# MCQ Three Dimensional Geometry for ISC Class-12 Maths

MCQ Three Dimensional Geometry for ISC Class-12 Maths .These MCQ  / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Maths.

## Three Dimensional Geometry MCQ  / Objective Type Questions for ISC Class-12 Maths

 Board ISC Class 12th (XII) Subject Maths Ch-Name Three Dimensional Geometry (Line) Syllabus on bifurcated syllabus (after reduction) Bifurcated pattern Semester-1 Session 2021-22 Topic MCQ / Objective Type Question

### ISC Class-12 Maths Three Dimensional Geometry MCQ Type Questions

Question 1: If the line joining the origin and the point (–2, 1, 2) makes angle θ1 ,θ2 and θ3 with the positive direction of the coordinate axes, then the value of cos 2θ1 + cos 2θ2 + cos 2θ3 is

(a) –1

(b) 1

(c) 2

(d) –2

Question 2: Direction cosines of a line are

(a) The tangents of the angles made by the line with the negative directions of the coordinate axes.

(b) The sines of the angles made by the line with the positive directions of the coordinate axes.

(c) The cotangents of the angles made by the line with the negative directions of the coordinate axes.

(d) The cosines of the angles made by the line with the positive directions of the coordinate axes.

Answer: (d) The cosines of the angles made by the line with the positive directions of the coordinate axes.

Question 3: Which of the following is false?

(a) 30°, 45°, 60° can be the direction angles of a line is space
(b) 90°, 135°, 45° can be the direction angles of a line is space
(c) 120°, 60°, 45° can be the direction angles of a line in space
(d) 60°, 45°, 60° can be the direction angles of a line in space

Answer: (a) 30°, 45°, 60° can be the direction angles of a line is space

Question 4:  If a line makes angles 90°, 60° and θ with x, y and z axes respectively, where θ is acute then the value of θ is

(a) 30

(b) 60

(c) 90

(d) 45

Question 5:  The angle between the lines passing through the points (4, 7, 8), (2, 3, 4) and (-1, -2, 1), (1, 2, 5) is

(a) 0
(b) π/2
(c) π/4
(d) π/6

Question 6: The direction cosines of the y-axis are

(a) (6, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)

Question 7:  The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

(a) (10, 0, 12)
(b) (5, 6, 0)
(c) (6, 5, 0)
(d) (5, 0, 6)

Question 8: If a line makes angles α, β, γ with the axes then cos2α + cos2β+cos2γ is equal to

(a) – 1

(b) 1

(c) 2

(d) – 2

Question 9: The co-ordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:

(a) (2, 0, 0)
(b) (0, 5, 0)
(c) (0, 0, 7)
(d) (0, 5, 7).

Question 10: If α, ß, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction-cosines of the line are:

(a) < sin α, sin ß, sin γ >
(b) < cos α, cos ß, cos γ >
(c) < tan α, tan ß, tan γ >
(d) < cos² α, cos² ß, cos² γ >.

Answer: (b) < cos α, cos ß, cos γ >

Question 11:  If l, m, n are the direction cosines of a line, then

(a) l2+ m2+ 2n2 = 1.

(b) l2+ 2m2+ n2 = 1.

(c) 2l2+ m2+ n2 = 1.

(d) l2+ m2+ n2 = 1.

Answer: (d) l2+ m2+ n2 = 1.

Question 12: If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are

(a) Proportional to the direction cosine l of the line

(b) Inversely Proportional to the direction cosines of the line

(c) Inversely Proportional to the direction cosine l of the line

(d) Proportional to the direction cosines of the line.

Answer: (d) Proportional to the direction cosines of the line.

Question 13: If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

(a) 3x + 5y – 6z + 3 = 0
(b) 2x – 5y – 6z + 3 = 0
(c) 2x + 5y – 6z + k = 0
(d) None of these

Answer: (c) 2x + 5y – 6z + k = 0

Question 14: 16 The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2), is equal to

(a) 9 sq. units
(b) 18 sq. units
(c) 27 sq. units
(d) 81 sq. units

Question 15: A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals:

(a) 30°
(b) 45°
(c) 60°
(d) 15°.

Question 16: If the lines x-2/1 =y-2/1 =z-4/k and x-1/k = y-4/2 = z-5/1 are coplanar, then k can have

(a) Exactly two values

(b) Exactly three values

(c) Exactly one value

(d) Any value

Question 17: The shortest distance between the lines x = y + 2 = 6z – 6 and x + 1 = 2y = -12z is

(a) 1/2
(b) 2
(c) 1
(d) 3/2

Question 18: A line makes angles α, β and γ with the co-ordinate axes. If α + β = 90°, then γ is equal to

(a) 0°
(b) 90°
(c) 180°
(d) None of these

Question 19: If a line makes an angle θ1, θ2, θ3 with the axis respectively, then cos 2θ1 + cos 2θ2 + cos 2θ3 =

(a) -4
(b) -2
(c) -3
(d) -1

Question 20: The angle between the line 2x = 3y = -z and 6x = -y = -4z is

(a) 30°
(b) 45°
(c) 90°
(d) 0°

Question 21: The distance of the point (-3, 4, 5) from the origin

(a) 50
(b) 5√2
(c) 6
(d) None of these

Question 22:  If a line makes angles Q1, Q21 and Q3 respectively with the coordinate axis then the value of cos² Q1 + cos² Q2 + cos² Q3

(a) 2
(b) 1
(c) 4
(d) 3/2

Question 23: The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are

(a) 3, 2, -1
(b) -3, 7, 5
(c) 1, -1, 2
(d) – 11, 4, -5

Question 24:  How many lines through the origin in make equal angles with the coordinate axis?

(a) 1
(b) 4
(c) 8
(d) 2

Question 25: he direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are(

(a) 2, -2, 0
(b) 1, -1, 0
(c) 1/2, – 1/2
(d) None of these

Question 26: The distance of the point (-3, 4, 5) from the origin

(a) 50
(b) 5√2
(c) 6
(d) None of these

Question 27: The line x = 1, y = 2 is

(a) parallel to x-axis
(b) parallel to y-axis
(c) parallel to z-axis
(d) None of these

Question 28: If the directions cosines of a line are A, k, k, then

(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) k = 1/3 or –1/3

Answer: (d) k = 1/3 or –1/3

Question 29: The cosines of the angle between any two diagonals of a cube is
(a) 1/3
(b) 1/2
(c) 2/3
(d) 1/3

Question 30: Distance of the point (a, β, γ) from y-axis is

(a) β
(b) |β|
(c) |β + γ|
(d) α² + γ²