f\left( \tau \right)d\tau } $$ is

A. $$sF\left( s \right) - f\left( 0 \right)$$

B. $$\frac{1}{s}F\left( s \right)$$

C. $$\int_0^5 {F\left( \tau \right)d\tau } $$

D. $$\frac{1}{s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$

Answer & Solution Discuss in Board Save for Later

Transform Theory MCQs Question and Answer in Engineering Maths

31. The inverse Laplace transform of the function $${\text{F}}\left( {\text{s}} \right) = \frac{1}{{{\text{s}}\left( {{\text{s}} + 1} \right)}}$$ is given by

Answer & Solution

32. Laplace transform analysis gives

Answer & Solution

33. Inverse Laplace transform of the function $$\frac{s}{{{s^2} + 3s + 2}},$$ is

Answer & Solution

34. Which of the following is the advantage of using Laplace transform techniques?

Answer & Solution

35. The initial value theorem does not hold good for which of the following functions?

Answer & Solution

36. Find the inverse Laplace transform of $$F\left( s \right) = \frac{{{s^2} + 2s - 2}}{{s\left( {s + 4} \right)\left( {s - 5} \right)}}$$

Answer & Solution

37. Give transfer function $$H\left( s \right) = \frac{{s + 2}}{{{s^2} + s + 4}},$$ under steady state condition, the sinusoidal input and output are, respectively x(t) = cos 2t, y(t) = cos(2t + $$\phi $$), then angle $$\phi $$ will be

Answer & Solution

38. Which of the following correctly defines Laplace transform of a function in the time domain?

Answer & Solution

39. The Laplace transform of $$I\left( t \right)$$ is given by $$I\left( s \right) = \frac{5}{{s\left( {{s^2} + 2} \right)}}.$$ As $$t \to \infty $$ the value of $$I\left( t \right)$$ tends to

Answer & Solution

40. Given that $$F\left( s \right)$$ is the one-side Laplace transform of $$f\left( t \right),$$ the Laplace transform of $$\int_0^t {f\left( \tau \right)d\tau } $$ is

Answer & Solution

31.
The inverse Laplace transform of the function $${\text{F}}\left( {\text{s}} \right) = \frac{1}{{{\text{s}}\left( {{\text{s}} + 1} \right)}}$$ is given by

32.
Laplace transform analysis gives

33.
Inverse Laplace transform of the function $$\frac{s}{{{s^2} + 3s + 2}},$$ is

34.
Which of the following is the advantage of using Laplace transform techniques?

35.
The initial value theorem does not hold good for which of the following functions?

36.
Find the inverse Laplace transform of $$F\left( s \right) = \frac{{{s^2} + 2s - 2}}{{s\left( {s + 4} \right)\left( {s - 5} \right)}}$$

37.
Give transfer function $$H\left( s \right) = \frac{{s + 2}}{{{s^2} + s + 4}},$$ under steady state condition, the sinusoidal input and output are, respectively x(t) = cos 2t, y(t) = cos(2t + $$\phi $$), then angle $$\phi $$ will be

38.
Which of the following correctly defines Laplace transform of a function in the time domain?

39.
The Laplace transform of $$I\left( t \right)$$ is given by $$I\left( s \right) = \frac{5}{{s\left( {{s^2} + 2} \right)}}.$$ As $$t \to \infty $$ the value of $$I\left( t \right)$$ tends to

40.
Given that $$F\left( s \right)$$ is the one-side Laplace transform of $$f\left( t \right),$$ the Laplace transform of $$\int_0^t {f\left( \tau \right)d\tau } $$ is