MCQOPTIONS
Saved Bookmarks
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. |
While solving an Ordinary Differential Equation using the unilateral Laplace Transform, it is possible to solve if there is no function in the right hand side of the equation in standard form and if the initial conditions are zero. |
| A. | True |
| B. | False |
| Answer» C. | |
| 2. |
For the Transient analysis of a circuit with capacitors, inductors, resistors, we use bilateral Laplace Transformation to solve the equation obtained from the Kirchoff s current/voltage law. |
| A. | True |
| B. | False |
| Answer» C. | |
| 3. |
What is the inverse Laplace Transform of a function y(t) if after solving the Ordinary Differential Equation Y(s) comes out to be (Y(s) = frac{s^2-s+3}{(s+1)(s+2)(s+3)} ) ? |
| A. | ( frac{1}{2} e^{-t}+ frac{9}{2} e^{-3t}-3e^{-2t} ) |
| B. | ( frac{-1}{2} e^{-t}+ frac{9}{2} e^{-2t}-3e^{-3t} ) |
| C. | ( frac{1}{2} e^{-t}- frac{3}{2} e^{-2t}-3e^{-3t} ) |
| D. | ( frac{-1}{2} e^{t}+ frac{9}{2} e^{2t}-3e^{3t} ) |
| Answer» C. ( frac{1}{2} e^{-t}- frac{3}{2} e^{-2t}-3e^{-3t} ) | |
| 4. |
Take Laplace Transformation on the Ordinary Differential Equation if y 3y + 3y y = t2 et if y(0) = 1, y (0) = b and y (0) = c. |
| A. | ((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)s+(-3a-c))= frac{2}{(s-1)^3} ) |
| B. | ((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)+(-3a-c)s)= frac{2}{(s-1)^3} ) |
| C. | ((s^3-3s^2+3s)Y(s)+(-as+(3a-b)s+(-3a-c))= frac{2}{(s-1)^3} ) |
| D. | ((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)s+(-3a-c))= frac{2}{(s-1)^3} ) |
| Answer» B. ((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)+(-3a-c)s)= frac{2}{(s-1)^3} ) | |
| 5. |
Solve the Ordinary Diferential Equation using Laplace Transformation y 3y + 3y y = t2 et when y(0) = 1, y (0) = 0 and y (0) = 2. |
| A. | (2e^t frac{t^5}{720}+e^t+2e^t frac{t}{6}+4e^t frac{t^2}{24} ) |
| B. | (e^t frac{t^5}{720}+2e^{-t}+2e^t frac{t}{6}+4e^t frac{t^2}{24} ) |
| C. | (e^{-t} frac{t^5}{720}+e^{-t}+2e^{-t} frac{t}{6}+4e^{-t} frac{t^2}{24} ) |
| D. | (2e^{-t} frac{t^5}{720}+e^{-t}+2e^{-t} frac{t}{6}+4e^{-t} frac{t^2}{24} ) |
| Answer» B. (e^t frac{t^5}{720}+2e^{-t}+2e^t frac{t}{6}+4e^t frac{t^2}{24} ) | |
| 6. |
Solve the Ordinary Differential Equation y + 2y + 5y = e-t sin(t) when y(0) = 0 and y (0) = 1.(Without solving for the constants we get in the partial fractions). |
| A. | (e^t [Acost+A1sint+Bcos(2t)+ frac{(B1)}{2} sin(2t)] ) |
| B. | (e^{-t} [Acost+A1sint+Bcos(2t)+B1sin(2t)] ) |
| C. | (e^{-t} [Acost+A1sint+Bcos(2t)+ frac{(B1)}{2} sin(2t)] ) |
| D. | (e^t [Acost+A1sint+Bcos(2t)+(B1)sin(2t)] ) |
| Answer» D. (e^t [Acost+A1sint+Bcos(2t)+(B1)sin(2t)] ) | |
| 7. |
Solve the Ordinary Differential Equation by Laplace Transformation y 2y 8y = 0 if y(0) = 3 and y (0) = 6. |
| A. | (3e^t cos(3t)+tsint(3t) ) |
| B. | (3e^t cos(3t)+te^{-t} sint(3t) ) |
| C. | (2e^{-t} cos(3t)-2 frac{t}{3} sint(3t) ) |
| D. | (2e^{-t} cos(3t)-2 frac{te^{-t}}{3} sint(3t) ) |
| Answer» B. (3e^t cos(3t)+te^{-t} sint(3t) ) | |
| 8. |
What is the laplce tranform of the first derivative of a function y(t) with respect to t : y (t)? |
| A. | sy(0) Y(s) |
| B. | sY(s) y(0) |
| C. | s<sup>2</sup> Y(s)-sy(0)-y'(0) |
| D. | s<sup>2</sup> Y(s)-sy'(0)-y(0) |
| Answer» C. s<sup>2</sup> Y(s)-sy(0)-y'(0) | |
| 9. |
With the help of _____________________ Mr.Melin gave inverse laplace transformation formula. |
| A. | Theory of calculus |
| B. | Theory of probability |
| C. | Theory of statistics |
| D. | Theory of residues |
| Answer» E. | |
| 10. |
While solving the ordinary differential equation using unilateral laplace transform, we consider the initial conditions of the system. |
| A. | True |
| B. | False |
| Answer» B. False | |