The Determinants Class 12 Exemplar Book page compiles NCERT Class 12 Mathematics Chapter 4 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
- CBSE Weightage: 5-7 marks (typically one 5-mark LA or split across SA + MCQ)
- JEE Main Weightage: 3-4% (1-2 questions per shift, almost guaranteed)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
This Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE Board and JEE Main determinant questions, and flagged for post-rationalisation overlap.
The page below carries the problem-range map, question-type distribution, an Exemplar vs textbook difficulty comparison, and a parallel-track study plan pairing each Exemplar section with the matching NCERT exercise.
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How the NCERT Exemplar Class 12 Maths Determinants on the NCERT Exemplar Class 12 Maths Determinants Help You
The NCERT Exemplar Class 12 Maths Determinants address this in the same order as the NCERT textbook.
The bare Exemplar print is a problem book with no reading aids. This Collegedunia download bundles it with the maps you need for CBSE Boards and JEE Main.
- Properties Reference Card: A one-page summary of the seven row-column properties used to collapse a 3 x 3 determinant to zero or to a clean factor.
- Question-Type Tagging: Every problem is tagged SA, LA, MCQ, Fill-in or True/False so you can drill one type at a time.
- Property-Application Map: Each LA problem is mapped to the operations it actually uses (e.g. R1 → R1 + R2 + R3 ).
- JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles.
Determinants NCERT Exemplar Video Walkthrough
Source: Class 12 PCMB on YouTube
What's Inside the NCERT Exemplar Class 12 Maths Determinants
Every entry in the NCERT Exemplar Class 12 Maths Determinants is reproduced in the order it appears in the NCERT textbook.
The 21 pages run as a single connected problem set. The table below maps the problem range to its question type and the page span inside the NCERT Exemplar Class 12 Maths Determinants.
| Section | Problem Range | Pages | What It Covers |
|---|---|---|---|
| Solved Examples (SA + LA + MCQ + Fill-in) | Ex 1 to Ex 14 | 5-13 | Solved problems on property application, area, adjoint, inverse and systems |
| Exercise: Short Answer | Q1 to Q17 | 13-15 | Evaluate, prove and find-x problems using row-column properties |
| Exercise: Long Answer | Q18 to Q23 | 15-16 | 5-mark adjoint, inverse, divisibility and 3-equation systems; closest to CBSE Board LA |
| Objective Type (MCQ) | Q24 to Q37 | 16-19 | Single-correct MCQs on properties, cofactors, area and adj A ; JEE Main pattern |
| Fill in the Blanks | Q38 to Q47 | 19-20 | Recall problems on |kA| , |adj A| , minors and cofactor sums |
| True / False | Q48 to Q58 | 20-21 | Counter-example problems on |A-1| and |adj A| identities |
Determinants Exemplar Question-Type Distribution
The NCERT Exemplar Class 12 Maths Determinants address this in the same order as the NCERT textbook.
The distribution below splits the 72 problems across five question types. CBSE-prep students prioritise SA and LA; JEE aspirants prioritise MCQ, Fill-in and True/False, which mirror the JEE Main single-correct pattern.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 14 | - | - | Skill modelling |
| Short Answer (SA) | 17 | 2-4 | ~51 | CBSE Boards |
| Long Answer (LA) | 6 | 5-6 | ~33 | CBSE Boards + JEE Advanced subjective |
| MCQ | 14 | 1 | 14 | JEE Main |
| Fill in the Blanks | 10 | 1 | 10 | Last-day recall |
| True / False | 11 | 1 | 11 | Counter-example training |
Old vs Rationalised Syllabus in the Class 12 Maths Chapter 4 Exemplar
The NCERT Exemplar was not updated when the NCERT Exemplar Class 12 Maths Determinants was revised in 2022-23. The Exemplar PDF still contains problems on topics whose framing has shifted in the current 2026-27 syllabus.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should You Solve? |
|---|---|---|---|
| Properties of determinants (7 row-column rules) | Yes | Yes | Yes, priority 1 |
| Area of triangle via determinants | Yes | Yes | Yes, priority 1 |
| Adjoint, inverse, |adj A| = |A|n-1 | Yes | Yes | Yes |
| System of linear equations (matrix method) | Yes | Yes | Yes |
| Consistency analysis using (adj A)B | Trimmed | Yes | Useful for JEE; skip if pure CBSE |
Roughly 10% of Exemplar problems are now beyond the strict CBSE-only syllabus. A board-only student who solves them is using extra study hours. JEE aspirants should attempt them all.
Detailed kept-trimmed-removed table: the chapter notes Maths NCERT Book PDF
How to Use the Exemplar with the NCERT Textbook: A Parallel-Track Plan
The Exemplar is not a replacement for the NCERT Exemplar Class 12 Maths Determinants. Interleave them: read a topic from the NCERT Exemplar Class 12 Maths Determinants, immediately attempt Exemplar problems on the same topic.
- Day 1 (Properties): Read NCERT Sections 4.1-4.2. Solve textbook Exercises 4.1 and 4.2. Attempt Exemplar SA Q1-Q9.
- Day 2 (Area, Minors): Read Sections 4.3-4.4. Solve Exercises 4.3 and 4.4. Attempt Exemplar SA Q10-Q17 under a 60-minute timer.
- Day 3 (Adjoint, Inverse, Systems): Read Sections 4.5-4.6. Solve Exercises 4.5, 4.6 and the Miscellaneous Exercise. Attempt Exemplar LA Q18-Q23 under a 75-minute timer.
- Day 4 (Objective drill): Attempt Exemplar MCQs Q24-Q37, Fill-in Q38-Q47 and True/False Q48-Q58 back to back. Target 1 minute per MCQ, 30 seconds per Fill-in, 20 seconds per True/False.
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Other Resources
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 4 | Determinants Exemplar Book PDF |
| Chapter 1 | Relations and Functions NCERT Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 3 | Matrices NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 6 | Application of Derivatives NCERT Exemplar Book PDF |
| Chapter 7 | Integrals NCERT Exemplar Book PDF |
| Chapter 8 | Application of Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 12 Maths Determinants: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Determinants Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
NCERT Exemplar Class 12 Maths Determinants - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Determinants for free?
Ans. You can download these notes Maths NCERT Exemplar Book PDF directly from the NCERT Exemplar Class 12 Maths Determinants. Both Normal and HD versions are available and both are free.
Ques. Is this NCERT Exemplar Class 12 Maths Determinants aligned with the 2026-27 NCERT syllabus?
Ans. The Exemplar itself was not updated during the 2022-23 revision, so it still contains a handful of consistency-analysis problems that are now beyond the strict CBSE-only scope. We have flagged those so you can skip them if you are not preparing for JEE.
Ques. How many pages and how many problems are in the Class 12 Maths Determinants Exemplar PDF?
Ans. The Exemplar PDF for Chapter 4 runs 21 pages. It contains 14 solved examples plus 58 unsolved problems split as 17 SA, 6 LA, 14 MCQ, 10 Fill-in-the-Blanks and 11 True/False.
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Determinants?
Ans. Yes. The Exemplar chains two or three row-column operations into one problem, asks for a factor extraction after the simplification, and uses counter-example True/False statements to test edge cases. This is the style CBSE Boards and JEE Main now use for HOTS questions on Determinants.
Ques. Should I attempt the Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar before the textbook usually leaves students stuck on multi-step row operations.
Ques. How important is the NCERT Exemplar for JEE Main preparation on Determinants?
Ans. Very important. Around 40% of JEE Main 2023-2025 questions on Determinants chained two or more row-column operations in a single step, which is exactly the Exemplar style. JEE aspirants should treat the Exemplar Chapter 4 problem set as mandatory practice.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?
Ans. Long Answer problems Q19, Q20 and Q22 most closely match CBSE Board 5-mark style on adjoint, inverse and matrix-method systems. These three have appeared in CBSE Boards in slightly modified form across the last five years.
Ques. What is the formula for the determinant of adjoint of a matrix?
Ans. For a square matrix A of order n, |adj A| = |A|n-1 . For a 3 x 3 matrix this becomes |adj A| = |A|2 . Exemplar True/False Q54 and Fill-in Q39 directly test this identity.
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