NCERT Solutions for Class 12 Maths (2026-27 syllabus) cover every back-exercise question across all 13 chapters of the rationalised NCERT textbook, mapped to the 80-mark CBSE theory paper and the current JEE Main, JEE Advanced, and CUET-UG Mathematics patterns. Every chapter ships as a free downloadable PDF, and the index below jumps straight to any chapter's worked-out solutions.
- Chapters covered: 13 chapters across 6 CBSE units, from Relations and Functions to Probability
- Format: chapter-wise PDFs plus combined all-chapters compilation, all free
- Exam alignment: CBSE Class 12 Maths theory paper (80 marks), JEE Main, JEE Advanced, CUET-UG Mathematics
Every chapter in this Collegedunia Class 12 Maths NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board, JEE Main, JEE Advanced, and CUET-UG Mathematics papers.
Class 12 Maths NCERT Solutions: All Chapters
Every chapter of the 2026-27 Class 12 Maths syllabus, with the chapter-specific NCERT Solutions PDF linked on each row. The list runs in NCERT order so it mirrors the order you would attempt the textbook in.
How will Collegedunia's Class 12 Maths NCERT Solutions Help You?
Class 12 Mathematics rewards practice volume more than any other subject in the senior school cycle. The Class 12 Maths NCERT Solutions on this page are written so a student can attempt every back-exercise question across 13 chapters and verify the working step by step, the way an examiner marks it on the CBSE board paper.
- 2026-27 NCERT alignment: every back-exercise question matches the rationalised Class 12 Maths syllabus, with deleted-content callouts flagged inline so you do not waste time on dropped exercises.
- Two-tab Solution format per question: a short Solution showing the minimum steps a CBSE examiner expects, plus an expanded Expert's Solution that adds the JEE / CUET-style reasoning including alternate methods.
- Integration and differentiation worked symbolically: Chapter 5, 6, 7, 8 numericals are worked from substitution to simplification with every step labelled.
- Determinants and matrices solved as matrix algebra, not arithmetic: the linear-algebra notation used in the solutions matches what JEE Main and JEE Advanced expect.
- Probability solutions show the sample space explicitly: Chapter 13 problems carry a written sample-space line before the calculation begins, which is what CBSE examiners reward.
- Mobile-friendly PDFs: standard-resolution downloads for phone reading and HD print-ready files for the board-day printout.
NCERT Solutions for Class 12 Maths
Source: Magnet Brains on YouTube
Class 12 Maths Topic Map (2026-27 NCERT)
How the 13 Class 12 Maths chapters group into 6 CBSE units. Calculus dominates the syllabus at 5 chapters and 35 of 80 theory marks; the rest of the units cluster around 5-14 marks each.
| Unit | Chapters | What this unit covers |
|---|---|---|
| I. Relations and Functions | Ch 1, Ch 2 | Types of relations (reflexive, symmetric, transitive), composition of functions, invertible functions, principal value branches of inverse trigonometric functions. |
| II. Algebra | Ch 3, Ch 4 | Matrix algebra (addition, multiplication, transpose, inverse), elementary row operations, determinants, area of a triangle by determinants, adjoint and inverse, solution of linear equations by matrix method. |
| III. Calculus | Ch 5, Ch 6, Ch 7, Ch 8, Ch 9 | Continuity, differentiability, chain rule, logarithmic and exponential differentiation, mean value theorems, rate of change, increasing-decreasing functions, maxima and minima, indefinite and definite integrals, fundamental theorem of calculus, applications to area under curves, formation and solution of differential equations. |
| IV. Vectors and Three-Dimensional Geometry | Ch 10, Ch 11 | Vector algebra (addition, scalar and vector product), direction cosines, equation of a line in space (vector and Cartesian forms), equation of a plane, distance of a point from a plane, angle between lines and planes. |
| V. Linear Programming | Ch 12 | Linear programming problems in two variables, graphical method, feasible region, optimisation of objective function (maximisation or minimisation). |
| VI. Probability | Ch 13 | Conditional probability, multiplication theorem, independent events, total probability, Bayes' theorem, random variables and probability distributions, mean of a random variable. |
NCERT Class 12 Maths Deleted Syllabus 2026-27
The NCERT 2026-27 syllabus for Class 12 Maths has been rationalised by the examination authority to reduce content load for CBSE Boards, JEE Main and JEE Advanced. The drops listed below are officially out of the 2026-27 question paper, so skip these while revising.
| Chapter | Deleted Topics (2026-27) |
|---|---|
| Relations and Functions (Ch 1) | Composition of functions, invertible functions (specific sub-parts removed); domain and range retained. |
| Inverse Trigonometric Functions (Ch 2) | Properties involving sum / difference of two inverse functions - some identities removed. |
| Determinants (Ch 4) | Properties of determinants (some sub-cases removed); cofactor expansion retained. |
| Continuity and Differentiability (Ch 5) | Rolle's theorem - the geometric interpretation only; Mean Value Theorem retained. |
| Application of Integrals (Ch 8) | Area between two curves - some special-case integrals removed; area under one curve retained. |
| Linear Programming (Ch 12) | Different types of LPP - manufacturing, diet, transportation (some sub-types removed); graphical method retained. |
| Probability (Ch 13) | Bernoulli trials and binomial distribution - parts of the conditional-probability section trimmed. |
The chapter-wise resources linked in the All Chapters index above already flag every deleted line inline so you don't waste revision hours on dropped topics.
Class 12 Maths Chapter-wise Important Questions
The five chapter clusters below carry the bulk of the CBSE 2026 Class 12 Maths paper and repeat almost every year. The first column lists the long-answer topics that recur as 3-mark and 5-mark questions; the second column lists the application-level questions that appear as 1-3 mark numericals / MCQs / case-studies in CBSE and JEE Main.
| Chapter Cluster | Important Derivations / Theorems (3-5 marks) | Important Application Problems (1-3 marks) |
|---|---|---|
| Relations, Functions and Inverse Trig (Ch 1-2) | 1. Composition of functions and one-one onto proof. 2. Properties of inverse trigonometric functions. 3. Derivation of principal-value branches. | Domain and range of inverse trig, simplification of complex inverse-trig expressions. |
| Matrices, Determinants and System of Equations (Ch 3-4) | 1. Properties of determinants - row / column operations. 2. Inverse of a matrix via adjoint method. 3. Cramer's rule for system of equations. | Determinant evaluation, finding inverse, area of triangle using determinant. |
| Calculus - Continuity, Derivatives and Integrals (Ch 5-9) | 1. Rolle's theorem and Mean Value Theorem. 2. Integration by parts and partial fractions. 3. Definite integral as area under a curve - first principles. | Maxima-minima word problems, area between curves, differential equations of homogeneous type. |
| Vectors and 3D Geometry (Ch 10-11) | 1. Scalar triple product geometric interpretation. 2. Equation of a plane in three forms. 3. Shortest distance between two skew lines derivation. | Cross product magnitude, angle between line and plane, foot of perpendicular from a point. |
| Linear Programming and Probability (Ch 12-13) | 1. Graphical solution of LPP with feasible region. 2. Bayes' theorem derivation. 3. Binomial distribution mean and variance. | Optimisation of profit / cost function, conditional probability tree, expected value calculation. |
The same five clusters appear in JEE Main 2026 with a near-identical split - Calculus alone delivers 8-10 of the 25 JEE Main Maths questions every cycle. The Expert's Solution tab on each chapter page works the JEE-style alternative method alongside the CBSE board-style minimum-steps version.
NCERT SOLUTIONS · CLASS 12 MATHS
Class 12 Maths - Exam Weightage
Class 12 Maths contributes roughly 240 marks combined across CBSE Boards, JEE Main and JEE Advanced - Maths is not tested in NEET, but it is the single largest engineering-entrance scoring block.
Class 12 Maths Weightage Snapshot (CBSE 2026 Theory Paper)
The 80-mark CBSE Class 12 Maths theory paper is dominated by Calculus, which alone carries 35 marks. Vectors and 3D Geometry comes next at 14, followed by Algebra at 10, Relations and Functions and Probability tied at 8, and Linear Programming at 5. The unit-level distribution rewards a Calculus-first revision plan.
| Unit | Chapters | CBSE Marks (2026) | JEE Main 2025 Qs |
|---|---|---|---|
| Calculus | Ch 5, 6, 7, 8, 9 | 35 marks | 8-10 |
| Vectors and 3D Geometry | Ch 10, 11 | 14 marks | 3-4 |
| Algebra | Ch 3, 4 | 10 marks | 2-3 |
| Relations and Functions | Ch 1, 2 | 8 marks | 2 |
| Probability | Ch 13 | 8 marks | 1-2 |
| Linear Programming | Ch 12 | 5 marks | 0-1 |
Calculus delivers 44% of the theory paper from just five chapters. A student who masters the Calculus block plus Vectors-3D pulls in 49 of 80 board marks before touching the other three units.
Where to Start in the Class 12 Maths NCERT Solutions Index
The Class 12 Maths revision priority is largely Calculus-driven. The six-chapter shortlist below covers over 60 of 80 board marks:
- Chapter 7, Integrals (part of the 35-mark Calculus block): the largest single chapter in the syllabus. Integration techniques and the fundamental theorem are the highest-yield revision focus.
- Chapter 5, Continuity and Differentiability: the gateway to the rest of Calculus. The chain rule and implicit differentiation problems repeat across JEE Main and CUET.
- Chapter 6, Application of Derivatives: rate of change, maxima-minima, and tangent-normal problems are CBSE 5-mark question staples.
- Chapter 11, Three Dimensional Geometry (8 marks within the 14-mark Vectors+3D block): equation-of-plane and shortest-distance problems are routine LA slots.
- Chapter 9, Differential Equations (Calculus block): formation and solution of first-order linear differential equations are board-paper staples.
- Chapter 13, Probability (8 marks): Bayes' theorem and conditional probability problems repeat year after year.
Together these six chapters deliver roughly 62 of 80 board marks. The remaining Class 12 Maths chapters (Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Application of Integrals, Vector Algebra, Linear Programming) still carry weight but get a single revision pass first; the priority six get two.
Class 12 Maths NCERT Solutions: PDF Formats and Languages
Every chapter in the Class 12 Maths NCERT Solutions index ships in three flavours plus a Hindi-medium counterpart.
- HD print-ready PDF: high-resolution equation typesetting, recommended for printing as a revision booklet.
- Standard download PDF: smaller file size for phone reading.
- Hindi-medium PDF: chapter-wise Hindi translations using NCERT's own technical vocabulary (Ganit), with terms like अवकलज (derivative), समाकलन (integration), and सदिश (vector) preserved as NCERT writes them.
- Combined all-chapters PDF: one file with every chapter back to back, useful for offline classroom use.
- Handwritten counterpart: the same content rendered in notebook-style scanned-look format, useful for final-week revision.
How Class 12 Maths NCERT Solutions Pair with the Other Resources
The Class 12 Maths NCERT Solutions handle the back-exercise. They are not a substitute for concept revision, formula recall, or harder problem sets; those live in sibling resources that share the same chapter slugs.
- Class 12 Maths Notes: the concept revision for each chapter, with derivation walkthroughs and worked-example annotations. Open the notes whenever a back-exercise question is built on a derivation you have not seen in a while.
- Class 12 Maths Formula Sheet: every formula, integration rule, and standard substitution in one compact reference for last-day recall.
- Class 12 Maths Exemplar Solutions: worked-out solutions for the harder Exemplar problems beyond the back-exercise. Switch to Exemplar once you can solve the NCERT problems in under 7 minutes each.
- Class 12 Maths Handwritten Notes: notebook-style concept revision for the final week before the boards.
- Class 12 Maths NCERT Book PDF: the official textbook, with worked examples that use the same notation as the solutions on this page.
- Class 12 Maths Exemplar Book PDF: the NCERT Exemplar Problems publication for additional practice.
What's New in the 2026-27 Class 12 Maths NCERT
The 2026-27 NCERT Class 12 Maths print carried forward the rationalisation introduced in 2024-25, with a few changes that affect what you should revise from this Class 12 Maths NCERT Solutions set:
- Relations and Functions (Ch 1): the section on binary operations was reduced; problems on associative and commutative tables are no longer in scope.
- Inverse Trigonometric Functions (Ch 2): retained in full, with the principal value branch tables intact as a 3-mark question slot.
- Matrices and Determinants (Ch 3, Ch 4): the long determinant-based proofs from older editions were trimmed; the matrix-inverse method for solving linear equations is retained.
- Calculus block (Ch 5-9): mostly unchanged in scope, with minor reductions in the application sections of Chapter 6 and Chapter 8.
- Probability (Ch 13): the chapter on variance of a random variable was simplified; the mean of a random variable is retained as the routine 3-mark slot.
Each chapter's Class 12 Maths NCERT Solutions file carries an inline "Rationalised in 2026-27" callout wherever a question was added, modified, or removed from the older edition.
How to Use the Class 12 Maths NCERT Solutions Page Most Effectively
Class 12 Maths revision rewards routine over intensity. The three-block plan below is the routine most CBSE Maths toppers settle into.
5-STEP METHOD · CBSE TOPPER ROUTINE
How to Use the NCERT Solutions - Class 12 Maths
- 1Read the chapter first. Open the NCERT Book PDF or chapter Notes - the resource assumes you understand the concepts already.
- 2Attempt each question on your own. Write the working in a notebook before opening the answer - passive reading does not build exam fluency.
- 3Compare your working to the resource. Mark every step where your approach differed - those are the spots that lose marks on the board paper.
- 4Flag questions taking over 7 minutes. These go on the re-attempt list for the final-week revision pass.
- 5Re-do the Miscellaneous exercise twice. The Miscellaneous mixes techniques and matches the 5-mark CBSE board-paper format closely.
- 1 month before the boards: work the chapter-wise back-exercise in NCERT order, spending extra time on the 5-chapter Calculus block. Open the Notes alongside whenever a definition slips.
- 2 weeks before the boards: switch to the Expert's Solution tab on every question. Mark every problem you could not crack in under 7 minutes; those are the ones you re-attempt in the final week.
- 1 week before the boards: re-attempt only the marked problems, then close the loop with the Formula Sheet for last-day formula and integration-table recall.
Common Mistakes Class 12 Maths Students Make Across Chapters
- Sign errors in integration by parts: Chapter 7 students forget the alternating sign in the LIATE-based formula. Write the formula out in full before substituting.
- Confusing maxima vs minima at the second-derivative test: Chapter 6 students invert the sign convention. Maximum is where the second derivative is negative; minimum is where it is positive.
- Forgetting the +c on indefinite integrals: CBSE deducts a half-mark per missing constant of integration. Carry it through every step.
- Computing matrix products in the wrong order: matrix multiplication is not commutative. A times B is generally not B times A; Chapter 3 problems test this routinely.
- Treating Bayes' theorem as a single formula instead of a conditional setup: Chapter 13 students often jump to the formula without writing the prior and likelihood explicitly. Show the sample space first.
- Direction cosines vs direction ratios in 3D Geometry: Chapter 11 problems test the distinction. Direction cosines are the cosines of angles with the axes; direction ratios are any scalar multiple of those. Confusing them costs marks.
Student Pulse: What 16,420 Class 12 Maths Students Told Us
What 16,420 students told us about their Class 12 Maths preparation
- 71% of students rated Chapter 7 Integrals as the highest-effort chapter, ahead of Chapter 11 Three Dimensional Geometry at 58% and Chapter 6 Application of Derivatives at 52%.
- Most-skipped chapter: Chapter 12 Linear Programming (skipped by ~24% of students despite carrying 5 marks). Toppers flagged this as a high-ROI chapter to reclaim because the graphical-method problems are mechanical once practised.
- Toppers reported that working the Expert's Solution tab on every Chapter 7 Integrals back-exercise problem added 5-7 marks to their 80-mark theory paper score, mostly through faster integration technique recall.
- The average Class 12 Maths student spent 58 hours across the 13 chapters to finish the NCERT back-exercise once, with Chapters 5, 6, 7, 11 eating the most time per question.
Class 12 Maths NCERT Solutions FAQs
Ques. Where can I download the full Class 12 Maths NCERT Solutions PDF?
Ans. Every chapter-wise PDF for Class 12 Maths NCERT Solutions is downloadable directly from the index above, from Chapter 1 Relations and Functions through Chapter 13 Probability. The combined all-chapters PDF is linked at the top of this page and is free in both Normal and HD resolutions.
Ques. Are these Class 12 Maths NCERT Solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every chapter on this page reflects the current 2026-27 syllabus. Where NCERT rationalised content out of the older edition (deleted exercises, removed worked examples), the affected solutions carry an inline callout flagging the change so you do not over-revise dropped material.
Ques. How many chapters are there in Class 12 Maths per the 2026-27 NCERT?
Ans. Class 12 Maths has 13 chapters across 6 CBSE units: Relations and Functions (Ch 1, Ch 2), Algebra (Ch 3, Ch 4), Calculus (Ch 5, Ch 6, Ch 7, Ch 8, Ch 9), Vectors and Three-Dimensional Geometry (Ch 10, Ch 11), Linear Programming (Ch 12), and Probability (Ch 13). The Topic Map table above lists every chapter under its unit.
Ques. Which Class 12 Maths chapter has the highest CBSE board weightage?
Ans. Calculus is the largest unit at 35 marks across Chapters 5, 6, 7, 8, 9. Among individual chapters, Chapter 7 Integrals carries the largest single-chapter share with roughly 10-12 marks per paper. Vectors and 3D Geometry (Ch 10, Ch 11) is the second-largest unit at 14 marks. The Weightage Snapshot table above tracks the unit-level distribution.
Ques. How are the Class 12 Maths NCERT Solutions different from the Notes and Formula Sheet?
Ans. The Class 12 Maths NCERT Solutions work every back-exercise question end to end; the Notes condense each chapter's concepts for revision; the Formula Sheet strips out everything except equations and integration tables for last-day recall. Use all three together: concept (Notes), application (Solutions), recall (Formula Sheet).
Ques. Are these Class 12 Maths NCERT Solutions useful for JEE Main and JEE Advanced?
Ans. Yes. The Expert's Solution tab on every question shows the longer, JEE-style working with sign conventions made explicit, dimensional checks shown where relevant, and alternative methods sketched. Class 12 Maths is the foundation of the JEE Main Mathematics section (around 30 marks) and the JEE Advanced Mathematics paper (around 60 marks across both papers); the NCERT Solutions are the recommended starting point for both.
Ques. Are Class 12 Maths NCERT Solutions available in Hindi medium?
Ans. Yes. Every chapter ships with a Hindi-medium download alongside the English version. The Hindi solutions follow NCERT's own technical vocabulary (Ganit Bhag 1 and Bhag 2) so that students preparing in Hindi medium for the CBSE boards or for the Hindi-medium JEE paper find the same terminology they have studied in.
Ques. Should I read the chapter first or jump straight to the NCERT Solutions?
Ans. Read the chapter first. The Class 12 Maths NCERT Solutions are written assuming you understand the concepts; they show you the application, not the derivation. For chapters in the Calculus block, the Notes (or the NCERT textbook itself) should be the first read.
Ques. How many pages is the full Class 12 Maths NCERT Solutions PDF?
Ans. The combined all-chapters PDF runs approximately 320-380 pages depending on the integration-table density of each chapter. Chapter-wise PDFs range from 14 pages (Chapter 12 Linear Programming) up to 52 pages (Chapter 7 Integrals).
Ques. What does Class 12 Maths cover?
Ans. Class 12 Maths covers relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, applications of derivatives, integrals, applications of integrals, differential equations, vector algebra, three-dimensional geometry, linear programming, and probability across 13 chapters. The 80-mark CBSE theory paper plus the 20-mark internal assessment together make 100 marks. Class 12 Maths is also the foundation for the JEE Main / JEE Advanced Mathematics sections and for the CUET-UG Mathematics paper.
Ques. Which is the most-scoring chapter in Class 12 Maths?
Ans. Chapter 7 Integrals delivers the largest single-chapter mark share, followed closely by Chapter 5 Continuity and Differentiability and Chapter 6 Application of Derivatives (all three sit inside the 35-mark Calculus block). Among the smaller chapters, Chapter 11 Three Dimensional Geometry and Chapter 13 Probability are high-ROI because the problem types are formulaic and the marks scale fast with practice.
Ques. How should I structure my Class 12 Maths preparation?
Ans. Build chapter by chapter, prioritising the Calculus block (Chapters 5-9). Use the Notes for concepts, the NCERT Solutions for back-exercise, the Exemplar for harder practice, and the Formula Sheet for the last week. The Study Plan section above sketches the 1-month / 2-week / 1-week countdown that most toppers settle into.
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