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NCERT Solutions for Class 12 Maths is a comprehensive study guide designed to help students learn and understand mathematical concepts in an effective manner. These solutions cover all the topics included in the Class 12 Mathematics curriculum prescribed by the National Council of Educational Research and Training (NCERT). 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, the NCERT Solutions for Class 12 Maths are an invaluable resource that can help students excel in their studies and score high marks in their exams.
NCERT Solutions for all chapters covered under Class 12 Mathematics syllabus have been listed in this article. Along with NCERT Solutions PDF, Important questions, Multiple Choice Questions, Important topics, concept notes and handwritten notes have been provided which the students can use for their strategic preparation. Chapterwise NCERT Solutions along with the respective exercise solutions are also provided in a PDF format.
NCERT Solutions for Class 12 Maths All Chapters
The chapter-wise NCERT Solutions for Class 12 Maths are given below:
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 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 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 value derived out of a square matrix. Important topics covered in 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 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
| NCERT Solutions for Class 12 Maths – 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 Integrals Chapter are:
- Double Integral
- Continuous Integration
- Properties of Definite Integral
- Line Integral
- Integrals of Particular Function
Total Weightage: 6 to 18 marks
| NCERT Solutions 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 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 2022-23
The weightage distribution for CBSE Class 12 Maths Term 1 syllabus is 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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