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 plane x + 2y + kz + 2 = 0 and directional ratios of a line (8, 3, 2), if they are parallel to each other.

A. 21
B. -17
C. 12
D. -7
Answer» E.
Discussion
2.

Find the angle between the planes 5x + 2y + 3z + 1 = 0 and (1, 1, -2).

A. 30.82
B. 3.43
C. 11.23
D. 7.54
Answer» C. 11.23
Discussion
3.

The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.

A. 4
B. -14
C. 6
D. -8
Answer» C. 6
Discussion
4.

Find the angle between x + 2y + 7z + 2 = 0 and (2, 4, 6).

A. 69.69
B. 84.32
C. 66.92
D. 83.25
Answer» D. 83.25
Discussion
5.

Find the angle between 2x + 3y 2z + 4 = 0 and (2, 1, 1).

A. 38.2
B. 19.64
C. 89.21
D. 29.34
Answer» E.
Discussion
6.

The condition ( frac {a}{a1} = frac{b}{b1} = frac{c}{c1} ) is for a plane and a line are _____ to each other.

A. perpendicular
B. parallel
C. differential
D. tangential
Answer» B. parallel
Discussion
7.

The condition a1a + b1b + c1c = 0 is for a plane and a line are _____ to each other.

A. integral
B. parallel
C. perpendicular
D. concentric
Answer» C. perpendicular
Discussion
8.

A plane and a line having an angle of 90 degrees between them are called _____

A. Orthogonal
B. Tangential
C. Normal
D. Parallel
Answer» B. Tangential
Discussion
9.

What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel 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 + b<sub>1</sub>b + c<sub>1</sub>c = 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 plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are perpendicular 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 {a}{a1} = frac{b}{b1} = frac{c}{c1} )
D. ( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )
Answer» D. ( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )
Discussion
11.

What is the plane equation involved in the formula sin = ( frac {a1a+b1b+c1c}{ sqrt {a^2+b^2+c^2} sqrt{a1^2+b1^2+c1^2 }} )?

A. a<sub>1</sub>x b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0
B. a<sub>1</sub>x<sup>2</sup> + b<sub>1</sub>y<sup>2</sup> + c<sub>1</sub>z<sup>2</sup> + d<sub>1</sub> = 0
C. ax + by + cz+ d = 0
D. a<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0 and ax + by + cz + d = 0
Answer» D. a<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0 and ax + by + cz + d = 0
Discussion
12.

Which trigonometric function is used to find the angle between a line and a plane?

A. Tangent
B. Cosecant
C. Secant
D. Sine
Answer» E.
Discussion
13.

Find the angle between the planes x + 2y + 3z + 1 = 0 and (4, 1, -7).

A. 29.34
B. 3.43
C. 11.23
D. 17.54
Answer» B. 3.43
Discussion
14.

If is the angle between line whose ratios are a1, b1, c1 and the plane ax + by + cz + d = 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 complement of the angle between the line L and a normal line to the plane .

A. Normal between a plane and a line
B. The angle between a line and a plane
C. Tangent between a plane and a line
D. Distance between a plane and a line
Answer» C. Tangent between a plane and a line
Discussion