MCQOPTIONS
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MCQOPTIONS
This section includes 8 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 \(L^{-1} \left (\frac{s}{(s^2+1)(s^2+2)(s^2+3)}\right )\). |
| A. | \(\frac{1}{2} cos(t)-cos(\sqrt3t)-\frac{1}{2} cos(\sqrt3t)\) |
| B. | \(\frac{1}{2} cos(t)+cos(\sqrt2t)-\frac{1}{2} cos(\sqrt3t)\) |
| C. | \(\frac{1}{2} cos(t)-cos(\sqrt2t)-\frac{1}{2} cos(\sqrt3t)\) |
| D. | \(\frac{1}{2} cos(t)+cos(\sqrt2t)+\frac{1}{2} cos(\sqrt3t)\) |
| Answer» D. \(\frac{1}{2} cos(t)+cos(\sqrt2t)+\frac{1}{2} cos(\sqrt3t)\) | |
| 3. |
Find the \(L^{-1} (\frac{1}{(s^2+4)(s^2+9)})\). |
| A. | \(\frac{1}{5} \left (\frac{sin(2t)}{2}-\frac{sin(t)}{3}\right )\) |
| B. | \(\frac{1}{5} \left (\frac{sin(2t)}{2}+\frac{sin(3t)}{3}\right )\) |
| C. | \(\frac{1}{5} \left (\frac{sin(t)}{2}-\frac{sin(3t)}{3}\right )\) |
| D. | \(\frac{1}{5} \left (\frac{sin(2t)}{2}-\frac{sin(3t)}{3}\right )\) |
| Answer» E. | |
| 4. |
Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\). |
| A. | e-t+6et+5e2t |
| B. | e-t-et+5e2t |
| C. | e-3t-6et+5e2t |
| D. | e-t-6et+5e2t |
| Answer» E. | |
| 5. |
Find the \(L^{-1} (\frac{s}{2s+9+s^2})\). |
| A. | \(e^{-t} \{cos(2\sqrt{2t})-sin(\sqrt{2t})\}\) |
| B. | \(e^{-t} \{cos(2\sqrt{2t})-sin(2\sqrt{2t})\}\) |
| C. | \(e^{-t} \{cos(2\sqrt{2t})-cos(\sqrt{2t})\}\) |
| D. | \(e^{-2t} \{cos(2\sqrt{2t})-sin(2\sqrt{2t})\}\) |
| Answer» C. \(e^{-t} \{cos(2\sqrt{2t})-cos(\sqrt{2t})\}\) | |
| 6. |
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. \(e^{-t} \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\) | |
| 7. |
Find the \(L^{-1} (\frac{1}{(s+2)^4})\). |
| A. | \(e^{-2t}×3\) |
| B. | \(e^{-2t}×\frac{t^3}{3}\) |
| C. | \(e^{-2t}×\frac{t^3}{6}\) |
| D. | \(e^{-2t}×\frac{t^2}{6}\) |
| Answer» D. \(e^{-2t}×\frac{t^2}{6}\) | |
| 8. |
Find the \(L^{-1} (\frac{s+3}{4s^2+9})\). |
| A. | \(\frac{1}{4} cos(\frac{3t}{2})+\frac{1}{2} cos(\frac{3t}{2})\) |
| B. | \(\frac{1}{4} cos(\frac{3t}{4})+\frac{1}{2} sin(\frac{3t}{2})\) |
| C. | \(\frac{1}{2} cos(\frac{3t}{2})+\frac{1}{2} sin(\frac{3t}{2})\) |
| D. | \(\frac{1}{4} cos(\frac{3t}{2})+\frac{1}{2} sin(\frac{3t}{2})\) |
| Answer» E. | |