The Class 12 Maths Determinants PYQ set brings together everything CBSE has asked on this chapter in one place: 179 board-paper questions across 2003 to 2026, sorted by marks and then by year.
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- 1-mark questions: 95 questions, mostly MCQ on the value of a small determinant and properties.
- 2, 3 and 4-mark questions: 10, 3 and 21 questions, built around adjoint, inverse and determinant equations.
- 5 and 6-mark questions: 20 and 30 questions, where you find a 3x3 inverse and solve a system of three equations.
The chapter is a heavyweight in the long-answer section, with a strong block of 5 and 6-mark questions on solving systems of equations.
Every question in this Class 12 Maths Determinants 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 Determinants Previous Year Questions Cover
The 179-question set maps every idea the NCERT chapter teaches. Properties of determinants drive both quick MCQs and full proof questions. Adjoint and inverse of a matrix set up the long answers, where you find the inverse of a 3x3 matrix. The matrix method for a system of linear equations fills most of the 5 and 6-mark band. Short determinant equations and scalar-multiple rules carry the 1 and 2-mark questions.
Marks-wise Distribution of the Determinants PYQs
The table below shows how the 179 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 | 95 | 95 | Section A | MCQ / Assertion-Reason |
| 2 mark | 10 | 20 | Section B | VSA (Very Short Answer) |
| 3 mark | 3 | 9 | Section C | SA (Short Answer) |
| 4 mark | 21 | 84 | Section D | Case Study |
| 5 mark | 20 | 100 | Section E | Long Answer |
| 6 mark | 30 | 180 | Section E | Long Answer |
Year-wise Spread of Class 12 Maths Determinants PYQs
The compilation draws from 21 CBSE board years. About 44% of the questions come from 2023 onwards, with the older years still contributing a deep bank of property proofs and system-of-equations long answers.
- 2026: A 1-mark MCQ solving a 2x2 determinant equation in x, and a 5-mark question finding a 3x3 inverse and using it to solve a system of equations.
- 2024 to 2025: Strong contribution years, with MCQs on the determinant of a scalar multiple, such as det of minus 6 AB, plus inverse-method long answers.
- 2019 to 2023: Reduced-syllabus papers, but property proofs and adjoint questions still appear in the 4-mark band.
- 2003 to 2018: A heritage block of property-of-determinant proofs and system-of-equation long answers, all still in the current syllabus.
Marks-Band Attempt Strategy for the Determinants PYQs
The 179 PYQs are arranged marks-ascending inside the PDF so you attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend no more than 45 seconds each. Most ask for the value of a small determinant or a scalar-multiple rule.
- 2 and 4-mark questions: An adjoint, a property proof, or a determinant equation. Aim for 4 to 6 minutes each.
- 5-mark questions: Find the 3x3 inverse, then solve the system. Always verify A times A inverse equals the identity before substituting.
- 6-mark questions: A full matrix-method system of three equations. Allocate 12 to 15 minutes and check consistency first.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Determinants
Three things have changed in the recent CBSE cycles that the Determinants previous year questions now reflect:
- Section A now carries a fixed block of 1-mark questions. The compilation includes 95 such questions, many on scalar-multiple rules like det of minus 6 AB from 2025.
- The 5 and 6-mark band almost always sets a combined question that finds a 3x3 inverse and then solves a system, as in the 2026 paper.
- Property-of-determinant proofs now carry an OR alternative, so the PDF keeps both branches and you can revise each option.
Sample Previous Year Questions from Determinants
Here are a few real previous year questions from the Determinants board papers, taken straight from the compilation. The full set is in the downloadable PDF.
Let A and B be two square matrices of order 3 such that (A)=3 and (B)=-4. Find the value of (-6AB).
[2025 • 2 mark]
Common Mistakes in the Determinants Board Questions
- Forgetting that det of kA equals k to the power n times det A for an n by n matrix, not just k times det A.
- Making a cofactor sign error when building the adjoint, which flips the inverse.
- Dividing by the determinant to find an inverse without first checking it is non-zero.
- Mixing up rows and columns when applying a property operation in a proof.
- Skipping the consistency check in a system of equations, so an inconsistent system is wrongly solved.
Student Reviews on Determinants PYQ Practice
- 68 per cent said the 3x3 inverse and system-of-equations long answer was the hardest part of the 5 and 6-mark bands.
- 57 per cent reported gaining 5 to 8 marks after solving all 50 long-answer PYQs from this PDF before the boards.
- 46 per cent said an inverse-and-system question appeared in their actual 2026 paper.
- Average time to finish all 179 PYQs: about 17 hours across 8 study sessions.
Other Resources for Class 12 Maths Chapter 4 Determinants
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Determinants.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Determinants | NCERT Solutions for Determinants |
| Notes | Concept revision notes covering every topic in the Determinants chapter | Determinants Class 12 Notes |
| Formula Sheet | All key formulas and results of Determinants on one page for last-day revision | Determinants Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Determinants for quick one-shot revision | Determinants Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Determinants solved in full for extra practice | NCERT Exemplar Solutions for Determinants |
| NCERT Book | Official NCERT Determinants chapter PDF for free download | Determinants NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Determinants problem book PDF for free download | Determinants Exemplar Book PDF |
How to Use the Determinants PYQ PDF Most Effectively
The 179 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 95 one-mark MCQs on values and scalar-multiple rules. Mark every wrong answer and re-read the property.
- Pass 2 (Day 3 to 4): Solve the 10 two-mark, 3 three-mark and 21 four-mark questions on adjoint and property proofs.
- Pass 3 (Day 5 to 8): Work through the 20 five-mark and 30 six-mark questions, finding each 3x3 inverse and solving each system in full.
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 Determinants pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Determinants PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Determinants PYQ PDF?
Ans. The PDF has 179 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 Determinants PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Maths syllabus. Older proofs are kept because the core ideas (properties of determinants, adjoint, inverse, system of equations) are unchanged in the current syllabus.
Ques. Which topics of Determinants appear most often in CBSE board papers?
Ans. From the 179-question set: properties of determinants (about 25 per cent), system of linear equations (about 22 per cent), inverse of a 3x3 matrix (about 18 per cent), adjoint of a matrix (about 15 per cent), and value and scalar-multiple rules (about 12 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 21 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Determinants alone, so you can see which topics CBSE repeats and how each idea is usually phrased.
Ques. Does the Determinants PYQ PDF include MCQs?
Ans. Yes. 95 of the 179 questions are 1-mark questions, mostly MCQ on determinant values and scalar-multiple rules, from 2023 onwards when CBSE introduced the Section A objective block.
Ques. Where can I download the Determinants Class 12 PYQ PDF for free?
Ans. The full Determinants 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 Determinants in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 95 MCQs, Day 3 to 4 solve the 2, 3 and 4-mark questions, Day 5 to 8 attempt all 50 long answers under a 12-minute timer. Always check the determinant is non-zero before finding an inverse.
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 system of equations method important for the CBSE Determinants questions?
Ans. Very. The matrix method for a system of equations drives most of the 5 and 6-mark band. Practising every inverse-and-system question in the PDF is the best way to secure the long-answer marks in this chapter.
Ques. What is a determinant?
Ans. A determinant is a single number computed from a square matrix. It tells you whether the matrix is invertible: a non-zero determinant means the inverse exists. For a 2x2 matrix it equals the product of the main diagonal minus the product of the other diagonal.
Ques. How is the adjoint of a matrix defined?
Ans. The adjoint of a matrix is the transpose of its cofactor matrix. For any square matrix A, the product A times adj A equals det A times the identity matrix. This relation is what lets you build the inverse from the adjoint.
Ques. What is the inverse of a matrix?
Ans. The inverse of a matrix A is the matrix A inverse such that A times A inverse equals the identity. It is found as adj A divided by det A, and it exists only when the determinant is not zero.
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