Explore topic-wise MCQs in Engineering Mathematics.

This section includes 15 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.

If L { f(t) } = F(s), then L {kf(t)} = ?

A. F(s)
B. k F(s)
C. Does not exist
D. F(<sup>s</sup> <sub>k</sub>)
Answer» C. Does not exist
Discussion
2.

If f(t)= ( frac{1}{b}e^{at}sinh(bt) ), then its Laplace transform is?

A. 1/s
B. Indeterminate
C. ( frac{b}{(s-a)^2-b^2} )
D. (f(t)= frac{1}{(s-a)^2-b^2} )
Answer» E.
Discussion
3.

f(t) = t, then its Laplace transform is?

A. ( frac{(s)sin(b)+acos(b)}{s^2+a^2} )
B. ( frac{2as^2}{(s^2+a^2)^2} )
C. ( frac{ Gamma(p+1)}{s^{p+1}} )
D. 1/s<sup>2</sup>
Answer» E.
Discussion
4.

If f(t) = u(t), then its Laplace transform is?

A. ( frac{scos(b)-asin(b)}{s^2+a^2} )
B. 1/2
C. ( frac{s}{s^2-a^2} )
D. ( frac{b}{(s-a)^2+b^2} )
Answer» C. ( frac{s}{s^2-a^2} )
Discussion
5.

If f(t) = te-at, then its Laplace transform is?

A. ( frac{1}{(s+a)^2} )
B. ( frac{2a}{(s-b)^2+b^2} )
C. ( frac{a^3}{s^2+a^2)^2} )
D. Indeterminate
Answer» B. ( frac{2a}{(s-b)^2+b^2} )
Discussion
6.

If f(t) = (t), then its Laplace transform is?

A. s + a (s a)<sup>2</sup> + b<sup>2</sup>
B. a<sup>3</sup> (s<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>
C. 1
D. Does not exist
Answer» D. Does not exist
Discussion
7.

If f(t) = t 2 a sinat, then its Laplace transform is?

A. b (s + a)<sup>2</sup> + b<sup>2</sup>
B. 2a (s b)<sup>2</sup> + b<sup>2</sup>
C. Indeterminate
D. s (s<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>
Answer» E.
Discussion
8.

If f(t) = 1 t, then its Laplace transform is?

A. ( frac{s^2-a^2}{(s-a)^2} )
B. S<sup>-1/2</sup>
C. ( frac{n!}{(s-a)^{n-1}} )
D. ( frac{n!}{(s-a)^{n-1}} )
Answer» C. ( frac{n!}{(s-a)^{n-1}} )
Discussion
9.

If f(t) = tn n, then its Laplace transform is?

A. ( frac{s+a}{(s-a)}{(s-a)^2+b^2} )
B. ( frac{b^2}{(s-a)}{(s-a)^2+b^2} )
C. ( frac{2a^3}{(s^2+a^2)} )
D. ( frac{(n-1)!}{s^{n+1}} )
Answer» E.
Discussion
10.

If f(t) = 1 a sinh(at), then its Laplace transform is?

A. 1 s<sup>2</sup>-a<sup>2</sup>
B. 2a (s b)<sup>2</sup> + b<sup>2</sup>
C. n! (s a)<sup>n-1</sup>
D. Does not exist
Answer» B. 2a (s b)<sup>2</sup> + b<sup>2</sup>
Discussion
11.

If f(t) = eat sinh(bt) then its Laplace transform is?

A. e<sup>-as</sup> s
B. s+a (s a)<sup>2</sup> + b<sup>2</sup>
C. b (s a)<sup>2</sup> b<sup>2</sup>
D. Does not exist
Answer» D. Does not exist
Discussion
12.

If f(t) = eat cos(bt), then its Laplace transform is?

A. 2a<sup>3</sup> (s<sup>2</sup> + a<sup>2</sup>)
B. s+a s-a
C. Indeterminate
D. s-a (s a)<sup>2</sup> + b<sup>2</sup>
Answer» E.
Discussion
13.

If f(t) = eat sin(bt), then its Laplace transform is given by?

A. s<sup>2</sup>-a<sup>2</sup> (s a)<sup>2</sup>
B. b (s + a)<sup>2</sup> + b<sup>2</sup>
C. b (s a)<sup>2</sup> + b<sup>2</sup>
D. Indeterminate
Answer» D. Indeterminate
Discussion
14.

If f(t) = coshat, its Laplace transform is given by?

A. s s<sup>2</sup>-a<sup>2</sup>
B. s+a s-a
C. Indeterminate
D. (sinh(at))<sup>2</sup>
Answer» B. s+a s-a
Discussion
15.

If f(t) = sinhat, then its Laplace transform is?

A. e<sup>at</sup>
B. s s<sup>2</sup>-a<sup>2</sup>
C. a s<sup>2</sup>-a<sup>2</sup>
D. Exists only if t is complex
Answer» D. Exists only if t is complex
Discussion