MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 12 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. |
Find the value of L(32t). |
| A. | ( frac{1}{s-2 log u2061(3)} ) |
| B. | ( frac{1}{s+2 log u2061(3)} ) |
| C. | ( frac{1}{s-3 log u2061(2)} ) |
| D. | ( frac{1}{s+3 log u2061(2)} ) |
| Answer» B. ( frac{1}{s+2 log u2061(3)} ) | |
| 2. |
If ((erf ( sqrt{t}))= frac{1}{s sqrt{s}} ), then what is (L(erf (2 sqrt{t})) )? |
| A. | ( frac{2}{ sqrt{s}} ) |
| B. | ( frac{1}{s sqrt{s}} ) |
| C. | ( frac{2}{s sqrt{s}} ) |
| D. | ( frac{4}{s sqrt{s}} ) |
| Answer» D. ( frac{4}{s sqrt{s}} ) | |
| 3. |
Which of the following is not a term present in the Laplace Transform of e2t sin4 t. |
| A. | ( frac{3}{8s} ) |
| B. | ( frac{3}{8(s-2)} ) |
| C. | ( frac{s}{8((s-2)^2+16)} ) |
| D. | ( frac{s}{2((s-2)^2+4)} ) |
| Answer» B. ( frac{3}{8(s-2)} ) | |
| 4. |
Find the (L( int_{0}^{t}sin (u) cos (2u)du) ). |
| A. | ( frac{1}{2s} left [ frac{3}{s^2+9}- frac{1}{s^2+1} right ] ) |
| B. | ( frac{1}{2s} left [ frac{9}{s^2+9}- frac{1}{s^2+1} right ] ) |
| C. | ( frac{1}{2s} left [ frac{3}{s^2+9}+ frac{1}{s^2+1} right ] ) |
| D. | ( frac{1}{s} left [ frac{3}{s^2+9}- frac{1}{s^2+1} right ] ) |
| Answer» B. ( frac{1}{2s} left [ frac{9}{s^2+9}- frac{1}{s^2+1} right ] ) | |
| 5. |
Find the (L left ( frac{d}{dt}( frac{sin t}{t}) right) ). |
| A. | s cot<sup>-1</sup> s-1 |
| B. | s tan<sup>-1</sup> s-1 |
| C. | s cot u2061(s)-1 |
| D. | s tan u2061(s)-1 |
| Answer» B. s tan<sup>-1</sup> s-1 | |
| 6. |
Find the (L left ( frac{sinh (at)}{t} right ) ). |
| A. | ( frac{1}{2} log u2061 left ( frac{s a}{s-a} right ) ) |
| B. | ( frac{1}{2} log u2061 left ( frac{s-a}{s+a} right ) ) |
| C. | ( frac{1}{2} log u2061 left ( frac{s+a}{s-a} right ) ) |
| D. | ( frac{1}{3} log u2061 left ( frac{s+a}{s-a} right ) ) |
| Answer» D. ( frac{1}{3} log u2061 left ( frac{s+a}{s-a} right ) ) | |
| 7. |
The L(te-3t cos (2t)cos (3t)) is given by (k left [ frac{25-(s+3)^2}{((s+3)^2+25)^2} + frac{(1-(s+3)^2)}{((s+3)^2+1)^2} right ] ). Find the value of k. |
| A. | 0 |
| B. | 1 |
| C. | ( frac{1}{2} ) |
| D. | ( frac{-1}{2} ) |
| Answer» E. | |
| 8. |
Find the L(t+sin(2t)). |
| A. | ( frac{1}{s}+ frac{2}{(s^2+4)} ) |
| B. | ( frac{1}{s}+ frac{3}{(s^2+4)} ) |
| C. | ( frac{1}{s}+ frac{2}{(s^2+2)} ) |
| D. | ( frac{2}{s}+ frac{2}{(s^2+4)} ) |
| Answer» B. ( frac{1}{s}+ frac{3}{(s^2+4)} ) | |
| 9. |
Find the L(t e-2t sinh (4t)). |
| A. | ( frac{8s+16}{(s^2+2s-12)^2} ) |
| B. | ( frac{2s+16}{(s^2+2s-12)^2} ) |
| C. | ( frac{8s+16}{(s^2+21s-12)^2} ) |
| D. | ( frac{8s+16}{(s^2+s-12)^2} ) |
| Answer» B. ( frac{2s+16}{(s^2+2s-12)^2} ) | |
| 10. |
Find the Laplace Transform of g(t) which has value (t-1)3 for t>1 and 0 for t<1. |
| A. | (e^{-2as} frac{6}{s^4} ) |
| B. | (e^{-as} frac{24}{s^5} ) |
| C. | (e^{-as} frac{6}{s^4} ) |
| D. | (e^{-as} frac{24}{s^4} ) |
| Answer» D. (e^{-as} frac{24}{s^4} ) | |
| 11. |
Find the (L(e^{2t} (1+t)^2) ). |
| A. | ( frac{1}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} ) |
| B. | ( frac{ u20613}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} ) |
| C. | ( frac{1}{s-2}+ frac{2}{(s+2)^3} + frac{2}{(s-2)^2} ) |
| D. | ( frac{1}{s-2}+ frac{2}{(s-2)^3} ) |
| Answer» B. ( frac{ u20613}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} ) | |
| 12. |
Find the L(sin3 t). |
| A. | ( frac{3}{4(s^2+1)}- frac{1}{4(s^2+9)} ) |
| B. | ( frac{3}{4(s^2+1)}- frac{3}{4(s^2+9)} ) |
| C. | ( frac{3}{4(s^2+1)}- frac{9}{4(s^2+9)} ) |
| D. | ( frac{3}{4(s^2-1)}- frac{3}{4(s^2+9)} ) |
| Answer» C. ( frac{3}{4(s^2+1)}- frac{9}{4(s^2+9)} ) | |