Inside this Class 12 Maths Three Dimensional Geometry set you will find every line-and-plane question CBSE has set, grouped so you can revise one idea at a time.
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- 1-mark questions: 81 questions, mostly MCQs on direction cosines, the equation of a line and short distance facts.
- 2 and 3-mark questions: 36 and 15 questions on points on a line, angle between lines and coplanarity.
- 4 to 6-mark questions: 38, 30 and 28 questions on shortest distance, the equation of a plane and the image of a point.
The Three Dimensional Geometry PYQ compilation holds 228 board-paper questions across 2003 to 2026, sorted by marks and then by year, latest first.
Every question in this Class 12 Maths Three Dimensional Geometry PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Three Dimensional Geometry Previous Year Questions Cover
The 228-question set covers every idea the NCERT chapter introduces. Direction cosines and direction ratios and the equation of a line drive the 1-mark MCQ band. The shortest distance between two skew lines and the equation of a plane fill almost all the 5 and 6-mark long answers. The angle between lines or planes, the image of a point in a plane and coplanarity of four points appear across the middle bands.
Marks-wise Distribution of the Three Dimensional Geometry PYQs
The table below shows how the 228 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 81 | 81 | Section A | MCQ / Assertion-Reason |
| 2 mark | 36 | 72 | Section B | VSA (Very Short Answer) |
| 3 mark | 15 | 45 | Section C | SA (Short Answer) |
| 4 mark | 38 | 152 | Section D | Case Study |
| 5 mark | 30 | 150 | Section E | Long Answer |
| 6 mark | 28 | 168 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Three Dimensional Geometry PYQs
The 228 PYQs are arranged marks-ascending inside the PDF so you can attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend under a minute each. Most ask for direction cosines, a quick distance, or whether two lines are perpendicular.
- 2 and 3-mark questions: A point on a line or an angle between lines. Aim for 3 to 4 minutes.
- 4-mark questions: The equation of a line or a plane through given points. Always write the direction ratios clearly before forming the equation.
- 5 and 6-mark long answers: Shortest distance between skew lines or the image of a point. Allocate 12 to 15 minutes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Three Dimensional Geometry
Three things have changed in the recent CBSE cycles that the Three Dimensional Geometry previous year questions now reflect:
- Section A now carries a fixed block of 1-mark MCQs. The compilation includes 81 such questions, mostly on direction cosines and short distance facts from 2023 onwards.
- Long answers increasingly combine two ideas in one question, like the 2026 5-mark question that asks you to prove two lines intersect and then find the line through that point and the origin.
- 5 and 6-mark questions almost always carry an OR alternative, so the PDF keeps both branches and you can revise each option.
Sample Previous Year Questions from Three Dimensional Geometry
Here are a few real previous year questions from the Three Dimensional Geometry board papers, taken straight from the compilation. The full set is in the downloadable PDF.
The length of perpendicular drawn from point (2, 5, 7) on line x1 = y2 = z3 is
- 2
- 5
- √74
- √78
[2026 • 1 mark]
Prove that the line through points A(0, -1, -1) and B(4, 5, 1) intersects the line through points C(3, 9, 4) and D(-4, 4, 4). Hence, write the equation of line passing through the point of intersection of lines AB and CD as well as origin.
[2026 • 5 mark]
Find the co-ordinates of the point on the line r = -j + 3k + λ(2i - 2j + k) such that the sum of co-ordinates is 3.
[2026 • 2 mark]
Common Mistakes in the Three Dimensional Geometry Board Questions
- Confusing direction cosines with direction ratios, so the sum-of-squares check fails.
- Using the line distance formula when the question asks for the shortest distance between two skew lines.
- Forgetting to normalise the normal vector when finding the distance of a plane from the origin.
- Taking the wrong foot of perpendicular when finding the image of a point in a plane.
- Not checking the scalar triple product properly in a coplanarity question, leading to a wrong conclusion.
Student Reviews on Three Dimensional Geometry PYQ Practice
- 69 per cent said the shortest distance between skew lines was the hardest part of the 5 and 6-mark bands.
- 60 per cent reported gaining 5 to 6 marks after solving all 28 six-mark PYQs from this PDF before the boards.
- 45 per cent said a line-and-plane long answer very similar to a past paper appeared in their actual 2026 exam.
- Average time to finish all 228 PYQs: about 16 hours across 8 study sessions.
Other Resources for Class 12 Maths Chapter 11 Three Dimensional Geometry
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Three Dimensional Geometry.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Three Dimensional Geometry | NCERT Solutions for Three Dimensional Geometry |
| Notes | Concept revision notes covering every topic in the Three Dimensional Geometry chapter | Three Dimensional Geometry Class 12 Notes |
| Formula Sheet | All key formulas and results of Three Dimensional Geometry on one page for last-day revision | Three Dimensional Geometry Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Three Dimensional Geometry for quick one-shot revision | Three Dimensional Geometry Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Three Dimensional Geometry solved in full for extra practice | NCERT Exemplar Solutions for Three Dimensional Geometry |
| NCERT Book | Official NCERT Three Dimensional Geometry chapter PDF for free download | Three Dimensional Geometry NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Three Dimensional Geometry problem book PDF for free download | Three Dimensional Geometry Exemplar Book PDF |
How to Use the Three Dimensional Geometry PYQ PDF Most Effectively
The 228 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 81 one-mark MCQs on direction cosines and the equation of a line. Mark every wrong answer and re-read the relevant NCERT paragraph.
- Pass 2 (Day 3 to 5): Solve the 36 two-mark, 15 three-mark and 38 four-mark questions on points on a line, angles and plane equations. Time yourself each band.
- Pass 3 (Day 6 to 10): Work through all 30 five-mark and 28 six-mark long answers on shortest distance and the image of a point, writing the full method each time.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Three Dimensional Geometry pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Three Dimensional Geometry PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Three Dimensional Geometry PYQ PDF?
Ans. The PDF has 228 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Three Dimensional Geometry PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Mathematics syllabus. Older questions are kept because the core ideas (direction cosines, line and plane equations, shortest distance) are unchanged in the current syllabus.
Ques. Which topics of Three Dimensional Geometry appear most often in CBSE board papers?
Ans. From the 228-question set: direction cosines and ratios (about 22 per cent), equation of a line (about 20 per cent), shortest distance between lines (about 18 per cent), and the equation of a plane (about 16 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together 22 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Three Dimensional Geometry alone, so you can see which line-and-plane questions CBSE repeats and how each is usually phrased.
Ques. Does the Three Dimensional Geometry PYQ PDF include MCQs?
Ans. Yes. 81 of the 228 questions are 1-mark questions, mostly MCQs on direction cosines, the equation of a line and short distance facts from 2023 onwards.
Ques. Where can I download the Three Dimensional Geometry Class 12 PYQ PDF for free?
Ans. The full Three Dimensional Geometry PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Three Dimensional Geometry in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 81 MCQs, Day 3 to 5 solve the 2 to 4-mark line and plane questions, Day 6 to 10 attempt all 28 six-mark long answers on shortest distance and the image of a point under a 12-minute timer.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Is the shortest distance between skew lines important for the CBSE Three Dimensional Geometry questions?
Ans. Very. The shortest distance between two skew lines drives close to a fifth of the set and many of the 5 and 6-mark long answers. Practising every skew-line question in the PDF is one of the best uses of your time for this chapter.
Ques. What are direction cosines of a line?
Ans. The direction cosines of a line are the cosines of the angles the line makes with the positive x, y and z axes. They are usually written as l, m, n, and they always satisfy l² + m² + n² = 1. They fix the direction of the line in space.
Ques. How is the shortest distance between two skew lines defined?
Ans. The shortest distance between two skew lines is the length of the common perpendicular between them. It is found from the scalar triple product of the difference of two points and the two direction vectors, divided by the magnitude of the cross product of the direction vectors. It is zero when the lines intersect.
Ques. What is the equation of a plane in normal form?
Ans. The equation of a plane in normal form uses the unit normal vector and the perpendicular distance of the plane from the origin. It is written as the dot product of the position vector with the unit normal equals that distance. It directly gives both the plane's direction and its distance from the origin.
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