NCERT Solutions for Class 12 Maths (2026-27 syllabus) solve every back-exercise question across all 13 chapters of the NCERT textbook. They match the 80-mark CBSE theory paper and the current JEE Main, JEE Advanced, and CUET-UG Maths patterns.
Class 12 Maths NCERT Solutions PDF Download
Here is every chapter of the 2026-27 Class 12 Maths syllabus. Each row links the chapter's NCERT Solutions PDF. The list follows NCERT order, so it matches the order you study the textbook in.
Every chapter comes as a free PDF. The index below takes you straight to any chapter's 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
Subject experts wrote every chapter in this Collegedunia Class 12 Maths NCERT Solutions set. Each one matches the 2026-27 NCERT and the last five years of CBSE Board, JEE Main, JEE Advanced, and CUET-UG Maths papers.
How will Collegedunia's Class 12 Maths NCERT Solutions Help You?
Class 12 Maths needs more practice than any other subject in these two years. The Class 12 Maths NCERT Solutions on this page help you solve every back-exercise question across 13 chapters. You can check your 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 current Class 12 Maths syllabus. Deleted topics are flagged inline, so you do not waste time on dropped exercises.
- Two-tab Solution format per question: a short Solution shows the minimum steps a CBSE examiner wants. An Expert's Solution adds JEE and CUET-style reasoning and other methods.
- Integration and differentiation worked in full: Chapter 5, 6, 7, 8 numericals are solved from substitution to the final answer, with every step labelled.
- Determinants and matrices done as matrix algebra: the notation matches what JEE Main and JEE Advanced expect.
- Probability solutions show the sample space: Chapter 13 problems write the sample space first, before the calculation. This is what CBSE examiners reward.
- Mobile-friendly PDFs: standard files 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)
Here is how the 13 Class 12 Maths chapters fall into 6 CBSE units. Calculus is the biggest, with 5 chapters and 35 of 80 theory marks. The other units carry about 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
NCERT trimmed the 2026-27 Class 12 Maths syllabus to reduce the 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 resources 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 most of the CBSE 2026 Class 12 Maths paper and repeat almost every year. The first column lists the long-answer topics that come up as 3-mark and 5-mark questions. The second column lists the application questions that appear as 1-3 mark numericals, MCQs and 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 almost the same split. Calculus alone gives 8-10 of the 25 JEE Main Maths questions every year. The Expert's Solution tab on each chapter page shows the JEE-style method next to the CBSE board-style short version.
NCERT SOLUTIONS · CLASS 12 MATHS
Class 12 Maths - Exam Weightage
Class 12 Maths gives you about 240 marks combined across CBSE Boards, JEE Main and JEE Advanced. Maths is not in NEET, but it is the single largest scoring block for engineering entrance.
Class 12 Maths Weightage Snapshot (CBSE 2026 Theory Paper)
Calculus rules the 80-mark CBSE Class 12 Maths theory paper. It alone carries 35 marks. Vectors and 3D Geometry comes next at 14, then Algebra at 10, Relations and Functions and Probability tied at 8, and Linear Programming at 5. So revise Calculus first.
| 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 gives 44% of the theory paper from just five chapters. Master the Calculus block plus Vectors-3D and you already have 49 of 80 board marks, before you touch the other three units.
Where to Start with Class 12 Maths NCERT Solutions
Class 12 Maths revision is mostly about Calculus. The six chapters below cover over 60 of 80 board marks:
- Chapter 7, Integrals (part of the 35-mark Calculus block): the largest chapter in the syllabus. Integration methods and the fundamental theorem give the most marks, so revise them first.
- Chapter 5, Continuity and Differentiability: the base for the rest of Calculus. 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 common CBSE 5-mark questions.
- Chapter 11, Three Dimensional Geometry (8 marks within the 14-mark Vectors+3D block): equation-of-plane and shortest-distance problems are common long-answer slots.
- Chapter 9, Differential Equations (Calculus block): forming and solving first-order linear differential equations are board-paper regulars.
- Chapter 13, Probability (8 marks): Bayes' theorem and conditional probability problems repeat year after year.
Together these six chapters give about 62 of 80 board marks. The other Class 12 Maths chapters (Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Application of Integrals, Vector Algebra, Linear Programming) still matter, but revise them once first. Revise the priority six twice.
Class 12 Maths NCERT Solutions: PDF Formats and Languages
Every chapter in the Class 12 Maths NCERT Solutions index comes in three formats plus a Hindi-medium version.
- HD print-ready PDF: sharp equation printing, best for printing as a revision booklet.
- Standard download PDF: smaller file size for phone reading.
- Hindi-medium PDF: chapter-wise Hindi versions using NCERT's own terms (Ganit). Words like अवकलज (derivative), समाकलन (integration), and सदिश (vector) are kept exactly as NCERT writes them.
- Combined all-chapters PDF: one file with every chapter back to back, handy for offline classroom use.
- Handwritten version: the same content in a notebook-style scanned look, handy 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 do not replace concept revision, formula recall, or harder problem sets. Those come from sibling resources that share the same chapter slugs.
- Class 12 Maths Notes: concept revision for each chapter, with step-by-step derivations and worked-example notes. Open the notes whenever a back-exercise question uses a derivation you have not seen in a while.
- Class 12 Maths Formula Sheet: every formula, integration rule, and standard substitution in one short reference for last-day recall.
- Class 12 Maths Exemplar Solutions: solutions for the harder Exemplar problems beyond the back-exercise. Move 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 last week before the boards.
- Class 12 Maths NCERT Book PDF: the official textbook, with worked examples in the same notation as the solutions on this page.
- Class 12 Maths Exemplar Book PDF: the NCERT Exemplar Problems book for extra practice.
What's New in the 2026-27 Class 12 Maths NCERT
The 2026-27 NCERT Class 12 Maths print keeps the syllabus cuts made in 2024-25. A few changes affect what you should revise from this Class 12 Maths NCERT Solutions set:
- Relations and Functions (Ch 1): the binary operations section was cut. Problems on associative and commutative tables are no longer in the syllabus.
- Inverse Trigonometric Functions (Ch 2): kept in full. The principal value branch tables stay as a 3-mark question slot.
- Matrices and Determinants (Ch 3, Ch 4): the long determinant proofs from older editions were cut. The matrix-inverse method for solving linear equations stays.
- Calculus block (Ch 5-9): mostly the same, with small cuts in the application parts of Chapter 6 and Chapter 8.
- Probability (Ch 13): the variance of a random variable was made simpler. The mean of a random variable stays as the usual 3-mark slot.
Each chapter's Class 12 Maths NCERT Solutions file has an inline "Rationalised in 2026-27" callout wherever a question was added, changed, or removed from the older edition.
How to Use the Class 12 Maths NCERT Solutions Page Most Effectively
For Class 12 Maths, a steady routine beats last-minute cramming. Most CBSE Maths toppers follow the three-block plan below.
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 solutions assume you already know the concepts.
- 2Try each question on your own. Write the working in a notebook before you open the answer. Just reading answers does not build exam speed.
- 3Compare your working to the solution. Mark every step where your method was different. 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. It mixes methods and closely matches the 5-mark CBSE board-paper format.
- 1 month before the boards: solve the back-exercise chapter by chapter in NCERT order. Give extra time to the 5-chapter Calculus block. Keep the Notes open whenever a definition slips.
- 2 weeks before the boards: move to the Expert's Solution tab on every question. Mark every problem you could not solve in under 7 minutes. You re-do those in the final week.
- 1 week before the boards: re-do only the marked problems. Then finish 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 changing sign in the LIATE formula. Write the formula out in full before you substitute.
- Mixing up maxima and minima in the second-derivative test: Chapter 6 students flip the sign rule. Maximum is where the second derivative is negative. Minimum is where it is positive.
- Forgetting the +c on indefinite integrals: CBSE cuts a half-mark for each missing constant of integration. Carry it through every step.
- Multiplying matrices in the wrong order: matrix multiplication does not commute. A times B is usually not B times A. Chapter 3 problems test this often.
- Treating Bayes' theorem as one formula instead of a conditional setup: Chapter 13 students often jump to the formula without writing the prior and likelihood. Show the sample space first.
- Direction cosines vs direction ratios in 3D Geometry: Chapter 11 problems test this difference. Direction cosines are the cosines of angles with the axes. Direction ratios are any scalar multiple of those. Mixing them up costs marks.
Student Feedback: 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 about 24% of students, even though it carries 5 marks). Toppers said this is an easy chapter to win back, because the graphical-method problems become routine once you practise them.
- Toppers said that using 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 from faster recall of integration methods.
- The average Class 12 Maths student spent 58 hours across the 13 chapters to finish the NCERT back-exercise once. Chapters 5, 6, 7, 11 took 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 follows the current 2026-27 syllabus. Where NCERT cut content from the older edition (deleted exercises, removed worked examples), the solutions carry an inline callout. This flags the change so you do not 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 solve every back-exercise question fully. The Notes shrink each chapter's concepts for revision. The Formula Sheet keeps only 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. It states the sign rules clearly, adds checks where useful, and sketches other methods. Class 12 Maths is the base of the JEE Main Maths section (around 30 marks) and the JEE Advanced Maths paper (around 60 marks across both papers). The NCERT Solutions are the best starting point for both.
Ques. Are Class 12 Maths NCERT Solutions available in Hindi medium?
Ans. Yes. Every chapter has a Hindi-medium download next to the English version. The Hindi solutions use NCERT's own terms (Ganit Bhag 1 and Bhag 2). So Hindi-medium students preparing for the CBSE boards or the Hindi-medium JEE paper see the same terms they have studied.
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 assume you already know the concepts. They show you how to apply them, not how to derive them. For the Calculus block, read the Notes (or the NCERT textbook) first.
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 make 100 marks in all. Class 12 Maths is also the base for the JEE Main and JEE Advanced Maths sections and the CUET-UG Maths paper.
Ques. Which is the most-scoring chapter in Class 12 Maths?
Ans. Chapter 7 Integrals gives the most marks, closely followed 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 pay off well. Their problems follow set patterns, so marks come fast with practice.
Ques. How should I structure my Class 12 Maths preparation?
Ans. Build chapter by chapter, and do the Calculus block (Chapters 5-9) first. Use the Notes for concepts, the NCERT Solutions for the back-exercise, the Exemplar for harder practice, and the Formula Sheet for the last week. The Study Plan section above shows the 1-month, 2-week, and 1-week countdown most toppers follow.
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