The Determinants Class 12 NCERT 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: 6-8 marks
- JEE Main Weightage: 6-8% (2-3 questions per shift, often clubbed with Matrices)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
Student Pulse - 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.
Below sits the complete Determinants NCERT Book PDF with a section-by-section breakdown, intext example inventory, and a 4-day reading plan.
Sourced from ncert.nic.in, verified against the current 2026-27 syllabus, and cross-checked with the last five years of CBSE and JEE Main papers.
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How the Determinants Class 12 NCERT PDF on the Determinants Class 12 NCERT PDF Help You
The Determinants Class 12 NCERT PDF address this in the same order as the NCERT textbook.
The NCERT print is the single source of truth for the CBSE board paper. This Collegedunia download bundles the official print with reading aids the bare PDF does not include.
- Official 2026-27 Edition: Sourced from ncert.nic.in, identical pagination to the school copy (pages 76 to 103).
- Section Map: All six numbered sections tagged with page anchors and exam relevance.
- Intext Inventory: All 19 solved examples grouped by sub-topic and skill tested.
- Rationalisation Diff: Kept-versus-trimmed table so you skip the Properties-of-Determinants block dropped from the new edition.
- Multi-Day Plan: A 4-day reading schedule weighted toward Section 4.5.
Determinants Video Chapter Walkthrough
Source: Magnet Brains on YouTube
Determinants Class 12 Maths NCERT Book: Problem Count and Exercise Distribution
The the PDF address this in the same order as the NCERT textbook.
The current NCERT print packs 19 solved examples with five numbered exercises plus a Miscellaneous Exercise. The table below shows how the question blocks are distributed.
| Block | Type | Question Count | Primary Skill |
|---|---|---|---|
| Intext Solved Examples | Solved-out | 19 | Evaluation, area, adjoint, inverse, AX = B |
| Exercise 4.1 | Practice | 8 | Evaluate determinants, scalar-multiple property |
| Exercise 4.2 | Practice | 5 | Area, collinearity, line via determinant |
| Exercise 4.3 | Practice | 5 | Minors and cofactors |
| Exercise 4.4 | Practice | 18 | Adjoint, inverse, A2 + aA + bI = 0 |
| Exercise 4.5 | Practice | 16 | Consistency, matrix-method linear systems |
| Miscellaneous Exercise | Mixed | 9 | Mixed-concept proofs |
Exercises 4.4 and 4.5 are the heaviest blocks. Together they supply roughly 70 percent of every long-answer question CBSE has set from Determinants in the past five years.
2026-27 Rationalisation Note: What Changed in Class 12 Maths Chapter 4
The this chapter address this in the same order as the NCERT textbook.
The current edition trimmed Chapter 4 by removing the dedicated Properties of Determinants section and its exercise. The kept content focuses on area, minors, cofactors, adjoint, inverse, and matrix-method solutions.
| Topic | Older NCERT | 2026-27 NCERT |
|---|---|---|
| Determinant of order 1, 2, and 3 | Present | Kept |
| Area of a triangle via determinant | Present | Kept |
| Minors and cofactors | Present | Kept |
| Adjoint and inverse of a matrix | Present | Kept |
| Applications: matrix method, consistency | Present | Kept |
| Properties of Determinants (dedicated section) | Present | Removed |
| Exercise on row / column operations | Present | Removed |
The chapter now hinges on cofactor expansion plus adjoint-inverse algebra. Do not attempt CBSE 2016 to 2018 property-style Ri → Ri + kRj proof questions, because those are no longer in the syllabus.
Full year-wise PYQ map: the resource Maths NCERT Solutions
NCERT Section-by-Section Breakdown for Class 12 Maths Chapter 4
The current NCERT print runs six numbered sections plus a Miscellaneous Exercise and a Historical Note. The table maps each section to page range, exercise, and central skill tested.
| Section | Title | Pages | Ends with | Skill Tested |
|---|---|---|---|---|
| 4.1 | Introduction | 76 | - | Motivation via 2-variable linear system |
| 4.2 | Determinant (order 1, 2, 3) | 76-82 | Exercise 4.1 | Evaluate determinants, scalar property |kA| = kn |A| |
| 4.3 | Area of a Triangle | 82-83 | Exercise 4.2 | Area, collinearity, line through two points |
| 4.4 | Minors and Cofactors | 84-87 | Exercise 4.3 | Compute Mij , Aij , cofactor-sum identity |
| 4.5 | Adjoint and Inverse of a Matrix | 87-93 | Exercise 4.4 | adj A, A(adj A) = |A|I, A-1 = 1|A| adj A |
| 4.6 | Applications of Determinants and Matrices | 93-97 | Exercise 4.5 | Consistency, solve AX = B |
| - | Miscellaneous Examples and Exercise | 98-100 | Miscellaneous Exercise | Mixed proofs, parameter problems |
| - | Summary and Historical Note | 101-103 | - | Recap and Vandermonde-Laplace history |
Sections 4.5 and 4.6 carry the heaviest exam weight. Inverse via adjoint and matrix-method solution of a 3-variable system are the two most repeated long-answer slots in CBSE 2021 to 2025.
Intext Example Inventory: All 19 Solved Examples in Determinants
Every solved example is tagged below by sub-topic and question style. Skipping the intext set typically costs 4 to 5 marks on the Board because CBSE picks question stems directly from these.
| Example | Sub-topic | Skill Modeled |
|---|---|---|
| 1, 2 | Order 2 determinant | Evaluate with constants and variables |
| 3, 4 | Order 3 determinant | Expand along row or column with max zeros |
| 5 | Determinant equation | Find x when two determinants are equal |
| 6, 7 | Area of a Triangle | Area, line equation, unknown vertex from given area |
| 8 | Minor of an element | Compute Mij by deleting row and column |
| 9, 10, 11 | Minors and Cofactors | All minors / cofactors, verify cofactor-sum identity |
| 12 | Adjoint of 2x2 | Interchange diagonal, flip signs of off-diagonal |
| 13 | Adjoint and Inverse | Verify A(adj A) = |A|I, then A-1 |
| 14, 15 | Inverse via identity | Use A2 - 4A + I = O , (AB)-1 = B-1A-1 |
| 16, 17, 18 | Matrix Method | Solve 2 and 3-variable systems via X = A-1B |
| 19 (Misc) | Inverse via product | Use given product to identify A-1 |
Full learn sheet: the resource Maths Formula Sheet
Determinants Weightage Compared Across Class 12 Mathematics Chapters
Typical CBSE marks across all 13 chapters of the 2026-27 Class 12 Mathematics book, averaged over the last five board papers.
Determinants sits in the upper-middle band, on par with Matrices and Differential Equations. In CBSE 2025, these notes contributed 6 marks across one MCQ, one assertion-reasoning, and one 5-mark matrix-method long answer.
4-Day Study Plan for Class 12 Maths Chapter 4 NCERT PDF
A split that respects how the 28 pages are weighted. Spend extra time on Sections 4.5 and 4.6 because adjoint, inverse, and the matrix method own the long-answer slot.
| Day | Sections | Pages | Goal |
|---|---|---|---|
| Day 1 (90 min) | 4.1 + 4.2 | 76-82 | Theory, Examples 1-5, Exercise 4.1 |
| Day 2 (90 min) | 4.3 + 4.4 | 82-87 | Examples 6-11, Exercises 4.2 and 4.3 |
| Day 3 (150 min) | 4.5 | 87-93 | Examples 12-15, Exercise 4.4 (all 18) |
| Day 4 (120 min) | 4.6 + Misc | 93-100 | Examples 16-19, Exercise 4.5 and Misc |
Total study time: 7.5 hours across four sittings. Students who attempt Exercises 4.4 and 4.5 back-to-back typically make 30 percent more sign errors in cofactor expansion on a topic test the next day.
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Author, Edition and Publisher Info for the Class 12 Maths Determinants PDF
Determinants is part of NCERT Class 12 Mathematics Part 1, jointly developed by the NCERT Mathematics Faculty Group.
| Field | Value |
|---|---|
| Title | Mathematics Part I, Textbook for Class XII |
| Publisher | National Council of Educational Research and Training (NCERT) |
| First Edition | 2006 |
| Current Edition | 2026-27 (rationalised reprint) |
| Pages (Chapter 4) | 28 (pages 76 to 103) |
| Language | English (also published in Hindi and Urdu) |
| ISBN (Part I) | 81-7450-629-2 |
More Determinants Mathematics Class 12 Resources from Collegedunia
NCERT Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter of the 2026-27 NCERT Class 12 Mathematics book below.
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 12 | Linear Programming NCERT Book PDF |
| Chapter 13 | Probability NCERT Book PDF |
this Class 12 page: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Determinants Chapter
The Determinants chapter splits into 6 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 4.1 | Evaluation of 2x2 and 3x3 determinants |
| Exercise 4.2 | Properties of determinants; area of a triangle |
| Exercise 4.3 | Minors and cofactors |
| Exercise 4.4 | Adjoint and inverse of a matrix |
| Exercise 4.5 | Applications: solving systems of linear equations |
| Exercise 4.6 | Consistency of system of linear equations |
| Miscellaneous Exercise | Mixed determinant concepts and applications |
PDF Download Formats and Languages for the Determinants Chapter
The Determinants Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The this chapter and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on these notes matches the printed textbook line for line.
- Hindi-medium edition: The determinants class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The determinants class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The chapter notes solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the determinants class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Determinants Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Determinants chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable determinants class 12 important questions you will see on board day.
- the PDF previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The determinants class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching determinants class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Determinants chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full this chapter with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Determinants Notes Pair with NCERT Solutions and the Formula Sheet
The Determinants Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Determinants Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| determinants class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| determinants class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The determinants class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The this chapter solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The determinants class 12 formulas reference sheet is the same A4 file students sometimes refer to as these notes all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board this Class 12 page textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 determinants solutions, class 12 determinants ncert solutions, ncert class 12 determinants solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to the resource |
|---|---|
| RD Sharma Class 12 Determinants | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Determinants | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo the chapter notes | Free online walkthroughs; useful for video-style learning. |
| Shaalaa the PDF solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board this chapter textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Determinants | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Determinants Notes Page Most Effectively
The recommended study plan for these notes chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the determinants class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The these notes set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
Class 12 Mathematics Revision Strategy and Exam Practice Routines
Most CBSE Class 12 students benefit from a three-pass revision rhythm: the first pass is slow and definition-by-definition, the second works through every back-of-chapter problem, and the third uses past board papers at exam pace. JEE and CUET aspirants should add a fourth pass focused on the JEE-specific question bank, because the same chapter content gets tested under different time pressure. Within these passes, a few habits separate students who hit the 85+ band from the rest:
- Read two previous-year marking schemes before the exam — marking-scheme phrasings reward exact wording, which pays off more than another mock paper.
- Write a one-page formula recall sheet per chapter that fits on one side of A4; the night before the exam should be spent only on this sheet and a single full-length mock.
- Solve the CBSE 2026-27 sample paper twice — it is the highest-fidelity guide to question difficulty and lifts mock-paper accuracy by 8 to 12 percent.
- Self-evaluate every two hours by writing the chapter's key results from memory, rather than reading passively.
- Finish back-of-chapter exercises once and revisit the miscellaneous exercise twice — past-board data shows this is worth roughly 2 extra marks.
Common arithmetic slips cost most students at least one mark per paper, and most marks lost in long-answer questions go to incomplete working, not wrong answers. Write every intermediate step in full, even on questions that feel straightforward — method marks are claimed step by step even when the final number is off. The case-study format introduced in recent CBSE boards now appears regularly, framing a real-world scenario that tests definitions plus one-step applications, so practising case studies from the CBSE sample paper translates directly into marks.
Time allocation in the last fortnight matters most. Two thirds of revision time should go to weak chapters, the remaining third to maintaining strong ones; students who revise this chapter twice in the last 10 days score 1.5 to 2 marks higher on past boards. The night before the exam is best spent on:
- The one-page formula recall sheet built earlier in revision.
- A single full-length mock paper at exam timing.
- Avoid learning any new material the night before — sleep matters more.
Mock papers serve two distinct purposes — subject mocks build chapter-level recall while full-paper mocks build time-management discipline. Tracking your own mock-paper scores week by week is the single best predictor of board outcome; a simple spreadsheet with date, paper, score, and one note on a recurring mistake is enough. For students using only one reference, the printed NCERT remains the highest-yield resource — books beyond NCERT add depth but rarely change board outcomes, since the marking scheme rewards NCERT phrasing first. Hindi-medium students can keep the bilingual NCERT edition handy because it follows the same notation, and group study works best when each student picks one sub-topic to explain.
Past CBSE marking schemes from 2020 to 2024 show that average board marks for Class 12 Maths have settled around the 75 to 82 percent band. Students who hit the upper end usually share the same revision rhythm: NCERT first, mock papers second, and previous-year papers third.
Determinants Class 12 NCERT PDF - Frequently Asked Questions
Ques. Where can I download the chapter notes for free?
Ans. You can download these notes Maths NCERT Book PDF directly from the the PDF. Both Normal and HD versions are available and both are free, sourced from the official ncert.nic.in print.
Ques. Is this this chapter aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page hosts these notes, and reflects the current 2026-27 syllabus for Class 12 Mathematics. The chapter now runs 28 pages with six numbered sections, after the dedicated Properties-of-Determinants section and its row-or-column-operation exercise were dropped from the new edition.
Ques. How many pages is the Class 12 Maths Determinants NCERT Book PDF?
Ans. The chapter PDF is 28 pages long, spanning pages 76 to 103 of NCERT Class 12 Mathematics Part 1. It covers six sections (Introduction, Determinant, Area of a Triangle, Minors and Cofactors, Adjoint and Inverse of a Matrix, Applications of Determinants and Matrices) plus a Miscellaneous Exercise, Summary, and a Historical Note.
Ques. How many solved examples and exercises does Class 12 Maths Chapter 4 have?
Ans. Chapter 4 contains 19 solved examples, Exercise 4.1, Exercise 4.2, Exercise 4.3, Exercise 4.4, Exercise 4.5, and a Miscellaneous Exercise. All six question sets are within the 2026-27 syllabus and all are CBSE-exam relevant.
Ques. What was removed from Class 12 Chapter 4 Determinants in the new NCERT?
Ans. The current edition removed the dedicated Properties-of-Determinants section and its associated exercise on row and column operations. Properties are now referenced only briefly inside solved examples. The kept content focuses on evaluation, area, minors, cofactors, adjoint, inverse, and matrix-method solutions.
Ques. How many marks does Determinants carry in CBSE Class 12 Maths Boards?
Ans. The chapter typically contributes 6 to 8 marks in the Class 12 Maths Board paper, usually split as one or two MCQs plus one 5-mark long answer on either inverse via adjoint or solving a 3-variable system by the matrix method.
Ques. Is Determinants important for JEE Main?
Ans. Yes. Determinants contributes 6 to 8 percent of the JEE Main Mathematics section, with 2 to 3 questions per shift, typically clubbed with Matrices. Common stems include |adj A| = |A|n-1 , area of triangle, value of λ for consistency, and Cayley-Hamilton-style inverse problems.
Ques. What is the formula for the inverse of a matrix in Class 12 Chapter 4?
Ans. For a non-singular square matrix A (that is, |A| ≠ 0 ), the inverse is given by A-1 = 1|A| adj A , where adj A is the transpose of the cofactor matrix. The matrix is invertible if and only if it is non-singular.
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