Explore topic-wise MCQs in Mathematics.

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.
Discussion
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
Discussion
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
Discussion
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
Discussion
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.
Discussion
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
Discussion
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
Discussion
8.

_____ planes have an angle 90 degrees between them.

A. Orthogonal
B. Tangential
C. Normal
D. Parallel
Answer» B. Tangential
Discussion
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
Discussion
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} )
Discussion
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.
Discussion
12.

Which trigonometric function is used to find the angle between two planes?

A. Tangent
B. Cosecant
C. Secant
D. Sine
Answer» C. Secant
Discussion
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 }} )
Discussion
14.

If is the angle between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c21z + d2 = 0 then cos = ( frac {a1a2.b1b2.c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt {a2^2+b2^2+c2^2 }} ).

A. True
B. False
Answer» C.
Discussion
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
Discussion