Senior Content Specialist | Updated On - Jan 25, 2024
NCERT Solutions for Class 12 Maths helps students learn and understand Class 12 Maths concepts effectively. These solutions cover all the topics included in the Class 12 Mathematics Syllabus 2023-24 prescribed by NCERT. Class 12 Maths NCERT Solutions are efficient for both practice and revision.
- The NCERT Class 12 Maths textbook is divided into two parts – Part 1 covers chapters 1-6, while Part 2 covers chapters 7-13.
- NCERT Solutions for all chapters covered under the Class 12 Mathematics syllabus have been listed in this article.
- The article also provides solutions for miscellaneous exercises offering a higher level of practice.
- Along with the NCERT Solutions PDF, Important questions, MCQs, Important topics, and notes have been provided.
- Chapterwise NCERT Solutions along with the respective exercise solutions are also provided in a PDF format.
- They offer a systematic resource for quick revisions during examinations.
NCERT Solutions for Class 12 Maths – All Chapters
The chapter-wise NCERT Solutions for Class 12 Maths are given below:
These solutions are presented in a simple, easy-to-understand language that enables students to grasp even the most complex concepts with ease. Whether it is calculus, algebra, geometry, or trigonometry, NCERT Solutions for Class 12 Maths 2024 is an invaluable resource that can help students excel in their studies and score high marks in their exams.
Class 12 Maths Chapter 1: Relation and Function
Relation is the subset of the cartesian product whereas function is a type of relation where each input will have one output. The important topics covered in the Relation and Function chapter are:
Total Weightage: 4 to 8 marks
| NCERT Solutions for Class 12 Maths Chapter 1 Relation and Functions Chapter Exercises | |
|---|---|
| Page No. 5 | Exercise- 1.1 |
| Page No. 10 | Exercise- 1.2 |
| Page No. 18 | Exercise- 1.3 |
| Page No. 24 | Exercise- 1.4 |
| Page No. 29 | Miscellaneous Exercises |
Additional Resources for Chapter 1- Relations and Functions:
Class 12 Maths Chapter 2: Inverse Trigonometric Functions
Reciprocal of the normal trigonometric functions is called inverse trigonometric functions. Important topics covered in the Inverse Trigonometric Functions chapter are:
- Sine function
- Cosine Function
- Tangent Function
- Secant Function
- Cotangent Function
- Cosecant Function
- Properties of Inverse Trigonometric Functions
Total Weightage: 4 to 8 marks
| NCERT Solutions for Class 12 Maths Inverse Trigonometric Functions Chapter Exercises | |
|---|---|
| Page No. 41 | Exercise - 2.1 |
| Page No. 47 | Exercise- 2.2 |
| Page No. 51 | Miscellaneous Exercises |
Additional Resources for Chapter 2 - Inverse Trigonometric Functions:
- Inverse Trigonometric Functions - List of Important Formulas
- Inverse Trigonometric Functions Handwritten Notes
Class 12 Maths Chapter 3: Matrices
Matrices are the arrangement of elements in the form of columns and rows. Important topics covered in Matrices chapter are:
- Types of Matrices
- Operations in Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Invertible Matrices
Total Weightage: 5 to 10 marks
| NCERT Solutions for Class 12 Maths – Matrices Chapter Exercises | |
|---|---|
| Page No. 64 | Exercise - 3.1 |
| Page No. 80 | Exercise- 3.2 |
| Page No. 88 | Exercise- 3.3 |
| Page No. 97 | Exercise- 3.4 |
| Page No. 100 | Miscellaneous Exercises |
Additional Resources for Chapter 3 - Matrices: Matrices Handwritten Notes
Class 12 Maths Chapter 4: Determinants
Determinants are the numerical values derived out of a square matrix. Important topics covered in the Determinants chapter are:
Total Weightage: 5 to 10 marks
| NCERT Solutions for Class 12 Maths – Determinants Chapter Exercises | |
|---|---|
| Page No. 108 | Exercise - 4.1 |
| Page No. 119 | Exercise- 4.2 |
| Page No. 88 | Exercise- 4.3 |
| Page No. 97 | Exercise- 4.4 |
| Page No. 122 | Exercise- 4.5 |
| Page No. 126 | Exercise- 4.6 |
| Page No. 141 | Miscellaneous Exercise |
Additional Resources for Chapter 4 - Determinants: Determinants Handwritten Notes
Class 12 Maths Chapter 5: Continuity and Differentiability
Continuity is the function’s characteristic of determining the continuity of the graphical form of the wave of that function. Important topics covered in the Continuity and Differentiability chapter are:
Total Weightage: 8 to 17 marks
| NCERT Solutions for Class 12 Maths – Continuity and Differentiability Chapter Exercises | |
|---|---|
| Page No. 159 | Exercise- 5.1 |
| Page No. 166 | Exercise- 5.2 |
| Page No. 169 | Exercise- 5.3 |
| Page No. 174 | Exercise- 5.4 |
| Page No. 178 | Exercise- 5.5 |
| Page No. 181 | Exercise- 5.6 |
| Page No. 183 | Exercise- 5.7 |
| Page No. 186 | Exercise- 5.8 |
| Page No. 191 | Miscellaneous Exercises |
Additional Resources for Chapter 5 - Continuity and Differentiability: Continuity and Differentiability Handwritten Notes
Class 12 Maths Chapter 6: Application of Derivatives
Derivatives are used to determine many results. It is used to find the rate of change of a quantity, temperature variation and approximation of any quantity. Important topics covered in Application of Derivatives chapter are:
Total Weightage: 8 to 17 marks
| Class 12 Maths NCERT Solutions – Application of Derivatives Chapter Exercises | |
|---|---|
| Page No. 197 | Exercise 6.1 |
| Page No. 205 | Exercise 6.2 |
| Page No. 211 | Exercise 6.3 |
| Page No. 216 | Exercise 6.4 |
| Page No. 231 | Exercise 6.5 |
| Page No. 241 | Miscellaneous Exercise |
Additional Resources for Chapter 6 - Application of Derivatives: Application of Derivatives Handwritten Notes
Class 12 Maths Chapter 7: Integrals
Integrals is the inverse of finding derivatives of a function. The process of finding integrals is called integration. Important topics covered in the Integrals Chapter are:
- Double Integral
- Continuous Integration
- Properties of Definite Integral
- Line Integral
- Integrals of Particular Function
Total Weightage: 6 to 18 marks
| NCERT Answers for Class 12 Maths – Integrals Chapter Exercises | |
|---|---|
| Page No. 299 | Exercise- 7.1 |
| Page No. 304 | Exercise- 7.2 |
| Page No. 307 | Exercise- 7.3 |
| Page No. 315 | Exercise- 7.4 |
| Page No. 322 | Exercise- 7.5 |
| Page No. 327 | Exercise- 7.6 |
| Page No. 330 | Exercise- 7.7 |
| Page No. 334 | Exercise- 7.8 |
| Page No. 338 | Exercise- 7.9 |
| Page No. 338 | Exercise- 7.10 |
| Page No. 347 | Exercise- 7.11 |
| Page No. 352 | Miscellaneous Exercises |
Additional Resources for Chapter 7 - Integrals: Integrals Handwritten Notes
Class 12 Maths Chapter 8: Application of Integrals
The major application of integrals lies in the field of two-dimensional area calculations. Important topics covered in the Application of Integrals Chapter are:
Total Weightage: 6 to 18 marks
| NCERT Solutions for Class 12 Maths – Application of Integrals Chapter Exercises | |
|---|---|
| Page No. 365 | Exercise - 8.1 |
| Page No. 371 | Exercise- 8.2 |
| Page No. 373 | Miscellaneous Exercises |
Additional Resources for Chapter 8 - Application of Integrals: Application of Integrals Handwritten Notes
Class 12 Maths Chapter 9: Differential Equation
Relation between two or more functions and their derivatives is established using a differential equation. Important topics covered in Differential Equation Chapter are:
- First order linear differential equations
- Partial differential equations
- Ordinary differential equations
- Homogeneous differential equations
Total Weightage: 6 to 18 marks
| NCERT Solutions for Class 12 Maths – Differential Equation Chapter Exercises | |
|---|---|
| Page No. 382 | Exercise - 9.1 |
| Page No. 385 | Exercise- 9.2 |
| Page No. 391 | Exercise- 9.3 |
| Page No. 395 | Exercise- 9.4 |
| Page No. 406 | Exercise- 9.5 |
| Page No. 413 | Exercise- 9.6 |
| Page No. 419 | Miscellaneous Exercises |
Additional Resources for Chapter 9 - Differential Equation: Differential Equation Handwritten Notes
Class 12 Maths Chapter 10: Vector Equation
A vector equation has a linear combination of vectors, constants and unknown variables. Important topics covered in Vector Equation Chapter are:
- Types of Vectors
- Addition of Vectors
- Negative of a Vector
- Triangle law of Vector addition
- Magnitude of a vector
Total Weightage: 7 to 14 marks
| NCERT Solutions for Class 12 Maths – Vector Equation Chapter Exercises | |
|---|---|
| Page No. 428 | Exercise - 10.1 |
| Page No. 440 | Exercise- 10.2 |
| Page No. 447 | Exercise- 10.3 |
| Page No. 454 | Exercise- 10.4 |
| Page No. 458 | Miscellaneous Exercises |
Additional Resources for Chapter 10 - Vector Equation: Vector Equation Handwritten Notes
Class 12 Maths Chapter 11: Three-Dimensional Geometry
Three-dimensional geometry involves the study of geometry formed along the x,y and z axis. Important topics covered in Three-dimensional geometry Chapter are:
Total Weightage: 7 to 14 marks
| NCERT Solutions for Class 12 Maths – Three-dimensional geometry Chapter Exercises | |
|---|---|
| Page No. 467 | Exercise - 11.1 |
| Page No. 477 | Exercise- 11.2 |
| Page No. 493 | Exercise- 11.3 |
| Page No. 497 | Miscellaneous Exercises |
Additional Resources for Chapter 11 - Three-dimensional geometry: Three-dimensional geometry Handwritten Notes
Class 12 Maths Chapter 12: Linear Programming
Linear programming is a mathematical modelling to produce the optimal outcome with variable constraints. Important topics covered in Linear Programming Chapter are:
Total Weightage: 5 marks
| NCERT Solutions for Class 12 Maths – Linear Programming Chapter Exercises | |
|---|---|
| Page No. 513 | Exercise - 12.1 |
| Page No. 519 | Exercise- 12.2 |
| Page No. 607 | Miscellaneous Exercises |
Additional Resources for Chapter 12 - Linear Programming: Linear Programming Handwritten Notes
Class 12 Maths Chapter 13: Probability
Probability is the numerical description of the likeliness of an event to happen or not. Important topics covered in Probability Chapter are:
Total Weightage: 8 marks
| NCERT Solutions for Class 12 Maths – Probability Chapter Exercises | |
|---|---|
| Page No. 538 | Exercise - 13.1 |
| Page No. 546 | Exercise- 13.2 |
| Page No. 555 | Exercise- 13.3 |
| Page No. 569 | Exercise- 13.4 |
| Page No. 576 | Exercise- 13.5 |
| Page No. 582 | Miscellaneous Exercises |
Additional Resources for Chapter 13 - Probability: Probability Handwritten Notes
Class 12 Maths Syllabus 2023-24
The weightage distribution for CBSE Class 12 Maths 2024 exam is as tabulated below.
| Unit No. | Units | Marks |
|---|---|---|
| I | Relations and Functions | 08 |
| II | Algebra | 10 |
| III | Calculus | 17 |
| IV | Vectors 3-Dimensional Geometry | 05 |
| V | Linear Programming | 40 |
| VI | Probability | 10 |
| Total | 80 | |
| Internal Assessment | 20 | |
In conclusion, NCERT solutions for class 12 Maths are an invaluable resource for students preparing for their board exams or competitive exams. These solutions provide comprehensive coverage of all topics in the NCERT textbook and are designed to help students develop a deeper understanding of mathematical concepts. By providing step-by-step solutions to all exercises and examples, these solutions enable students to practice and hone their problem-solving skills.
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