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NCERT Solutions for class 12 Maths | Chapter 11 - Three Dimensional Geometry

Free download in PDF Class 12 Maths Chapter 11 Three Dimensional Geometry Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(1) 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)
Answer: (5, 0, 6)t
(2) The direction cosines of the y-axis are
[A] (6, 0, 0)
[B] (1, 0, 0)
[C] (0, 1, 0)
[D] (0, 0, 1)
Answer: (0, 1, 0)
(3) The direction ratios of a line are 1,3,5 then its direction cosines are
[A] 1/√35, 3/√35, 5/√35
[B] 1/9, 1/3, 5/9
[C] 5/√35, 3/√35, 1/√35
[D] None of these
Answer: 1/√35, 3/√35, 5/√35
(4) The points A (1, 1, 0), B(0, 1, 1), C(1, 0, 1) and D(2/3, 2/3, 2/3)
[A] Coplanar
[B] Non-coplanar
[C] Vertices of a parallelogram
[D] None of these
Answer: Coplanar
(5) The distance of the plane from the orgin is Class 12 Maths Chapter 11 Three Dimensional Geometry
[A] 1
[B] 7
[C] 1/7
[D] None of these
Answer: 1
(6) 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
Answer: 1/3
(7) The planes and
[A] parallel
[B] at right angles
[C] equidistant front origin
[D] None of these
Answer: parallel
(8) The sine of the angle between the straight line and the plane 2x – 2y + z = 5 is
[A]
[B]
[C]
[D]
Answer:
(9) The plane 2x – 3y + 6z – 11 = 0 makes an angle sin-1 (α) with .e-axis. The value of a is equal to
[A] √3/2
[B] √2/3
[C] 2/7
[D] 3/7
Answer: 2/7
(10) The distance of the points (2, 1, -1) from the plane x- 2y + 4z – 9 is
[A] √31/21
[B] 13/21
[C] 13/√21
[D] √π/2
Answer: 13/21
(11) 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: 1/√2, – 1/√2
(12) 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] 2/3
[D] 2
Answer: 2
(13) If the directions cosines of a line are A, k, k, then
[A] k > 0
[B] 0 < k < 1
[C] k = 1
[D]
Answer:
(14) Distance of the point (a, β, γ) from y-axis is
[A] β
[B] |β|
[C] 60 J
[D]
Answer:
(15) If the planes a1x + b, y + c, z + d1 = 0 and a2x + b, y + c2z + d2 = 0 are perpendicular to each other then
[A]
[B]
[C] a1a2 + b1b2 + c1c2 = 0
[D]
Answer: a1a2 + b1b2 + c1c2 = 0
(16) The direction ratios of the line joining the points (x, y, z) and (x2, y2, z1) are
[A] x1 + x2, y1 + y2, z1 + z2
[B]
[C]
[D] x2 – x1, y2 – y1, z2 – z1
Answer: x2 – x1, y2 – y1, z2 – z1
(17) The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are
[A] 2/7, −3/7, −6/7
[B] 2/7, 3/7, 6/7
[C] −2/7, −3/7, −6/7
[D] None of these
Answer: 2/7, −3/7, −6/7
(18) The shortest distance between the lines
[A] 0
[B]
[C]
[D]
Answer: 0
(19) The lines of intersection of the planes is parallel to the vector
[A]
[B]
[C]
[D]
Answer:
(20) The angle between the planes 2x – y + z = 6 and x + y + 2z = 7 is
[A] π/4
[B] π/6
[C] π/3
[D] π/2
Answer: π/3

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