**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) l^{2}+ m^{2}+ 2n^{2} = 1

(b) l^{2}+ 2m^{2}+ n^{2} = 1

(c) 2l^{2}+ m^{2}+ n^{2} = 1

(d) l^{2}+ m^{2}+ n^{2} = 1

**Answer: (d) l ^{2}+ m^{2}+ n^{2} = 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 Q _{1}, Q_{21} and Q_{3} respectively with the coordinate axis then the value of cos² Q_{1} + cos² Q_{2} + cos² Q_{3}**

(a) 2

(b) 1

(c) 4

(d) 3/2

**Answer: (b) 1
**

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

-: also visit :-

- ISC Sem-2 Question Bank Class-12
- Sem-2 ISC Specimen Paper for Class-12
- ISC Class-12 Textbook Solutions ,Syllabus, Solved Paper
- Previous Year Question Paper for ISC Class-12

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