Maths Class 12 Three Dimensional Geometry MCQs: The Central Board of Secondary Education is responsible for conducting the annual board exam for class 12, which is considered the most important test for students. The question paper follows a pre-defined format every year and comprises questions of various types like MCQs, short-answer and long-answer.
Each question requires a different answering approach depending on its difficulty level and marks. Multiple choice questions are usually a core part of all papers, but unlike other subjects, they aren’t straightforward in mathematics. Solving MCQs requires fast calculation skills and quick thinking from students. So it becomes essential to thoroughly go through several MCQs before appearing in the exam. You can check out the MCQs for CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry below.
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Related: CBSE Class 12 Maths Chapter 10 Vector Algebra MCQs with Solutions: Download
MCQs for CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry with Solutions
1: If the direction cosines of a line are k/3,k/3,k/3, then value of k is
(a) k > 0
(b) 0 < k < 1.
(c) ±1
(d) k = ±3
2: 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
Related: CBSE Class 12 Maths Syllabus 2025-26: 12th Maths Syllabus Download PDF
3: The direction cosines of the y-axis are:
(a) (9, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)
4: 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
Also Check: NCERT Solutions for Class 12 Maths PDF: Updated for 2025-26
5: The distance between the planes 2x−3y + 6z+12=0 and 2x−3y+6z−2=0 is
(a) 10/7
(b) 2/7
(c) 2
(d) 24/7
6: 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
7: 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)
Related: CBSE Class 12 Maths Sample Paper 2025-26 with Solutions PDF - Download Model Paper
8: Three line segments are drawn by joining any two of the points A(-1, 3), B(-2, 1), and C(-5, -1). How many of them are intersected by the y-axis?
(a) 1
(b) 0
(c) 2
(d) 3
9: 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
10: 
Answers
| Question | Answer |
| 1 | (d) k = ±3 |
| 2 | (b) ⅔, -⅓, -⅔ |
| 3 | (c) (0, 1, 0) |
| 4 | (d) x + y – 2 = 0 |
| 5 | (c) 2 |
| 6 | (a) A pair of parallel planes |
| 7 | (c) -i+2k+ λ(4i + 4j + 4k) |
| 8 | (b) 0 |
| 9 | (d) l2+ m2+ n2 = 1 |
| 10 | (b) |
MCQs for CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry with Solutions: Download PDF
Students can download PDF from the link shared below. The PDF contains the MCQs shared here for CBSE Class 12 Maths Chapter-11 Three dimensional geometry with solutions. This can be saved for later, to practice the questions at any day and time.
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