Are you searching for Latest accurate and detailed Class 12 Maths NCERT Solutions to ace your board exams? Look no further! Our comprehensive, step-by-step NCERT solutions cover all chapters, ensuring a strong foundation in calculus, algebra, vectors, and more.
Whether you’re preparing for CBSE board exams, JEE, or other competitive tests, these solutions will help you understand concepts, solve problems efficiently, and score high marks.
Chapter-wise Class 12 Maths NCERT Solutions 2025-2026:
| S.no | Chapter Name | Solutions |
|---|---|---|
| 1 | Relations and Functions | Ex_1.1 Ex _1.2 Ex_Misc |
| 2 | Inverse trigonometric functions | Ex_2.1 Ex_2.2 Ex_Misc |
| 3 | Matrices | Ex_3.1 Ex_3.2 Ex_3.3 Ex_3.4 Ex_Misc |
| 4 | Determinants | Ex_4.1 Ex_4.2 Ex_4.3 Ex_4.4 Ex_4.5 Ex_Misc |
| 5 | Continuity and Differentiability | Ex_5.1 Ex_5.2 Ex_5.3 Ex_5.4 Ex_5.5 Ex_5.6 Ex_5.7 Ex_Misc |
| 6 | Applications of Derivatives | Ex_6.1 Ex_6.2 Ex_6.3 Ex_Misc |
| 7 | Integrals | Ex_7.1 Ex_7.2 Ex_7.3 Ex_7.4 Ex_7.5 Ex_7.6 Ex_7.7 Ex_7.8 Ex_7.9 Ex_7.10 Ex_Misc |
| 8 | Applications of Integrals | Ex_8.1 Ex_Misc |
| 9 | Differential Equations | Ex_9.1 Ex_9.2 Ex_9.3 Ex_9.4 Ex_9.5 Ex_Misc |
| 10 | Vector Algebra | Ex_10.1 Ex_10.2 Ex_10.3 Ex_10.4 Ex_Misc |
| 11 | Three Dimensional Geometry | Ex_11.1 Ex_11.2 Ex_Misc |
| 12 | Linear Programming | Ex_12.1 |
| 13 | Probability | Ex_13.1 Ex_13.2 Ex_13.3 Ex_Misc |
The CBSE Class 12 Mathematics exam pattern for the current academic session (2024-2025 onwards) consists of a single annual board examination for a total of 100 marks. This is split into an 80-mark Theory Paper and a 20-mark Internal Assessment.
1. Class 12 Maths Exam Marks Distribution 💯
The total marks are divided as follows:
| Component | Marks | Duration |
| Theory Paper | 80 | 3 Hours |
| Internal Assessment | 20 | Throughout the Year |
| Grand Total | 100 |
Internal Assessment Breakdown (20 Marks)
The 20 marks for Internal Assessment are generally distributed among:
- Periodic Tests/Best Two out of Three Tests: 10 Marks
- Mathematics Activities/Practicals: 10 Marks
2. Unit-wise Weightage (80 Marks Theory) 📊
The official unit-wise weightage for the 80-mark theory paper is crucial for preparation planning. Calculus carries the highest weightage.
| Unit No. | Unit Name | Weightage (Marks) |
| I | Relations and Functions | 08 |
| II | Algebra (Matrices & Determinants) | 10 |
| III | Calculus (Continuity, Differentiation, Integration, Diff. Eq.) | 35 |
| IV | Vectors and Three-Dimensional Geometry | 14 |
| V | Linear Programming | 05 |
| VI | Probability | 08 |
| Total Theory Marks | 80 |
3. Question Paper Design & Competency Focus (80 Marks) 📝
A significant change in the latest pattern is the increased focus on Competency-Based Questions (CBQ), which test application, analysis, and critical thinking rather than rote memorization.
| Type of Question | Weightage Percentage | Focus |
| Competency Focused Questions (MCQs, Case-Based/Source-Based Questions) | ~50% | Application, Analysis, Evaluation |
| Select Response Type Questions (MCQs/Objective) | ~20% | Recall and Understanding |
| Constructed Response Questions (Short/Long Answer) | ~30% | Understanding, Application, Procedure |
Typical Section Breakdown (Based on Sample Papers)
The 80-mark paper usually has 5 Sections (A, B, C, D, E) with a total of 38 questions:
| Section | Question Type | Marks per Q | Total Qs (Approx.) | Total Marks |
| A | MCQs and Assertion-Reason | 1 | 20 | 20 |
| B | Very Short Answer (VSA) | 2 | 5 | 10 |
| C | Short Answer (SA) | 3 | 6 | 18 |
| D | Long Answer (LA) | 5 | 4 | 20 |
| E | Case-Based/Source-Based Questions | 4 | 3 (12 marks total) | 12 |
Note: Internal choices are provided in a limited number of questions across Sections C, D, and E.
The CBSE Class 12 Mathematics syllabus for the academic year 2024-2025 (and typically for 2025-2026 as well) is divided into six major units. The examination structure is a single annual board exam for a total of 100 marks, split into an 80-mark Theory Paper and a 20-mark Internal Assessment.
1. Unit-wise Weightage (80 Marks Theory Paper) 📊
Calculus is the most crucial unit, contributing nearly half of the total theory marks.
Unit No. Unit Name Chapters Included Weightage (Marks) I Relations and Functions Relations and Functions, Inverse Trigonometric Functions 08 II Algebra Matrices, Determinants 10 III Calculus Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of the Integrals, Differential Equations 35 IV Vectors and Three-Dimensional Geometry Vectors, Three-Dimensional Geometry 14 V Linear Programming Linear Programming 05 VI Probability Probability 08 Total Theory Marks 80
2. Detailed Syllabus and Key Topics (Included) 📚
Unit I: Relations and Functions (8 Marks)
- Relations and Functions: Types of relations (reflexive, symmetric, transitive, and equivalence), One-to-one and onto functions.
- Inverse Trigonometric Functions: Definition, range, domain, principal value branch, and graphs.
Unit II: Algebra (10 Marks)
- Matrices: Types, operations (addition, multiplication, scalar multiplication), transpose, symmetric, and skew-symmetric matrices. Invertible matrices and the uniqueness of the inverse.
- Determinants: Determinant of a square matrix (up to $3 \times 3$), minors, co-factors, application in finding the area of a triangle, Adjoint and Inverse of a matrix, solving a system of linear equations (unique solution only) using the inverse of a matrix.
Unit III: Calculus (35 Marks)
- Continuity and Differentiability: Continuity, differentiability, Chain Rule, derivatives of inverse trigonometric functions, implicit functions, exponential/logarithmic functions, Logarithmic differentiation, parametric forms, and Second-order derivatives.
- Applications of Derivatives: Rate of change of quantities, increasing/decreasing functions, Maxima and Minima (using first and second derivative tests).
- Integrals: Integration by substitution, partial fractions, and by parts. Evaluation of definite integrals, Fundamental Theorem of Calculus (without proof), and basic properties of definite integrals.
- Applications of the Integrals: Applications in finding the area under simple curves (lines, circles, parabolas, ellipses in standard form only).
- Differential Equations: Definition, order, and degree. Solution by separation of variables, solutions of homogeneous differential equations of first order and first degree, and solutions of linear differential equations of the type $\frac{dy}{dx} + Py = Q$ or $\frac{dx}{dy} + Px = Q$.
Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)
- Vectors: Types, addition, scalar multiplication, position vector, scalar (dot) product, and vector (cross) product.
- Three-Dimensional Geometry: Direction cosines and direction ratios of a line, Cartesian and vector equations of a line, Shortest Distance between two skew lines, and angle between two lines.
Unit V: Linear Programming (5 Marks)
- Linear Programming: Terminology (constraints, objective function, optimization), mathematical formulation of L.P. Problems, and graphical method of solution for problems in two variables (feasible/infeasible regions, optimal feasible solutions).
Unit VI: Probability (8 Marks)
- Probability: Conditional probability, multiplication theorem on probability, independent events, Total Probability, and Bayes’ Theorem.
The most essential book for CBSE Class 12 Mathematics is the NCERT Textbook (Parts I and II). These books form the foundation of your preparation, and every question in the board exam is strictly based on the syllabus and concepts covered in them.
For practice, in-depth understanding, and aiming for top scores, supplementary reference books are highly recommended.
1. Essential Core Books for Class 12 Mathematics📘
| Book | Publisher/Author | Primary Focus | Use for |
| NCERT Mathematics Textbook (Part I & II) | NCERT | Absolute must-read; foundation of the CBSE syllabus. | Conceptual clarity, solving all exercises, and board exam mandatory coverage. |
| NCERT Exemplar Problems | NCERT | Contains higher-order thinking skills (HOTS) questions and MCQs. | Advanced practice, strengthening concepts, and preparing for competitive exam basics. |
2. Top Reference Books for Practice and Mastery 💡
These books offer a vast collection of problems, detailed step-by-step solutions, and alternative methods for problem-solving. Choose one from this category.
- R.D. Sharma – Mathematics for Class XII (Volumes 1 & 2):
- Best for: Students needing a massive number of practice questions for every concept and aiming for competitive exams like JEE Main/Advanced (though dedicated JEE books are better for competitive focus).
- Benefit: Provides exhaustive, detailed explanations and numerous solved examples.
- R.S. Aggarwal – Senior Secondary School Mathematics for Class 12:
- Best for: Students aiming specifically for high scores in the CBSE Board Exam.
- Benefit: Contains a good variety of questions that align closely with the board exam pattern, without the overwhelming volume of R.D. Sharma.
3. Exam-Oriented Practice and Revision Books 🎯
Once your concepts are clear using NCERT and a core reference book, these materials are essential for practicing the latest exam pattern.
| Type of Book | Popular Choices | Key Benefit |
| Question Banks | Arihant All in One, Xam Idea, Oswaal CBSE Question Bank, Together with | Chapter-wise segregation of questions, often includes previous year’s questions, Competency-Based Questions (CBQs), and mind maps. Excellent for structured practice. |
| Previous Year Question (PYQ) Books | Arihant/Oswaal/MTG Chapterwise Topicwise Solved Papers | Gives a clear idea of the type and difficulty of questions asked in past board exams and their marking schemes. Crucial for final preparation. |
| Sample Papers | Arihant i-Succeed 15 Sample Question Papers, Oswaal Sample Papers, Together with Sample Papers | Helps practice time management and simulates the actual 3-hour exam environment with the latest competency-based paper pattern. |
🧠 Frequently Asked Questions (FAQs)
Q1. Are NCERT Maths solutions enough for CBSE Class 12 board exams?
Yes, NCERT textbook questions cover almost 90–95% of board questions. Practicing from NCERT thoroughly is sufficient to score high.
Q2. Where can I get free Class 12 Maths NCERT solutions PDF?
You can download them for free from ToppersGuru.com
Q3. Which is the toughest chapter in Class 12 Maths?
Students often find “Integrals” and “3D Geometry” challenging due to complex calculations.
Q4. Can I score 90+ in Maths with NCERT?
Absolutely! NCERT provides a strong base. Practice additional problems and sample papers for higher marks.