MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is the foot of the normal if the straight line x + y + 7 = 0 is normal to the hyperbola 3x2 4y2 = 12 whose normal is at the point (x1, y1)? |
| A. | (4, 3) |
| B. | (-4, 3) |
| C. | (4, -3) |
| D. | (-4, -3) |
| Answer» E. | |
| 2. |
What is the nature of the straight line x + y + 7 = 0 to the hyperbola 3x2 4y2 = 12 whose normal is at the point (x1, y1)? |
| A. | Chord to hyperbola |
| B. | Tangent to hyperbola |
| C. | Normal to hyperbola |
| D. | Segment to hyperbola |
| Answer» D. Segment to hyperbola | |
| 3. |
What will be the equation of normal to the hyperbola 3x2 4y2 = 12 at the point (x1, y1)? |
| A. | 3x<sub>1</sub>y + 4y<sub>1</sub>x + 7x<sub>1</sub>y<sub>1</sub> = 0 |
| B. | 3x<sub>1</sub>y + 4y<sub>1</sub>x 7x<sub>1</sub>y<sub>1</sub> = 0 |
| C. | 3x<sub>1</sub>y 4y<sub>1</sub>x 7x<sub>1</sub>y<sub>1</sub> = 0 |
| D. | 3x<sub>1</sub>y 4y<sub>1</sub>x + 7x<sub>1</sub>y<sub>1</sub> = 0 |
| Answer» C. 3x<sub>1</sub>y 4y<sub>1</sub>x 7x<sub>1</sub>y<sub>1</sub> = 0 | |
| 4. |
What is the equation of the tangent to the parabola y2 = 8x, which is inclined at an angle of 45 with the x axis? |
| A. | x + y 2 = 0 |
| B. | x + y + 2 = 0 |
| C. | x y + 2 = 0 |
| D. | x y 2 = 0 |
| Answer» D. x y 2 = 0 | |
| 5. |
What will be the equation of the tangent to the circle x2 + y2 6x + 4y 7 = 0, which are perpendicular to the straight line 2x y + 3 = 0? |
| A. | x + 2y 9 = 0 |
| B. | x + 2y + 9 = 0 |
| C. | x + 2y 10 = 0 |
| D. | x + 2y + 10 = 0 |
| Answer» B. x + 2y + 9 = 0 | |
| 6. |
At which point does the normal to the hyperbola xy = 4 at (2, 2) intersects the hyperbola again? |
| A. | (-2, -2) |
| B. | (-2, 2) |
| C. | (2, -2) |
| D. | (0, 2) |
| Answer» B. (-2, 2) | |
| 7. |
What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)? |
| A. | x + y = 0 |
| B. | x y = 0 |
| C. | 2x y = 0 |
| D. | x + 2y = 0 |
| Answer» C. 2x y = 0 | |
| 8. |
If X and Y are given as current co-ordinates, what is the equation of the tangent at a specific point of x3 3axy + y3 = 0 at (x, y)? |
| A. | (x<sup>2</sup> ay)X + (y<sup>2</sup> ax)Y = -2axy |
| B. | (x<sup>2</sup> ay)X + (y<sup>2</sup> ax)Y = 2axy |
| C. | (x<sup>2</sup> ay)X + (y<sup>2</sup> ax)Y = axy |
| D. | (x<sup>2</sup> ay)X + (y<sup>2</sup> ax)Y = -axy |
| Answer» D. (x<sup>2</sup> ay)X + (y<sup>2</sup> ax)Y = -axy | |
| 9. |
What is the equation of the tangent at a specific point of y2 = 4ax at (0, 0)? |
| A. | x = 0 |
| B. | x = 1 |
| C. | x = 2 |
| D. | x = 3 |
| Answer» B. x = 1 | |