MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The (L^{-1} left ( frac{3s+8}{s^2+4s+25} right ) ) is (e^{-st} (3cos ( sqrt{21}t+ frac{2sin ( sqrt{21}t)}{ sqrt{21}}) ). What is the value of s? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 2. |
Find the (L^{-1} left ( frac{s+1}{(s-1)(s+2)^2} right ) ). |
| A. | ( frac{2}{7} e^t- frac{2}{9} e^{-2t}+ frac{1}{3} e^{-2t} t ) |
| B. | ( frac{2}{9} e^t- frac{2}{9} e^{-2t}+ frac{1}{3} e^{-2t} t ) |
| C. | ( frac{2}{9} e^t- frac{2}{9} e^{-3t}+ frac{1}{3} e^{-2t} t ) |
| D. | ( frac{2}{9} e^t- frac{2}{9} e^{-2t}+ frac{1}{3} e^{-2t} ) |
| Answer» C. ( frac{2}{9} e^t- frac{2}{9} e^{-3t}+ frac{1}{3} e^{-2t} t ) | |
| 3. |
Find the (L^{-1} left ( frac{s}{(s^2+1)(s^2+2)(s^2+3)} right ) ). |
| A. | ( frac{1}{2} cos u2061(t)-cos u2061( sqrt3t)- frac{1}{2} cos u2061( sqrt3t) ) |
| B. | ( frac{1}{2} cos u2061(t)+cos u2061( sqrt2t)- frac{1}{2} cos u2061( sqrt3t) ) |
| C. | ( frac{1}{2} cos u2061(t)-cos u2061( sqrt2t)- frac{1}{2} cos u2061( sqrt3t) ) |
| D. | ( frac{1}{2} cos u2061(t)+cos u2061( sqrt2t)+ frac{1}{2} cos u2061( sqrt3t) ) |
| Answer» D. ( frac{1}{2} cos u2061(t)+cos u2061( sqrt2t)+ frac{1}{2} cos u2061( sqrt3t) ) | |
| 4. |
Find the (L^{-1} ( frac{1}{(s^2+4)(s^2+9)}) ). |
| A. | ( frac{1}{5} left ( frac{sin u2061(2t)}{2}- frac{sin u2061(t)}{3} right ) ) |
| B. | ( frac{1}{5} left ( frac{sin u2061(2t)}{2}+ frac{sin u2061(3t)}{3} right ) ) |
| C. | ( frac{1}{5} left ( frac{sin u2061(t)}{2}- frac{sin u2061(3t)}{3} right ) ) |
| D. | ( frac{1}{5} left ( frac{sin u2061(2t)}{2}- frac{sin u2061(3t)}{3} right ) ) |
| Answer» E. | |
| 5. |
Find the (L^{-1} left ( frac{(3s+9)}{(s+1)(s-1)(s-2)} right ) ). |
| A. | e<sup>-t</sup>+6e<sup>t</sup>+5e<sup>2t</sup> |
| B. | e<sup>-t</sup>-e<sup>t</sup>+5e<sup>2t</sup> |
| C. | e<sup>-3t</sup>-6e<sup>t</sup>+5e<sup>2t</sup> |
| D. | e<sup>-t</sup>-6e<sup>t</sup>+5e<sup>2t</sup> |
| Answer» E. | |
| 6. |
Find the (L^{-1} left ( frac{(s+1)}{(s+2)(s+3)} right ) ). |
| A. | 2e<sup>-3t</sup>-e<sup>-2t</sup> |
| B. | 3e<sup>-3t</sup>-e<sup>-2t</sup> |
| C. | 2e<sup>-3t</sup>-3e<sup>-2t</sup> |
| D. | 2e<sup>-2t</sup>-e<sup>-t</sup> |
| Answer» B. 3e<sup>-3t</sup>-e<sup>-2t</sup> | |
| 7. |
Find the (L^{-1} ( frac{s}{2s+9+s^2}) ). |
| A. | (e^{-t} {cos u2061(2 sqrt{2t})-sin u2061( sqrt{2t}) } ) |
| B. | (e^{-t} {cos u2061(2 sqrt{2t})-sin u2061(2 sqrt{2t}) } ) |
| C. | (e^{-t} {cos u2061(2 sqrt{2t})-cos( sqrt{2t}) } ) |
| D. | (e^{-2t} {cos u2061(2 sqrt{2t})-sin u2061(2 sqrt{2t}) } ) |
| Answer» C. (e^{-t} {cos u2061(2 sqrt{2t})-cos( sqrt{2t}) } ) | |
| 8. |
Find the (L^{-1} ( frac{s}{(s-1)^7}) ). |
| A. | (e^{-t} left ( frac{t^6}{5!}+ frac{t^5}{6!} right ) ) |
| B. | (e^t left ( frac{t^6}{5!}+ frac{t^5}{6!} right ) ) |
| C. | (e^t left ( frac{t^6}{6!}+ frac{t^5}{5!} right ) ) |
| D. | (e^{-t} left ( frac{t^6}{6!}+ frac{t^5}{5!} right ) ) |
| Answer» D. (e^{-t} left ( frac{t^6}{6!}+ frac{t^5}{5!} right ) ) | |
| 9. |
Find the (L^{-1} ( frac{1}{(s+2)^4}) ). |
| A. | (e^{-2t} 3 ) |
| B. | u2061 (e^{-2t} frac{t^3}{3} ) |
| C. | (e^{-2t} frac{t^3}{6} ) |
| D. | (e^{-2t} frac{t^2}{6} ) |
| Answer» D. (e^{-2t} frac{t^2}{6} ) | |
| 10. |
Find the (L^{-1} ( frac{s+3}{4s^2+9}) ). |
| A. | ( frac{1}{4} cos u2061( frac{3t}{2})+ frac{1}{2} cos u2061( frac{3t}{2}) ) |
| B. | ( frac{1}{4} cos u2061( frac{3t}{4})+ frac{1}{2} sin u2061( frac{3t}{2}) ) |
| C. | ( frac{1}{2} cos u2061( frac{3t}{2})+ frac{1}{2} sin u2061( frac{3t}{2}) ) |
| D. | ( frac{1}{4} cos u2061( frac{3t}{2})+ frac{1}{2} sin u2061( frac{3t}{2}) ) |
| Answer» E. | |