MCQOPTIONS
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MCQOPTIONS
This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y z + 2 = 0, if they are perpendicular to each other. |
| A. | 21 |
| B. | 17 |
| C. | 12 |
| D. | 11 |
| Answer» E. | |
| 2. |
Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y 2z + 6 = 0. |
| A. | 30.82 |
| B. | 34.91 |
| C. | 11.23 |
| D. | 7.54 |
| Answer» C. 11.23 | |
| 3. |
The planes 5x + y + 3z + 1 = 0 and x + y kz + 6 = 0 are orthogonal, find k. |
| A. | 4 |
| B. | 2 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 4. |
Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0. |
| A. | 69.69 |
| B. | 84.32 |
| C. | 63.25 |
| D. | 83.25 |
| Answer» D. 83.25 | |
| 5. |
Find the angle between 2x + 3y 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0. |
| A. | 38.2 |
| B. | 19.64 |
| C. | 89.21 |
| D. | 54.54 |
| Answer» E. | |
| 6. |
The condition ( frac {a1}{a2} = frac{b1}{b2} = frac{c1}{c2} ) is for the planes whose normals are _____ to each other. |
| A. | perpendicular |
| B. | parallel |
| C. | differential |
| D. | tangential |
| Answer» B. parallel | |
| 7. |
The condition a1a2 + b1b2 + c1c2 = 0 is for the planes whose normals are _____ to each other. |
| A. | integral |
| B. | parallel |
| C. | perpendicular |
| D. | concentric |
| Answer» D. concentric | |
| 8. |
_____ planes have an angle 90 degrees between them. |
| A. | Orthogonal |
| B. | Tangential |
| C. | Normal |
| D. | Parallel |
| Answer» B. Tangential | |
| 9. |
What is the relation between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are perpendicular to each other? |
| A. | a<sub>1</sub>a<sub>2</sub> . b<sub>1</sub>b<sub>2</sub> . c<sub>1</sub>c<sub>2</sub> = 0 |
| B. | a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> + c<sub>1</sub>c<sub>2</sub> = 0 |
| C. | a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0 |
| D. | a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0 |
| Answer» C. a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0 | |
| 10. |
What is the relation between the the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0, if their normal are parallel to each other? |
| A. | ( frac {a1}{b1} = frac{a2}{c1} = frac{c2}{b2} ) |
| B. | ( frac {a1}{a2} = frac{b1}{c2} = frac{c1}{b2} ) |
| C. | ( frac {a1}{a2} = frac{b1}{b2} = frac{c1}{c2} ) |
| D. | ( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} ) |
| Answer» D. ( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} ) | |
| 11. |
Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z 2 = 0, if they are perpendicular to each other. |
| A. | 21 |
| B. | 7 |
| C. | 12 |
| D. | 8 |
| Answer» E. | |
| 12. |
Which trigonometric function is used to find the angle between two planes? |
| A. | Tangent |
| B. | Cosecant |
| C. | Secant |
| D. | Sine |
| Answer» C. Secant | |
| 13. |
What is the formula to find the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0? |
| A. | cos = ( frac {a1a2+b1b2+c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt {a2^2+b2^2+c^2 }} ) |
| B. | sec = ( frac {a1a2+b1b2+c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt{a2^2+b2^2+c2^2 }} ) |
| C. | cos = ( frac {a1a2.b1b2.c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt{a2^2+b2^2+c2^2 }} ) |
| D. | cot = ( frac {a1a2+b1b2+c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt{a2^2+b2^2+c2^2 }} ) |
| Answer» B. sec = ( frac {a1a2+b1b2+c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt{a2^2+b2^2+c2^2 }} ) | |
| 14. |
If is the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0 then
|
| A. | True |
| B. | False |
| Answer» C. | |
| 15. |
_____ is the angle between the normals to two planes. |
| A. | Normal between the planes |
| B. | The angle between the planes |
| C. | Tangent between the planes |
| D. | Distance between the planes |
| Answer» C. Tangent between the planes | |