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- 1-mark questions: 105 questions, by far the largest band, mostly MCQs on dot product, perpendicularity and unit vectors.
- 2-mark questions: 50 questions on projection, angle between vectors and a vector of a given magnitude.
- 3 to 5-mark questions: 18, 33 and 1 questions on cross product, coplanarity and short vector-geometry proofs.
This Vector Algebra PYQ set gives you 207 board-paper questions across 2003 to 2026, sorted by marks and then by year, so you can drill the exact short questions CBSE keeps repeating.
Every question in this Class 12 Maths Vector Algebra 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 Vector Algebra Previous Year Questions Cover
The 207-question set covers every idea the NCERT chapter introduces. Dot product and perpendicularity, the angle between two vectors and the projection of one vector on another drive almost all the 1 and 2-mark band. The cross product, the unit vector perpendicular to two vectors and coplanarity of vectors fill the 4-mark questions. The position vector and the section formula and collinearity of points appear across both bands.
Marks-wise Distribution of the Vector Algebra PYQs
The table below shows how the 207 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 | 105 | 105 | Section A | MCQ / Assertion-Reason |
| 2 mark | 50 | 100 | Section B | VSA (Very Short Answer) |
| 3 mark | 18 | 54 | Section C | SA (Short Answer) |
| 4 mark | 33 | 132 | Section D | Case Study |
| 5 mark | 1 | 5 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Vector Algebra PYQs
The 207 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 45 seconds each. Most are a single dot-product or magnitude calculation, like finding p so two vectors are perpendicular.
- 2-mark questions: A projection, an angle, or a vector of a given magnitude. Aim for 3 minutes.
- 3-mark questions: Usually a cross-product application. Always write the determinant form before expanding it.
- 4 and 5-mark questions: Coplanarity, the unit vector perpendicular to two vectors, or a short proof. Allocate 6 to 8 minutes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Vector Algebra
Three things have changed in the recent CBSE cycles that the Vector Algebra previous year questions now reflect:
- Section A carries a large block of 1-mark MCQs. The compilation includes 105 such questions, the most of any band, with many from 2023 onwards.
- Single-line numerical MCQs are common, like the 2026 question on the value of p for which two vectors are perpendicular, which needs just one dot-product step.
- 4-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 Vector Algebra
Here are a few real previous year questions from the Vector Algebra board papers, taken straight from the compilation. The full set is in the downloadable PDF.
The value of p for which vectors i + 2j + 3k and 2i - pj + k are perpendicular to each other is
- 0
- 1
- 52
- -52
[2026 • 1 mark]
The value of m for which the points with position vectors -i - j + 2k, 2i + mj + 5k and 3i + 11j + 6k are collinear, is
- 8
- -8
- 2
- 53
[2026 • 1 mark]
Find the vector of magnitude 14 in the direction of QP, where P and Q are the points (1, 3, 2) and (-1, 0, 8) respectively.
[2026 • 2 mark]
Common Mistakes in the Vector Algebra Board Questions
- Mixing up the dot product and the cross product, so a scalar answer is given where a vector is needed.
- Forgetting to divide by the magnitude when the question asks for a unit vector.
- Using the wrong sign in the projection formula when the angle between the vectors is obtuse.
- Setting only one ratio equal in a collinearity check instead of testing all the direction ratios.
- Writing the cross product components in the wrong order, which flips the sign of the result.
Student Reviews on Vector Algebra PYQ Practice
- 62 per cent said the cross product and the unit-vector questions were the trickiest in the 4-mark band.
- 57 per cent reported gaining 5 to 7 marks in Section A after drilling all 105 one-mark PYQs from this PDF.
- 49 per cent said a perpendicularity or projection MCQ very similar to a past paper appeared in their actual 2026 exam.
- Average time to finish all 207 PYQs: about 15 hours across 7 study sessions.
Other Resources for Class 12 Maths Chapter 10 Vector Algebra
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Vector Algebra.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Vector Algebra | NCERT Solutions for Vector Algebra |
| Notes | Concept revision notes covering every topic in the Vector Algebra chapter | Vector Algebra Class 12 Notes |
| Formula Sheet | All key formulas and results of Vector Algebra on one page for last-day revision | Vector Algebra Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Vector Algebra for quick one-shot revision | Vector Algebra Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Vector Algebra solved in full for extra practice | NCERT Exemplar Solutions for Vector Algebra |
| NCERT Book | Official NCERT Vector Algebra chapter PDF for free download | Vector Algebra NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Vector Algebra problem book PDF for free download | Vector Algebra Exemplar Book PDF |
How to Use the Vector Algebra PYQ PDF Most Effectively
The 207 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 105 one-mark MCQs on dot product, perpendicularity and unit vectors. Mark every wrong answer and re-read the relevant NCERT paragraph.
- Pass 2 (Day 3 to 4): Solve the 50 two-mark questions on projection, angle and vector magnitude. Time yourself: 3 minutes each.
- Pass 3 (Day 5 to 8): Work through the 18 three-mark, 33 four-mark and 1 five-mark questions on cross product, coplanarity and short proofs.
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 Vector Algebra pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Vector Algebra PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Vector Algebra PYQ PDF?
Ans. The PDF has 207 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 5) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Vector Algebra 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 (dot product, cross product, projection, coplanarity) are unchanged in the current syllabus.
Ques. Which topics of Vector Algebra appear most often in CBSE board papers?
Ans. From the 207-question set: dot product and perpendicularity (about 24 per cent), projection and angle between vectors (about 21 per cent), cross product and unit vector (about 18 per cent), and the position vector and section formula (about 15 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 Vector Algebra alone, so you can see which short questions CBSE repeats and how each idea is usually phrased.
Ques. Does the Vector Algebra PYQ PDF include MCQs?
Ans. Yes. 105 of the 207 questions are 1-mark questions, the largest band of any chapter, mostly MCQs on dot product, perpendicularity and unit vectors from 2023 onwards.
Ques. Where can I download the Vector Algebra Class 12 PYQ PDF for free?
Ans. The full Vector Algebra 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 Vector Algebra in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 105 one-mark MCQs, Day 3 to 4 solve the 50 two-mark projection and angle questions, Day 5 to 8 attempt the 33 four-mark cross-product and coplanarity questions under a 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 dot product the most tested idea in the CBSE Vector Algebra questions?
Ans. Yes. The dot product, used for perpendicularity, angle and projection, drives close to a quarter of all the questions and most of the 1-mark band. Drilling every dot-product MCQ in the PDF is the fastest way to lock in easy marks for this chapter.
Ques. What is the dot product of two vectors?
Ans. The dot product of two vectors is a scalar equal to the product of their magnitudes and the cosine of the angle between them. It is zero when the vectors are perpendicular. You can also compute it by multiplying matching components and adding them.
Ques. How is the projection of a vector defined?
Ans. The projection of a vector a on a vector b is the length of the shadow of a along the direction of b. It is defined as the dot product of a and b divided by the magnitude of b. It can be negative when the angle between the vectors is obtuse.
Ques. What is the cross product of two vectors?
Ans. The cross product of two vectors is a vector perpendicular to both, with magnitude equal to the product of their magnitudes and the sine of the angle between them. Its magnitude equals the area of the parallelogram formed by the two vectors. You evaluate it as a determinant.
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