MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constantlength k. What is the equation of such curve passing through (0, k)? |
| A. | x<sup>2</sup> + 2y<sup>2</sup> = k<sup>2</sup> |
| B. | 2x<sup>2</sup> + y<sup>2</sup> = k<sup>2</sup> |
| C. | x<sup>2</sup> y<sup>2</sup> = k<sup>2</sup> |
| D. | x<sup>2</sup> + y<sup>2</sup> = k<sup>2</sup> |
| Answer» E. | |
| 2. |
A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constantlength k. Then what is the differential equation describing such curve? |
| A. | y(dy/dx) = (k<sup>2</sup> + x<sup>2</sup>) |
| B. | y(dy/dx) = (k<sup>2</sup> 2y<sup>2</sup>) |
| C. | y(dy/dx) = (k<sup>2</sup> y<sup>2</sup>) |
| D. | Depends on the value of k |
| Answer» D. Depends on the value of k | |
| 3. |
What is the solution of the equation(y + x( xy)(x + y))dx (y + y( xy)(x + y))dy = 0? |
| A. | x<sup>2</sup> + y<sup>2</sup> = 2tan<sup>-1</sup>( (y/x)) + c |
| B. | x<sup>2</sup> + y<sup>2</sup> = 4tan<sup>-1</sup>( (y/x)) + c |
| C. | x<sup>2</sup> + y<sup>2</sup> = tan<sup>-1</sup>( (y/x)) + c |
| D. | x<sup>2</sup> + y<sup>2</sup> = 2tan<sup>-1</sup>( (x/y)) + c |
| Answer» C. x<sup>2</sup> + y<sup>2</sup> = tan<sup>-1</sup>( (y/x)) + c | |
| 4. |
What will be the value of x(x 1)dy/dx y = x2(x 1)2? |
| A. | xy = (x + 1)(x<sup>3</sup>/3 + c) |
| B. | depends on x |
| C. | depends on y |
| D. | xy = (x 1)(x<sup>3</sup>/3 + c) |
| Answer» E. | |
| 5. |
What will be the value of the differential equation dy/dx = (x + y)2/(x + 2)(y 2)? |
| A. | ke<sup>Y/X</sup> where, X = x + 2 and Y = y 2 |
| B. | ke<sup>2Y/X</sup> where, X = x + 2 and Y = y 2 |
| C. | ke<sup>2Y/X</sup> where, X = x and Y = 2y |
| D. | ke<sup>2X/Y</sup> where, X = x 2 and Y = y + 2 |
| Answer» C. ke<sup>2Y/X</sup> where, X = x and Y = 2y | |
| 6. |
What will be the value of dy/dx = (x + 2y + 3)/(2x + 3y + 4)? |
| A. | [(2 + 3)/2 3 * (log ( 3(y + 2) (x 1))) + (2 3)/2 3 * (log ( 3(y + 2) (x 1)))] |
| B. | [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) + (x 1)))] |
| C. | [(2 + 3)/2 3 * (log ( 3(y + 2) (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))] |
| D. | [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))] |
| Answer» D. [(2 + 3)/2 3 * (log ( 3(y + 2) + (x 1))) (2 3)/2 3 * (log ( 3(y + 2) (x 1)))] | |
| 7. |
What will be the general solution of differential equation for 2x y dx + 2y x dy = 0? |
| A. | 2<sup>2x</sup> + 2<sup>2y</sup> = c |
| B. | 2(2<sup>2x</sup> + 2<sup>2y</sup>) = c |
| C. | 3(2<sup>2x</sup> + 2<sup>2y</sup>) = c |
| D. | 4(2<sup>2x</sup> + 2<sup>2y</sup>) = c |
| Answer» B. 2(2<sup>2x</sup> + 2<sup>2y</sup>) = c | |
| 8. |
What is the order of the differential equation of the family of circles with one diameter along the line y = x axis? |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 9. |
What is the value of the solution of dy/dx = (6x + 9y 7)/(2x + 3y 6)? |
| A. | -c/3 |
| B. | 3c/2 |
| C. | 2c/3 |
| D. | -2c/3 |
| Answer» B. 3c/2 | |
| 10. |
What is the differential equation whose solution represents the family c(y + c)2 = x3? |
| A. | [2x/3 *(dy/dx) y][x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup> |
| B. | [x/3 *(dy/dx) y][x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup> |
| C. | [2x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup> |
| D. | [x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup> |
| Answer» D. [x/3 *(dy/dx) y][ 2x/3 *dy/dx]<sup>2</sup> = x<sup>3</sup> | |