Explore topic-wise MCQs in Engineering Mathematics.

This section includes 12 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the inverse laplace transform of ( frac{1}{s(s-1)(s^2+1)} ).

A. <sup>1</sup> <sub>2</sub> e<sup>-t</sup> + <sup>1</sup> <sub>2</sub> Sin(-t) <sup>1</sup> <sub>2</sub> Cos(-t)
B. <sup>1</sup> <sub>2</sub> e<sup>t</sup> + <sup>1</sup> <sub>2</sub> Sin(t) <sup>1</sup> <sub>2</sub> Cos(t)
C. <sup>1</sup> <sub>2</sub> e<sup>t</sup> + <sup>1</sup> <sub>2</sub> Sin(t) + <sup>1</sup> <sub>2</sub> Cos(t)
D. <sup>1</sup> <sub>2</sub> e<sup>t</sup> <sup>1</sup> <sub>2</sub> Sin(t) <sup>1</sup> <sub>2</sub> Cos(t)
Answer» C. <sup>1</sup> <sub>2</sub> e<sup>t</sup> + <sup>1</sup> <sub>2</sub> Sin(t) + <sup>1</sup> <sub>2</sub> Cos(t)
Discussion
2.

Find the inverse laplace transform of (Y(s)= frac{2s}{1-s^2}e^{-s} ).

A. -e<sup>-t + 1</sup> + e<sup>t 1</sup>
B. -e<sup>-t + 1</sup> e<sup>t + 1</sup>
C. -e<sup>-t + 1</sup> + e<sup>t + 1</sup>
D. -e<sup>-t + 1</sup> e<sup>t 1</sup>
Answer» E.
Discussion
3.

Find the inverse lapace of ( frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]} ).

A. <sup>1</sup> <sub>3</sub> e<sup>t</sup> [Cos(t) Cos(2t)].
B. <sup>1</sup> <sub>3</sub> e<sup>-t</sup> [Cos(t) + Cos(2t)].
C. <sup>1</sup> <sub>3</sub> e<sup>t</sup> [Cos(t) + Cos(2t)].
D. <sup>1</sup> <sub>3</sub> e<sup>-t</sup> [Cos(t) Cos(2t)].
Answer» E.
Discussion
4.

Find the value of x(0) if (X(s)= frac{2s^2+5s+12/s}{s^3+4s^2+14s+20} ).

A. 5
B. 4
C. 12
D. 2
Answer» E.
Discussion
5.

Find the value of x( ) if (X(s)= frac{2s^2+5s+12/s}{s^3+4s^2+14s+20} ).

A. 5
B. 4
C. <sup>12</sup> <sub>20</sub>
D. 2
Answer» D. 2
Discussion
6.

Initial value theorem states that ___________

A. x(0)= ( lim_{x rightarrow } sX(s) )
B. x( )= ( lim_{x rightarrow } sX(s) )
C. x(0)= ( lim_{x rightarrow 0} sX(s) )
D. x( )= ( lim_{x rightarrow 0} u2061sX(s) )
Answer» B. x( )= ( lim_{x rightarrow } sX(s) )
Discussion
7.

Final value theorem states that _________

A. x(0)= ( lim_{x rightarrow } sX(s) )
B. x( )= ( lim_{x rightarrow } sX(s) )
C. x(0)= ( lim_{x rightarrow 0} sX(s) )
D. x( )= ( lim_{x rightarrow 0} u2061sX(s) )
Answer» E.
Discussion
8.

Find the inverse laplace transform of ( frac{s}{(s^2+ 4)^2} ).

A. <sup>1</sup> <sub>4</sub> sin(2t)
B. <sup>t<sup>2</sup></sup> <sub>4</sub> sin(2t)
C. <sup>t</sup> <sub>4</sub> sin(2t)
D. <sup>t</sup> <sub>4</sub> sin(2t<sup>2</sup>)
Answer» D. <sup>t</sup> <sub>4</sub> sin(2t<sup>2</sup>)
Discussion
9.

Find the inverse laplace transform of ( frac{1}{(s^2+1)(s 1)(s + 5)} ).

A. <sup>1</sup> <sub>12</sub> e<sup>t</sup> <sup>1</sup> <sub>13</sub> Cos(-t) <sup>1</sup> <sub>12</sub> Sin(-t) <sup>1</sup> <sub>156</sub> e<sup>-5t</sup>
B. <sup>1</sup> <sub>12</sub> e<sup>-t</sup> <sup>1</sup> <sub>13</sub> Cos(t) <sup>1</sup> <sub>12</sub> Sin(t) <sup>1</sup> <sub>156</sub> e<sup>5t</sup>
C. <sup>1</sup> <sub>12</sub> e<sup>t</sup> <sup>1</sup> <sub>13</sub> Cos(t) <sup>1</sup> <sub>12</sub> Sin(t) <sup>1</sup> <sub>156</sub> e<sup>-5t</sup>
D. <sup>1</sup> <sub>12</sub> e<sup>t</sup> + <sup>1</sup> <sub>13</sub> Cos(t) + <sup>1</sup> <sub>12</sub> Sin(t) + <sup>1</sup> <sub>156</sub> e<sup>-5t</sup>
Answer» D. <sup>1</sup> <sub>12</sub> e<sup>t</sup> + <sup>1</sup> <sub>13</sub> Cos(t) + <sup>1</sup> <sub>12</sub> Sin(t) + <sup>1</sup> <sub>156</sub> e<sup>-5t</sup>
Discussion
10.

Inverse laplace transform of ( frac{1}{(s-1)^2 (s+5)} ) is?

A. <sup>1</sup> <sub>6</sub> e<sup> t</sup> <sup>1</sup> <sub>36</sub> e<sup>t</sup> + <sup>1</sup> <sub>36</sub> e<sup>-5t</sup>
B. <sup>1</sup> <sub>6</sub> e<sup>t</sup>t <sup>1</sup> <sub>36</sub> e<sup>t</sup> + <sup>1</sup> <sub>36</sub> e<sup>-5t</sup>
C. <sup>1</sup> <sub>6</sub> e<sup>-t</sup>t<sup>2</sup> <sup>1</sup> <sub>36</sub> e<sup>-t</sup> + <sup>1</sup> <sub>36</sub> e<sup>5t</sup>
D. <sup>1</sup> <sub>6</sub> e<sup>-t</sup> t-<sup>1</sup> <sub>36</sub> e<sup>-t</sup> + <sup>1</sup> <sub>36</sub> e<sup>5t</sup>
Answer» B. <sup>1</sup> <sub>6</sub> e<sup>t</sup>t <sup>1</sup> <sub>36</sub> e<sup>t</sup> + <sup>1</sup> <sub>36</sub> e<sup>-5t</sup>
Discussion
11.

Inverse Laplace transform of ( frac{1}{(s+1)(s-1)(s+2)} ) is?

A. <sup>1</sup> <sub>2</sub> e<sup>t</sup> + <sup>1</sup> <sub>6</sub> e<sup>-t</sup> + <sup>1</sup> <sub>3</sub> e<sup>2t</sup>
B. <sup>1</sup> <sub>2</sub> e<sup>-t</sup> + <sup>1</sup> <sub>6</sub> e<sup>t</sup> + <sup>1</sup> <sub>3</sub> e<sup>-2t</sup>
C. <sup>1</sup> <sub>2</sub> e<sup>-t</sup> <sup>1</sup> <sub>6</sub> e<sup>t</sup> <sup>1</sup> <sub>3</sub> e<sup>-2</sup>
D. <sup>1</sup> <sub>2</sub> e<sup>-t</sup> + <sup>1</sup> <sub>6</sub> e<sup>-t</sup> + <sup>1</sup> <sub>3</sub> e<sup>-2</sup>
Answer» C. <sup>1</sup> <sub>2</sub> e<sup>-t</sup> <sup>1</sup> <sub>6</sub> e<sup>t</sup> <sup>1</sup> <sub>3</sub> e<sup>-2</sup>
Discussion
12.

Time domain function of ( frac{s}{a^2+s^2} ) is given by?

A. Cos(at)
B. Sin(at)
C. Cos(at)Sin(at)
D. Sin(t)
Answer» B. Sin(at)
Discussion