NCERT Solutions for Class 12 Mathematics

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Jasmine Grover

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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:

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:


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:

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:

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:

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:

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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CBSE CLASS XII Related Questions

1.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix}  -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that (i)(A+B)'=A'+B'  (ii)(A-B)'=A'-B'

      2.
      Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 &  3\\ 2 & 7\end{bmatrix}\)

          3.
          Find \(\frac {dy}{dx}\)\(2x+3y=sin\ x\)

              4.

              Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

                  5.
                  For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?

                      6.

                      Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta  &-sin\alpha \\   -sin\beta&cos\beta  &0 \\   sin\alpha cos\beta&sin\alpha\sin\beta  &cos\alpha  \end{vmatrix}\)

                          CBSE CLASS XII Previous Year Papers

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