Explore topic-wise MCQs in Engineering Mathematics.

This section includes 8 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_F(T)_=_TCOS(AT),_ITS_LAPLACE_TRANSFORM_IS_GIVEN_BY?$

A. 1 ‚ÅÑ s-a
B. s<sup>2</sup> – a<sup>2</sup> ⁄ (s<sup>2</sup>+a<sup>2</sup>)<sup>2</sup>
C. Indeterminate
D. s<sup>2</sup>at
Answer» C. Indeterminate
Discussion
2.

If f(t) = sin(at) – atcos(at), then its Laplace transform is given by$#
A. Indeterminate form is encountered
B. a<sup>3</sup> ‚ÅÑ (s<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>
C. 2a<sup>3</sup> ⁄ (s<sup>2</sup> – a<sup>2</sup>)<sup>2</sup>
D. 2a<sup>3</sup> ‚ÅÑ (s<sup>2</sup> + a<sup>2</sup>)<sup>2</sup>
Answer» E.
Discussion
3.

If f(t) = cos(at), its Laplace transform is given b?

A. s ‚ÅÑ s<sup>2</sup>+a<sup>2</sup>
B. a ‚ÅÑ s<sup>2</sup>+a<sup>2</sup>
C. √π ⁄ 2√s
D. Does not exist
Answer» B. a ‚Äö√Ñ√∂‚àö√ñ‚àö√´ s<sup>2</sup>+a<sup>2</sup>
Discussion
4.

If f(t) = eat, its Laplace Transform is given by

A. a ‚ÅÑ s<sup>2</sup>+a<sup>2</sup>
B. √π ⁄ 2√s
C. 1 ‚ÅÑ s-a
D. Does not exist
Answer» D. Does not exist
Discussion
5.

If f(t) = sin(at), then its Laplace Transform is given by

A. cos(at)
B. 1 ‚ÅÑ a<sup>sin(at)</sup>
C. Indeterminate
D. a ‚ÅÑ s<sup>2</sup>+a<sup>2</sup>
Answer» E.
Discussion
6.

If f(t)=‚àöt, then its Laplace Transform is given by$

A. <sup>1</sup>‚ÅÑ<sub>2</sub>
B. <sup>1</sup>‚ÅÑ<sub>s</sub>
C. √π ⁄ 2√s
D. Does not exist
Answer» D. Does not exist
Discussion
7.

If f(t) = tn where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by$

A. n!
B. t<sup>n+1</sup>
C. n! ‚ÅÑ s<sup>n+1</sup>
D. Does not exist
Answer» D. Does not exist
Discussion
8.

If f(t) = 1, then its Laplace Transform is given by
A. s
B. <sup>1</sup>‚ÅÑ<sub>s</sub>
C. 1
D. Does not exist
Answer» C. 1
Discussion