MCQOPTIONS
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MCQOPTIONS
This section includes 14 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) = cos(at + b), its Laplace transform is given by? |
| A. | ( frac{a}{s^2+a^2} ) |
| B. | ( frac{2as}{(s^2+a^2)^2} ) |
| C. | ( frac{scos(b)-asin(b)}{s^2+a^2} ) |
| D. | Does not exist |
| Answer» D. Does not exist | |
| 2. |
If f(t) = sin(at + b), its Laplace transform is given by? |
| A. | Indeterminate |
| B. | ( frac{(s)sin(b)+acos(b)}{s^2+a^2} ) |
| C. | ( frac{s^2-a^2}{(s-a)^2} ) |
| D. | ( frac{2a^3}{(s^2+a^2)} ) |
| Answer» C. ( frac{s^2-a^2}{(s-a)^2} ) | |
| 3. |
If f(t) = cos(at) + atsin(at), its Laplace transform is given by? |
| A. | ( frac{s+a}{s-a} ) |
| B. | ( frac{a^3}{(s^2+a^2)^2} ) |
| C. | ( frac{s(s^2+3a^2)}{(s^2+a^2)^2} ) |
| D. | Does not exist |
| Answer» D. Does not exist | |
| 4. |
If f(t) = cos(at) atsin(at), then its Laplace transform is given by? |
| A. | sinat<sup>2</sup> |
| B. | ( frac{s(s^2-a^2)}{(s^2+a^2)^2} ) |
| C. | ( frac{ Gamma(p+1)}{s^{p+1}} ) |
| D. | Does not exist |
| Answer» C. ( frac{ Gamma(p+1)}{s^{p+1}} ) | |
| 5. |
If f(t) = sin(at) atcos(at), then its Laplace transform is given by? |
| A. | Indeterminate form is encountered |
| B. | a<sup>3</sup> (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> (s<sup>2</sup> + a<sup>2</sup>)<sup>2</sup> |
| Answer» E. | |
| 6. |
If f(t) = tcos(at), its Laplace transform is given by? |
| A. | 1 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 | |
| 7. |
If f(t) = cos(at), its Laplace transform is given by? |
| A. | s s<sup>2</sup>+a<sup>2</sup> |
| B. | a s<sup>2</sup>+a<sup>2</sup> |
| C. | 2 s |
| D. | Does not exist |
| Answer» B. a s<sup>2</sup>+a<sup>2</sup> | |
| 8. |
If f(t) = tp where p > 1, its Laplace Transform is given by? |
| A. | 2 s |
| B. | f(t) = tsin(at) |
| C. | (p+1) s<sup>p+1</sup> |
| D. | Does not exist |
| Answer» E. | |
| 9. |
If f(t) = eat, its Laplace Transform is given by? |
| A. | a s<sup>2</sup>+a<sup>2</sup> |
| B. | 2 s |
| C. | 1 s-a |
| D. | Does not exist |
| Answer» D. Does not exist | |
| 10. |
If f(t) = tsin(at) then its Laplace Transform is given by? |
| A. | 2as (s<sup>2</sup>+a<sup>2</sup>)<sup>2</sup> |
| B. | a s<sup>2</sup>+a<sup>2</sup> |
| C. | Indeterminate |
| D. | 2 s |
| Answer» B. a s<sup>2</sup>+a<sup>2</sup> | |
| 11. |
If f(t) = sin(at), then its Laplace Transform is given by? |
| A. | cos(at) |
| B. | 1 a<sup>sin(at)</sup> |
| C. | Indeterminate |
| D. | a s<sup>2</sup>+a<sup>2</sup> |
| Answer» E. | |
| 12. |
If f(t)= t, then its Laplace Transform is given by? |
| A. | <sup>1</sup> <sub>2</sub> |
| B. | <sup>1</sup> <sub>s</sub> |
| C. | 2 s |
| D. | Does not exist |
| Answer» D. Does not exist | |
| 13. |
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! s<sup>n+1</sup> |
| D. | Does not exist |
| Answer» D. Does not exist | |
| 14. |
If f(t) = 1, then its Laplace Transform is given by? |
| A. | s |
| B. | <sup>1</sup> <sub>s</sub> |
| C. | 1 |
| D. | Does not exist |
| Answer» C. 1 | |