MCQOPTIONS
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MCQOPTIONS
This section includes 5 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. |
Which among the following is true for the curve rn = a sin n ? |
| A. | Given family of curve is Self orthogonal |
| B. | Orthogonal trajectory is r<sup>n</sup>=k cos u2061n where k is an constant |
| C. | Orthogonal trajectory is r<sup>n</sup>=k cosec u2061n where k is an constant |
| D. | Orthogonal trajectory is r<sup>n</sup>=k sin u2061n where k is an constant |
| Answer» C. Orthogonal trajectory is r<sup>n</sup>=k cosec u2061n where k is an constant | |
| 2. |
Find the orthogonal trajectories of the family r=a(1+sin ). |
| A. | r=k(sin ) |
| B. | r<sup>2</sup>=k(cos )<sup>2</sup> |
| C. | r=k(1-cos ) |
| D. | r=k(1-sin ) |
| Answer» E. | |
| 3. |
The Orthogonal DE for family of parabola y2=4a(x+a) is same as _______(where DE stands for Differential equation) |
| A. | DE of parabola y<sup>2</sup>=4a(x+a) |
| B. | DE of parabola y<sup>2</sup>=4ax |
| C. | DE of parabola x<sup>2</sup>=4ay |
| D. | DE of parabola x<sup>2</sup>=4a(y+a) |
| Answer» B. DE of parabola y<sup>2</sup>=4ax | |
| 4. |
Find the orthogonal trajectories of the family of curves ( frac{x^2}{a^2} + frac{y^2}{b^2+k} = 1 ) where k is the parameter. |
| A. | x<sup>2</sup>-y<sup>2</sup>-3a<sup>2</sup> log u2061x-k = 0 |
| B. | x<sup>2</sup>+2y<sup>2</sup> ( frac{a^2}{2} ) log u2061x-k = 0 |
| C. | x<sup>2</sup>+y<sup>2</sup>-2a<sup>2</sup> log u2061x-k = 0 |
| D. | 2x<sup>2</sup>-y<sup>2</sup> ( frac{a^2}{3} ) log u2061x-k = 0 |
| Answer» D. 2x<sup>2</sup>-y<sup>2</sup> ( frac{a^2}{3} ) log u2061x-k = 0 | |
| 5. |
Find the orthogonal trajectories of the family of parabolas y2=4ax. |
| A. | 2x<sup>2</sup>+y<sup>2</sup>=k |
| B. | 2y<sup>2</sup>+x<sup>2</sup>=k |
| C. | x<sup>2</sup>-2y<sup>2</sup>=k |
| D. | 2x<sup>2</sup>-y<sup>2</sup>=k |
| Answer» B. 2y<sup>2</sup>+x<sup>2</sup>=k | |