CBSE Class 12 Mathematics Three Dimensional Geometry MCQs

Refer to CBSE Class 12 Mathematics Three Dimensional Geometry MCQs provided below. CBSE Class 12 Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Class 12 Mathematics with answers have been prepared as per the latest syllabus, CBSE books and examination pattern suggested in Class 12 by CBSE, NCERT and KVS. Multiple Choice Questions for Chapter 11 Three Dimensional Geometry are an important part of exams for Class 12 Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 12 Mathematics and also download more latest study material for all subjects

MCQ for Class 12 Mathematics Chapter 11 Three Dimensional Geometry

Class 12 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 11 Three Dimensional Geometry in Class 12. These MCQ questions with answers for Class 12 Mathematics will come in exams and help you to score good marks

Chapter 11 Three Dimensional Geometry MCQ Questions Class 12 Mathematics with Answers

Question : 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) 300
b) 600
c) 900
d) 450
Answer :  A

 

Question : The plane containing the line x - 1/1 = y - 2/2 = z - 3/3 and parallel to the line x/1 = y/1 = z/4 passes through the point:
(a) (1, – 2, 5)
(b) (1, 0, 5)
(c) (0, 3, –5)
(d) (– 1, – 3, 0)
Answer : B

Question : A vector n is inclined to x-axis at 45 , to y-axis at 60 and at an acute angle to z-axis. If is a normal to a plane passing through the point (√2,-1,1) then the equation of the plane is :
(a) 4√2x + 7y + z - 2
(b) 2x + y + 2z = 2√2 +1
(c) 3√2x - 4y -3z = 7
(d) √2x - y - z = 2
Answer : B

 

Question : If the angle between the line 2(x + 1) = y = + 4 and the plane 2x – y + √λ + 4 = 0 is π/6, then the value of l is:
(a) 135/7
(b) 45/11
(c) 45/7
(d) 135/11
Answer : C

Question : If the distance between planes, 4x – 2y – 4 + 1 = 0 and 4x – 2y – 4 + d = 0 is 7, then d is:
(a) 41 or – 42
(b) 42 or – 43
(c) – 41 or 43
(d) – 42 or 44
Answer : C

Question : A 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

Question : The equation of a plane through the line of intersection of the planes x + 2y = 3, y –2 + 1= 0, and perpendicular to the first plane is :
(a) 2x – y – 10z = 9
(b) 2x – y + 7z = 11
(c) 2x – y + 10z = 11
(d) 2x – y – 9z = 10
Answer : C

 

Question : Let the line x–2/3 = y – 1/-5 = z + 2/2 lie in the plane x + 3y – a + β = 0. Then (a, β) equals 
(a) (–6, 7)
(b) (5, –15)
(c) (–5, 5)
(d) (6, –17)
Answer : A

Question : The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius
(a) 3
(b) 1
(c) 2
(d) √2
Answer : B

Question : Let Q be the foot of perpendicular from the origin to the plane 4x – 3y + z + 13 = 0 and R be a point (– 1, – 6) on the plane. Then length QR is :
(a) √14
(b) √19/2
(c) 3√7/2
(d) 3/√2
Answer : C

Question : The equation of a plane containing the line x + 1 /-3 = y - 3/2 = z + 2 /1 and the point (0, 7, – 7) is
(a) x + y + z = 0 
(b) x + 2y + z = 21
(c) 3x – 2y + 5z + 35 = 0
(d) 3x + 2y + 5z + 21 = 0
Answer : A

 

Question : The distance of the point (1, – 5, 9) from the plane x – y + z = 5 measured along a straight x = y = z is 
(a) 10√3
(b) 5√3
(c) 3√10
(d) 3√5
Answer : A

 

Question : Distance between two parallel planes 2x + y + 2 = 8 and 4x + 2y +4 + 5 = 0 is 
(a) 2/9
(b) 2/5
(c) 2/7
(d) 2/3
Answer : C

Question : The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane 
(a) 2x - y - z = 1
(b) x - 2y - z = 1
(c) x - y - 2z = 1
(d) x - y - z = 1
Answer : A

Question : If the angle between the line x = y - 1/2 = z - 3/ λ and the plane x + 2y + 3z = 4 is cos–1 (√5/14) then λ equals
(a) 3/2
(b) 2/5
(c) 5/3
(d) 2/3
Answer : D

Question : Consider the following planes
P : x + y – 2z + 7 = 0
Q : x + y + 2z + 2 = 0
R : 3x + 3y – 6z – 11 = 0 
(a) P and R are perpendicular
(b) Q and R are perpendicular
(c) P and Q are parallel
(d) P and R are parallel
Answer : D

Question : If the three planes x = 5, 2x – 5ay + 3z – 2 = 0 and 3bx + y – 3z = 0 contain a common line, then(a, b) is equal to 
(a) (8/15, 1/5)
(b) (1/5, - 8/15)
(c) (- 8/15, 1/5)
(d) (- 1/5, 8/15)
Answer : B

Question : A line with positive direction cosines passes through the point P (2, – 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane 2x + y + z = 9 at point Q, then the length PQ equals 
(a) √2
(b) 2
(c) √3
(d) 1
Answer : C

 

Question : Equation of the plane which passes through the point of intersection of lines x - 1/3 = y - 2/1 = z - 3/2 and has the largest distance from the origin is:
(a) 7x + 2y + 4 = 54
(b) 3x + 4y + 5 = 49
(c) 4x + 3y + 5 = 50
(d) 5x + 4y + 3 = 57
Answer : C

Question : Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
(a) 3/2
(b) 5/2
(c) 7/2
(d) 9/2
Answer : C

Question : The values of a for which the two points (1, a, 1) and (– 3, 0, a) lie on the opposite sides of the plane 3x + 4y – 12z + 13 = 0, satisfy 
(a) 0 < a < 1/3
(b) – 1 < a < 0
(c) a < – 1 or a < 1/3
(d) a = 0
Answer : D

Question : Statement -1 : The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x – y + z = 5.
Statement -2: The plane x – y + z = 5 bisects the line segment oining A(3, 1, 6) and B(1, 3, 4). 
(a) Statement -1 is true, Statement -2 is true ; Statement - 2 is not a correct explanation for Statement -1.
(b) Statement -1 is true, Statement -2 is false.
(c) Statement -1 is false, Statement -2 is true .
(d) Statement - 1 is true, Statement 2 is true ; Statement -2 is a correct explanation for Statement -1.
Answer : A

 

Question : Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle a with the positive x-axis, then cos a equals 
(a) 1
(b) 1/√2
(c) 1/3
(d) 1/√2
Answer : C

Question : The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle p /4 with plane x + y = 3 are
(a) 1, √2 ,1
(b) 1, 1, √2
(c) 1, 1, 2
(d) √2 , 1, 1
Answer : B

Question : If the plane 2ax – 3ay + 4a + 6 = 0 passes through the midpoint of the line oining the centres of the spheres x2 + y2 + z2 + 6x - 8y - 2z = 13 and x2 + y2 + z2 -10x + 4y - 2z = 8 then a equals
(a) – 1
(b) 1
(c) – 2
(d) 2
Answer : C

Question : The line passing through the points (5, 1, a) and (3, b, 1) crosses the y -plane at the point (0, 17/2, –13/2) Then
(a) a = 2, b = 8
(b) a = 4, b = 6
(c) a = 6, b = 4
(d) a = 8, b = 2
Answer : C

Question : A plane which passes through the point (3, 2, 0) and the line x - 4/1 = y - 7/5 = z - 4/4 is
(a) x – y + z =1
(b) x + y + z = 5
(c) x + 2y – z = 1
(d) 2x – y + z = 5
Answer : A

Question : The image of the point (–1, 3, 4) in the plane x - 2y = 0 is
(a) (- 17/3, - 19/3, 4)
(b) (15,11, 4)
(c) (- 17/3, - 19/3, 1)
(d) None of these
Answer : D

Question : If the angle q between the line x + 1/1 = y - 1/2 = z - 2/2 and the plane 2x – y + √λ z + 4 = 0 is such that sin θ = 3/1 then the value of λ is
(a) 5/3
(b) -3/5
(c) 3/4
(d) -4/3
Answer : A

Question : The radius of the circle in which the sphere x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0 is 
(a) 4
(b) 1
(c) 2
(d) 3
Answer : D

Question : If (2, 3, 5) is one end of a diameter of the sphere x2 + y2 + z– 6x – 12y – 2z + 20 = 0, then the cooordinates of the other end of the diameter are 
(a) (4, 3, 5)
(b) (4, 3, – 3)
(c) (4, 9, – 3)
(d) (4, –3, 3).
Answer : C

Question : The shortest distance from the plane 12x + 4y +3z = 327 to the sphere 4 2 6 155 x2 + y2 + z2 + x - y - z = is
(a) 39
(b) 26
(c) 11(13/4)
11 (d) 13.
Answer : D

Question : 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

Question : The acute angle between the planes 2x – y+z = 6 and x+y+2z = 3 is
a) 600
b) 300
c) 750
d) 450
Answer : A

Question : 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

Question :

a) Sin-1 (-2/√42)
b) Sin-1 (2/√42)
c) cos-1 (2/√42)
d) None of these
Answer :  A

Question : 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

Question : 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

Question :  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

Question : 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

Question : The angle between two diagonals of a cube is
a)

b)

c)

d)

Answer : A

 

CBSE Class 12 Mathematics Three Dimensional Geometry MCQs Set A 1

CBSE Class 12 Mathematics Three Dimensional Geometry MCQs Set A 2

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