Planes MCQs Type Questions with Answer for ISC Class 12 Maths

Planes MCQs Type Questions with Answer for ISC Class 12 Maths . These MCQs / 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 Sem-2 exam of council. Visit official website CISCE for detail information about ISC Class-12 Maths.

  ISC Class 12 Maths Planes MCQs Type Questions with Answer

Board	ISC
Class	12th (XII)
Subject	Maths
Chapter	Planes
Syllabus	on bifurcated syllabus (after reduction)
Session	2021-22
Bifurcated	Sem-2
Topic	MCQs / Objective Type Question

MCQs Planes for ISC Class 12 Questions with Answers

Question 1: 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

Answer : (a) 30

Question 2:  The length of the ⊥^er from the point (0, – 1, 3) to the plane 2x + y – 2z + 1 = 0 is

(a) 0
(b) 2√3
(c) 23
(d) 2

Answer: (d) 2

Question 3:  The 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

Answer: (c) 1/√2, – 1/√2

Question 4:  Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:

(a)  (−3, −5, −3)

(b)  (−3, 1, −3)

(c)  (−1, −5, −3)

(d)  (−3, −5, 5)

Answer: (a)  (−3, −5, −3)

Question 5:  If a line has direction ratios 2, – 1, – 2, determine its direction cosines:

(a) ⅓, ⅔, -⅓

(b) ⅔, -⅓, -⅔

(c) -⅔, ⅓, ⅔

(d) None of the above

Answer: (b) ⅔, -⅓, -⅔

Question 6: The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is

(a) x + y + z = 1

(b) x + y + z = 0

(c) x + y – z = 1

(d) x + y + z = 2

Answer : (a) x + y + z = 1

Question 7:  If the lines x-1/2 = y+1/3 = z-1/4  and x-3/1 = y-k/2 = z/1  intersect at a point , then the value of k is

(a) 9/2

(b) 2/9

(c) 2

(d) 3/2

Answer : (a) 9/2

Question 8:  Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).

(a)  x + 2y = 0

(b) x – y – 2 = 0

(c)  -x + 2y – 2 = 0

(d) x + y – 2 = 0

Answer: (d) x + y – 2 = 0

Question 9: The equation x² – x – 2 = 0 in three-dimensional space is represented by:

(a)  A pair of parallel planes

(b)  A pair of straight lines

(c)  A pair of the perpendicular plane

(d)  None of these

Answer: (a)  A pair of parallel planes

Question 10:  The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are:

(a)  7, 4,-2

(b)  7, 4, 5

(c)  7, 4, 2

(d)  4, -2, 5

Answer: (a)  7, 4,-2

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 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 13: The reflection of the point (α, ß, γ) in the xy-plane is:

(a) (α, ß, 0)
(b) (0, 0, γ)
(c) (-α, -ß, γ)
(d) (α, ß, -γ).

Answer: (d) (α, ß, -γ).

Question 14: The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:

(a) i + 2k + λ(4i + 4j + 4k)

(b) i – 2k + λ(4i + 4j + 4k)

(c) -i+2k+ λ(4i + 4j + 4k)

(d) -i+2k+ λ(4i – 4j – 4k)

Answer: (c) -i+2k+ λ(4i + 4j + 4k)

Question 15: The distance between the planes 2x + 2y – z + 2 = 0 and 4x + 4y – 2z + s = 0 is

(a) 1/6

(b) 1

(c) 1/4

(d) 1/2

Answer : (a) 1/6

Question 16: The acute angle between the planes 2x – y+z = 6 and x+y+2z = 3 is

(a) 60

(b) 30

(c) 75

(d) 45

Answer : (a) 60

Question 17: The equation of the plane containing the line: 2x – 5y + z = 3; x + y + 4z = 5 and parallel to the plane: x + 3y + 6z = 1 is:

(a) 2x + 6y+ 12z = 13
(b) x + 3y + 6z = – 7
(c) x + 3y + 6z = 7
(d) 2x + 6y – 12z = -13.

Answer: (c) x + 3y + 6z = 7

Question 18: Four points (0, -1, -1) (-4, 4, 4) (4, 5, 1) and (3, 9, 4) are coplanar. Find the equation of the plane containing them.

(a) 5x + 7y + 11z – 4 =0
(b) 5x – 7y + 11z + 4 = 0
(c) 5x – 7y – 11z – 4 = 0
(d) 5x + 7y – 11z + 4 = 0

Answer: (b) 5x – 7y + 11z + 4 = 0

Question 19: 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

Answer : (a) – 1

Question 20: 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

Answer : (a) Exactly two values

Question 21: What are the direction cosines of the equation of the plane 2x + 3y – z = 5?

(a) 1/√14, 3/√14, -2/√14

(b) 2/√14, 3/√14, -1/√14

(c) 2/√14, 1/√14, -1/√14

(d) 2/√14, -2/√14, -3/√14

Answer: (b) 2/√14, 3/√14, -1/√14

Question 22: Distance between two planes:

2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 is

(a) 2 units
(b) 4 units
(c) 8 units
(d) √1/29 units.

Answer: (d) √1/29 units.

Question 23: The planes 2x – y + 4z = 3 and 5x – 2.5y +10 z = 6 are

(a) perpendicular
(b) parallel
(c) intersect along y-axis
(d) passes through (0, 0, 5/4)

Answer: (b) parallel

Question 24: The direction cosines of the normal to the plane x + 2y – 3z – 4 = 0 are

(a) 1/√14, 2/√14, 3/√14,

(b) -1/√14, 2/√14, 3/√14,

(c) -1/√14, -2/√14, 3/√14,

(d) -1/√14, -2/√14, -3/√14,

Answer : (a) 1/√14, 2/√14, 3/√14

Question 25: The direction cosines of the y-axis are:

(a)  (9, 0, 0)

(b) (1, 0, 0)

(c)  (0, 1, 0)

(d) (0, 0, 1)

Answer: (c)  (0, 1, 0)

Question 26: (2, – 3, – 1) 2x – 3y + 6z + 7 = 0

(a) 4
(b) 3
(c) 2
(d) 1/5

Answer: (c) 2

Question 27: 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).

Answer: (a) (2, 0, 0)

Question 28: What is the distance (in units) between two planes:
3x + 5y + 7z = 3 and 9x + 15y + 21z = 9?

(a) 0
(b) 3
(c) 6√83
(d) 6.

Answer: (a) 0

Question 29: 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°

Answer: (c) 60°

Question 30: The distance of the point (1, -5, 9) from the plane x – y + z = 5, measured along a straight line x = y = z is:

(a) 10√3
(b) 5√3
(c) 3√10
(d) 3√5

Answer: (a) 10√3

Question 31: The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is

(a) 3x + 3y – 2z = 0
(b) x – 2y + z = 2
(c) 2x + y – z = 2
(d) 5x – 3y + 2z = 0

Answer: (c) 2x + y – z = 2

Question 32: An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is:

(a) x – 2y + 2z – 3 = 0
(b) x – 2y + 2z + 1 = 0
(c) x – 2y + 2z – 1 = 0
(d) x – 2y + 2z + 5 = 0.

Answer: (a) x – 2y + 2z – 3 = 0

Question 33: How many lines through the origin in make equal angles with the coordinate axis?

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

Answer: (c) 8

Question 34: The equation x² – x – 2 = 0 in three dimensional space is represented by

(a) A pair of parallel planes
(b) A pair of straight lines
(c) A pair of perpendicular plane
(d) None of these

Answer: (a) A pair of parallel planes

Question 35: The vector equation of the plane passing through the origin and the line of intersection of the plane r.a = λ and r.b = µ is

(a) r.(λa – µb) = 0
(b) r.(λb – µa) = 0
(c) r.(λa + µb)= 0
(d) r.(λb + µa) = 0

Answer: (b) r.(λb – µa) = 0

Question 36: The distance of the point (-3, 4, 5) from the origin

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

Answer: (b) 5√2

Question 37: The equation xy = 0 in three dimensional space is represented by

(a) a plane
(b) two plane are right angles
(c) a pair of parallel planes
(d) a pair of st. line

Answer: (b) two plane are right angles

Question 38: 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

Answer: (b) 1

–: End of Planes MCQs Type Questions with Answer  :–