MCQOPTIONS
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MCQOPTIONS
This section includes 12 Mcqs, each offering curated multiple-choice questions to sharpen your Signals & Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Given x(t)=e-t u(t). Find the inverse Laplace transform of e-3s X(2s). |
| A. | ( frac{1}{2} ) e<sup>-(t-3)/2</sup> u(t+3) |
| B. | ( frac{1}{2} ) e<sup>-(t-3)/2</sup> u(t-3) |
| C. | ( frac{1}{2} ) e<sup>(t-3)/2</sup> u(t-3) |
| D. | ( frac{1}{2} ) e<sup>(t-3)/2</sup> u(t+3) |
| Answer» C. ( frac{1}{2} ) e<sup>(t-3)/2</sup> u(t-3) | |
| 2. |
Find the inverse Laplace transform for the function X(s) = ( frac{1+e^{-2s}}{3s^2+2s} ). |
| A. | e<sup>-(2/3)t</sup> u(t) u(t) + e<sup>-(2/3)(t-2)</sup> u(t-2)-u(t-2) |
| B. | e<sup>-(2/3)t</sup> u(t) + e<sup>-(2/3)(t-2)</sup> u(t-2) |
| C. | e<sup>-(2/3)(t-2)</sup> u(t-2) u(t-2) |
| D. | e<sup>-(2/3)t</sup> u(t) u(t) |
| Answer» B. e<sup>-(2/3)t</sup> u(t) + e<sup>-(2/3)(t-2)</sup> u(t-2) | |
| 3. |
Find the inverse Laplace transform for the function X(s) = ( frac{2s-1}{s^2+4s+8} ). |
| A. | e<sup>-2t</sup> cos u20612t u(t) e<sup>-2t</sup> sin u20612t u(t) |
| B. | 2e<sup>-2t</sup> cos u20612t u(t) ( frac{5}{2} ) e<sup>-2t</sup> sin u20612t u(t) |
| C. | 2e<sup>-2t</sup> cos u20612t u(t) e<sup>-2t</sup> sin u20612t u(t) |
| D. | e<sup>-2t</sup> cos u20612t u(t) ( frac{5}{2} ) e<sup>-2t</sup> sin u20612t u(t) |
| Answer» C. 2e<sup>-2t</sup> cos u20612t u(t) e<sup>-2t</sup> sin u20612t u(t) | |
| 4. |
Find the inverse Laplace transform for X(s) = (ln ( frac{s+a}{s+b}) ). |
| A. | ( frac{e^{-at} e^{-bt}}{t} ) |
| B. | ( frac{e^{-bt} e^{-at}}{t} ) |
| C. | ( frac{e^{-at} + e^{-bt}}{t} ) |
| D. | ( frac{e^{bt} + e^{-at}}{t} ) |
| Answer» C. ( frac{e^{-at} + e^{-bt}}{t} ) | |
| 5. |
Find the inverse Laplace transform for X(s) = ( frac{s}{2s^2-8} ). |
| A. | cosh u20612t |
| B. | ( frac{1}{2} ) cosh u20612t |
| C. | sinh u20612t |
| D. | ( frac{1}{2} ) sinh u20612t |
| Answer» C. sinh u20612t | |
| 6. |
If F1 (s) = ( frac{1}{s+2} ) and F2 (s) = ( frac{1}{s+3} ), find the inverse Laplace transform of F(s) = F1 (s) F2 (s). |
| A. | [e<sup>-2t</sup> + e<sup>-3t</sup>]u(t) |
| B. | [e<sup>-2t</sup> e<sup>-3t</sup>]u(t) |
| C. | [e<sup>2t</sup> + e<sup>3t</sup>]u(t) |
| D. | [e<sup>2t</sup> + e<sup>-3t</sup>]u(t) |
| Answer» C. [e<sup>2t</sup> + e<sup>3t</sup>]u(t) | |
| 7. |
Find the inverse Laplace transform of X(s) = ( frac{s}{(s^2+a^2)^2} ). |
| A. | ( frac{1}{a} ) t sin u2061at |
| B. | ( frac{1}{2a} ) t sin u2061at |
| C. | ( frac{1}{a} ) t cos u2061at |
| D. | ( frac{1}{2a} ) t cos u2061at |
| Answer» C. ( frac{1}{a} ) t cos u2061at | |
| 8. |
Find the inverse Laplace transform of X(s) = ( frac{s}{s^2 a^2+b^2} ). |
| A. | ( frac{1}{a^2} ,cos u2061( frac{a}{b})t ) |
| B. | ( frac{1}{a^2} ,cos u2061( frac{b}{a})t ) |
| C. | ( frac{1}{a^2} ,sin u2061( frac{b}{a})t ) |
| D. | ( frac{1}{a^2} ,sin u2061( frac{a}{b})t ) |
| Answer» C. ( frac{1}{a^2} ,sin u2061( frac{b}{a})t ) | |
| 9. |
Find the inverse Laplace transform for ( frac{s}{(s+2)^2+1} ). |
| A. | [2e<sup>-2t</sup> cos u2061t + e<sup>-2t</sup> sin u2061t]u(t) |
| B. | [e<sup>-2t</sup> cos u2061t + 2e<sup>-2t</sup> sin u2061t]u(t) |
| C. | [2e<sup>-2t</sup> cos u2061t e<sup>-2t</sup> sin u2061t]u(t) |
| D. | [e<sup>-2t</sup> cos u2061t 2e<sup>-2t</sup> sin u2061t]u(t) |
| Answer» E. | |
| 10. |
Find the inverse Laplace transform for ( frac{s}{(s+2)^2} ). |
| A. | te<sup>-t</sup> u(t) |
| B. | e<sup>-t</sup> sin u2061t u(t) |
| C. | e<sup>-2t</sup> (1-2t)u(t) |
| D. | e<sup>2t</sup> (1-2t)u(t) |
| Answer» D. e<sup>2t</sup> (1-2t)u(t) | |
| 11. |
Find the inverse Laplace transform for ( frac{1}{(s+1)^2+1} ). |
| A. | te<sup>-t</sup> u(t) |
| B. | e<sup>-t</sup> sin u2061t u(t) |
| C. | e<sup>-t</sup> cos u2061t u(t) |
| D. | e<sup>-t</sup> u(t) |
| Answer» C. e<sup>-t</sup> cos u2061t u(t) | |
| 12. |
Find the inverse Laplace transform for ( frac{1}{(s+1)^2} ). |
| A. | te<sup>t</sup> u(t) |
| B. | te<sup>-t</sup> u(t) |
| C. | tu(t) |
| D. | e<sup>t</sup> u(t) |
| Answer» C. tu(t) | |