The NCERT Solutions of Class 12 Maths in Hindi and English Medium are updated for Session 2023-2024 to provide detailed explanations of all chapters.

**Class 12 Chapter Wise Maths NCERT Solutions**

Chapter 1: Relations and Functions

Chapter 2: Inverse Trigonometric Functions

Chapter 3: Matrices

Chapter 4: Determinants

Chapter 5: Continuity and Differentiability

Chapter 6: Application of Derivatives

Chapter 7: Integrals

Chapter 8: Application of Integrals

Chapter 9: Differential Equations

Chapter 10: Vector Algebra

Chapter 11: Three Dimensional Geometry

Chapter 12: Linear Programming

Chapter 13: Probability

It also includes examples that will help students better understand the concepts. The Tiwari Academy provides NCERT Solutions of Class 12 Maths which can be of great help to students.

## NCERT Solutions for Class 12 Maths in Hindi and English Medium

Class: 12 | Mathematics |

Content: | NCERT and Extra Questions |

Content Type: | Text, PDF and Video Format |

Mode of Study: | Online and Offline |

Session: | CBSE 2023-2024 |

Medium: | Hindi and English Medium |

These solutions are prepared by expert mathematicians and can help students understand the concepts better and score good marks in the exams. NCERT Solutions for Class 12 Maths in English and Hindi Medium updated for CBSE session. It provides a detailed explanation to promote a better conceptual understanding in students for all the topics included in CBSE Class 12 Maths Syllabus.

Get the Solution for Class 12 Maths UP Board for the preparation of undergraduate level engineering entrance exams like JEE Main, VITEEE, BITSAT, MHTCET etc. NCERT Solutions Class 12, designed by our Expert Maths Teacher to facilitate smooth and clear understanding of concepts and logic. These solution covers all the formulae and theorems with step by step method so that student can easily understand. You can get all chapter wise all exercise solutions for the Class 12 Maths NCERT Books. Students who are practising with these class 12th Maths solution for the academic year 2023-24 can pass the 12th class board exam.

You can download NCERT Class 12 Maths Solutions App for all exercises by just click these links here. Class 12th Maths Solution is beneficial for the class student 12 as it not only help you to score maximum marks in your CBSE, UP Board, MP Board as well as other boards examinations but also prepares you for undergraduate competition exams. You can also get all solutions online, and you can also download of Class 12 Maths Chapter Wise Solutions in PDF. NCERT Exemplar Class 12 Maths Solutions are also available here which help you to get an overall idea of board exam pattern.

### NCERT Class 12 Maths all Chapters

Class 12 Maths provided here covers all chapters s on each of the class 12 Maths syllabus topics along with their sub-topics. With these all exercise wise solutions, the student can able to get a deeper understanding of the concepts and develop problem-solving abilities. NCERT Class 12 Maths Chapters includes there are 13 chapters in total like Relations and Functions, Inverse Trigonometric Functions, Matrices, Continuity and Differentiability, Applications of Derivatives, Integrals, Application of Integrals, Vector Algebra, Probability etc.

#### NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions

Class 12 Maths, Relations and Functions is the first chapter of the Class 12 Maths NCERT Book. There are 3 exercises in this NCERT Solutions for class 12 Maths Chapter 1.

Class 12 Maths Exercise 1.1

Class 12 Maths Exercise 1.2

Class 12 Maths Miscellaneous 1

Class 12 Maths Exercise 1.1 in Hindi

Class 12 Maths Exercise 1.2 in Hindi

Class 12 Maths Miscellaneous 1 in Hindi

These exercises cover types of relations and functions, the composition of functions, domain, co-domain, and composite functions, the inverse of a function and invertible function etc. NCERT Solutions for class 12 Maths Chapter 1 Relations and Functions is an important chapter which provides detail knowledge of relation and functions. All 12th class Maths book solution given here are well solved each problem sums by the experienced Maths teacher. The solution of class 12 Maths chapter 1 are in dual language – Hindi and English.

#### NCERT Solutions for Class 12 Maths Chapter 2- Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions covers various topics such as concepts of inverse trigonometric functions, inverse trigonometric functions properties, and miscellaneous examples.

Class 12 Maths Exercise 2.1

Class 12 Maths Exercise 2.2

Class 12 Maths Miscellaneous 2

Class 12 Maths Exercise 2.1 in Hindi

Class 12 Maths Exercise 2.2 in Hindi

Class 12 Maths Miscellaneous 2 in Hindi

There are two exercises which explain ranges of trigonometric functions and observe the behaviour in the graphical representation. Study Material for Class 12 Maths Chapter 2 for all exercises are prepared by Mathematics teacher and solutions are well-structured so that it would be easier to learn and understand.

#### NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

NCERT Solutions for Class 12 Maths Chapter 3 Matrices you can get the definition of Matrices, various types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of matrices by a scalar.

Class 12 Maths Exercise 3.1

Class 12 Maths Exercise 3.2

Class 12 Maths Exercise 3.3

Class 12 Maths Exercise 3.4

Class 12 Maths Miscellaneous 3

Class 12 Maths Exercise 3.1 in Hindi

Class 12 Maths Exercise 3.2 in Hindi

Class 12 Maths Exercise 3.3 in Hindi

Class 12 Maths Exercise 3.4 in Hindi

Class 12 Maths Miscellaneous 3 in Hindi

You will learn here about the properties of matrices addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of matrices, properties of the transpose of the matrices, symmetric and elementary operation or transformation of a matrix, skew symmetric matrices, inverse of a matrix with by elementary operations, and at last, it covers miscellaneous examples. Matrices exercise answers of 12th Maths are given here in Hindi and English medium text and videos format.

#### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants covers all topic of determinants. You can learn and study here about the definition and meaning of determinants.

Class 12 Maths Exercise 4.1

Class 12 Maths Exercise 4.2

Class 12 Maths Exercise 4.3

Class 12 Maths Exercise 4.4

Class 12 Maths Exercise 4.5

Class 12 Maths Miscellaneous 4

Class 12 Maths Exercise 4.1 in Hindi

Class 12 Maths Exercise 4.2 in Hindi

Class 12 Maths Exercise 4.3 in Hindi

Class 12 Maths Exercise 4.4 in Hindi

Class 12 Maths Exercise 4.5 in Hindi

Class 12 Maths Miscellaneous 4 in Hindi

There are six exercises in this chapter which explains remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors, adjoint, and cofactors of determinants, systems of linear equation in two as well as three variables using the inverse of matrices.

#### Class 12 Maths Chapter 5 – Continuity and Differentiability

Class 12 Maths Chapter 5 Continuity and Differentiability textbook has eight exercises which are based on 12th Class Maths Book Solution, in the 1st exercise you just learn about the definition of continuity.

Class 12 Maths Exercise 5.1

Class 12 Maths Exercise 5.2

Class 12 Maths Exercise 5.3

Class 12 Maths Exercise 5.4

Class 12 Maths Exercise 5.5

Class 12 Maths Exercise 5.6

Class 12 Maths Exercise 5.7

Class 12 Maths Miscellaneous 5

Class 12 Maths Exercise 5.1 in Hindi

Class 12 Maths Exercise 5.2 in Hindi

Class 12 Maths Exercise 5.3 in Hindi

Class 12 Maths Exercise 5.4 in Hindi

Class 12 Maths Exercise 5.5 in Hindi

Class 12 Maths Exercise 5.6 in Hindi

Class 12 Maths Exercise 5.7 in Hindi

Class 12 Maths Miscellaneous 5 in Hindi

Then you proceed with continuity, algebra of continuous function, definition and meaning of differentiability, derivative of implicit functions, derivatives of composite functions, derivative of inverse trigonometric functions, logarithmic differentiation, Concept of exponential and logarithmic functions, derivatives of functions in parametric forms, exponential and logarithmic functions, second order derivatives, mean value theorem with different examples for practice in board preparation.

#### NCERT Solutions for Class 12 Maths Chapter 6 – Applications of Derivatives

NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives has five exercises which cover the definition of derivatives, tangents and normal, and rate of change of quantities, increasing and decreasing functions.

Class 12 Maths Exercise 6.1

Class 12 Maths Exercise 6.2

Class 12 Maths Exercise 6.3

Class 12 Maths Miscellaneous 6

Class 12 Maths Exercise 6.1 in Hindi

Class 12 Maths Exercise 6.2 in Hindi

Class 12 Maths Exercise 6.3 in Hindi

Class 12 Maths Miscellaneous 6 in Hindi

It describes the use of derivatives in approximation maxima and minima, approximations, first derivative test, function in a closed interval and miscellaneous examples. Here in this NCERT Solutions for 12th Mathematics Chapter 6 you can get a detailed knowledge of Applications of Derivatives. Student can learn Chapter 6 in Hindi and English Medium as per their requirement.

#### NCERT Solutions for Class 12 Maths Chapter 7 – Integrals

Class 12 Maths Chapter 7 Integration has twelve exercises which cover the definition of integration, definite and indefinite integrations and limit of sums based questions.

Class 12 Maths Exercise 7.1

Class 12 Maths Exercise 7.2

Class 12 Maths Exercise 7.3

Class 12 Maths Exercise 7.4

Class 12 Maths Exercise 7.5

Class 12 Maths Exercise 7.6

Class 12 Maths Exercise 7.7

Class 12 Maths Exercise 7.8

Class 12 Maths Exercise 7.9

Class 12 Maths Exercise 7.10

Class 12 Maths Miscellaneous 7

Class 12 Maths Exercise 7.1 in Hindi

Class 12 Maths Exercise 7.2 in Hindi

Class 12 Maths Exercise 7.3 in Hindi

Class 12 Maths Exercise 7.4 in Hindi

Class 12 Maths Exercise 7.5 in Hindi

Class 12 Maths Exercise 7.6 in Hindi

Class 12 Maths Exercise 7.7 in Hindi

Class 12 Maths Exercise 7.8 in Hindi

Class 12 Maths Exercise 7.9 in Hindi

Class 12 Maths Exercise 7.10 in Hindi

Class 12 Maths Miscellaneous 7 in Hindi

#### NCERT Solutions for Class 12 Maths Chapter 8 – Applications of Integrals

In NCERT Solutions for Class 12 Maths Chapter 8 Applications of Integrals, students can get an overall knowledge about the Integrals and specific application of integrals.

Class 12 Maths Exercise 8.1

Class 12 Maths Miscellaneous 8

Class 12 Maths Exercise 8.1 in Hindi

Class 12 Maths Miscellaneous 8 in Hindi

It covers the definition of Integrals, especially lines, circles/ parabolas/ellipses, area under simple curves, area between two curves and at last miscellaneous examples. There are two exercises in NCERT Solutions for Class 12 Maths Chapter 8. We have prepared the solutions based on 12th Class Maths NCERT Book part 2. Get Applications of Integrals Class 12 Maths Solutions in Hindi medium.

#### NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations

Students can find concentrate on the definition of Differential Equations in the NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations.

Class 12 Maths Exercise 9.1

Class 12 Maths Exercise 9.2

Class 12 Maths Exercise 9.3

Class 12 Maths Exercise 9.4

Class 12 Maths Exercise 9.5

Class 12 Maths Miscellaneous 9

Class 12 Maths Exercise 9.1 in Hindi

Class 12 Maths Exercise 9.2 in Hindi

Class 12 Maths Exercise 9.3 in Hindi

Class 12 Maths Exercise 9.4 in Hindi

Class 12 Maths Exercise 9.5 in Hindi

Class 12 Maths Miscellaneous 9 in Hindi

It clears basic concepts related to differential equations and many more with step by step solutions so that students can easily understand. It covers all the solutions based on 12th Class Maths Book Solution including the degree of a differential equation, order of a differential equation, general and particular solutions of a differential equation, homogeneous differential equations, linear differential equations, procedure involved formation of a differential equation etc. Student can use Differential Equations of 12th standard in Hindi and English medium.

#### NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra, you can understand the introduction of vector algebra. And you can know how to find position vector, some basic concepts related to vector algebra etc.

Class 12 Maths Exercise 10.1

Class 12 Maths Exercise 10.2

Class 12 Maths Exercise 10.3

Class 12 Maths Exercise 10.4

Class 12 Maths Miscellaneous 10

Class 12 Maths Exercise 10.1 in Hindi

Class 12 Maths Exercise 10.2 in Hindi

Class 12 Maths Exercise 10.3 in Hindi

Class 12 Maths Exercise 10.4 in Hindi

Class 12 Maths Miscellaneous 10 in Hindi

In this chapter, you can also learn about algebraic as well as geometric properties. And multiplication of a vector by a scalar, r, vector joining two points, components of a vector, section formula, product of two vector etc. This chapter 10 has four exercises excluding miscellaneous. All solutions are based on 12th Class Maths Book Solution. Get the complete solutions with step by step description in Hindi and English medium.

#### NCERT Solutions for Class 12 Maths Chapter 11 – Three Dimensional Geometry

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, you can get know about Three Dimensional Geometry. The student can constitute topics related to three dimensional geometry, direction cosines and direction ratios.

Class 12 Maths Exercise 11.1

Class 12 Maths Exercise 11.2

Class 12 Maths Miscellaneous 11

Class 12 Maths Exercise 11.1 in Hindi

Class 12 Maths Exercise 11.2 in Hindi

Class 12 Maths Miscellaneous 11 in Hindi

Learn the properties of line, equation of a line through a given point and parallel direction cosines of a line passing through two points, relation between the direction cosines of a line, equation of a line in space, plane passing through the intersection of two given planes, angle between two planes, co-planarity of two lines and many more. And last it contains miscellaneous examples. There are three exercises and a miscellaneous exercise in chapter 11 of 12th Mathematics NCERT.

#### NCERT Solutions for Class 12 Maths Chapter 12 – Linear Programming

You can get introduced with to NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming. Here this chapter covered linear programming problem and its mathematical formulation.

Class 12 Maths Exercise 12.1

Class 12 Maths Exercise 12.1 in Hindi

You will learn about the mathematical formulation of the problem, different types of all linear programming problems graphical feasible and infeasible method solution. NCERT Solutions for Class 12 Maths Chapter 12 covers two exercises in all. Take the Linear Programming of 12th Mathematics in Hindi and English medium here.

#### NCERT Solutions for Class 12 Maths Chapter 13 – Probability

In this last NCERT Solutions for Class 12 Maths Chapter 13 Probability, you can find deals with probability and Multiplication rule of Probability.

Class 12 Maths Exercise 13.1

Class 12 Maths Exercise 13.2

Class 12 Maths Exercise 13.3

Class 12 Maths Miscellaneous 13

Class 12 Maths Exercise 13.1 in Hindi

Class 12 Maths Exercise 13.2 in Hindi

Class 12 Maths Exercise 13.3 in Hindi

Class 12 Maths Miscellaneous 13 in Hindi

You can understand here the concept of random variables and its probability in this chapter. Other than this chapter also covers mean of random variable, variance of random variable, and binomial distribution and Bernoulli trials with miscellaneous examples. NCERT Solutions for Class 12 Maths Chapter 13 describes about the five topics with well-defined solutions by the expert math teacher.

As Class 12 Maths is an important subject that plays a vital role in your future career. Class 12 Maths NCERT Solutions acts as the best tool for students in their exam Class 12 boards and undergraduate competitive examination in future. These above NCERT Class 12 Maths solutions for all chapter exercises can be your best education support for board exam preparations. Mathematics is a subject you cannot get good marks in the exam by reading and memorizing the formulae. So you need to practice well to succeed. Learning from Tiwari Academy’s NCERT solutions will help students of Class 12 to clear all the logics of every problem quite effectively.

##### Importance of Learn NCERT Solutions for Class 12 Maths from Tiwari Academy

Students can get many benefits if they learn and practice with Maths Class 12 NCERT Solutions from Tiwari Academy. Class 12th Maths plays an important role for the preparation of many undergraduate competition exams. So well described Maths solution at Tiwari Academy help you to clear all doubts and concepts of all chapters. It is the best study material to score more marks in your class 12 board exam and competitive exams in future. There are total of 13 chapters which are given by the expert math teachers with extensive reviewed. By learning properly and practice this NCERT solution for Class 12 Maths, you will be top on 12th class board exam.

**Provides Authentic Information to the Students**

All Maths Class 12 NCERT Solutions are provided by the experienced Math after extensive research on each and every chapter to provide correct and authentic information to the students.

**Follows the CBSE Curriculum**

This is another most prominent reason that why you learn NCERT Solutions from us. These solutions for every chapter strictly adhere to the CBSE curriculum.

**Clears all Fundamental Logic & Concepts**

These NCERT solutions help the students to make their concepts crystal clear once you clear the concept then you no need to read the whole stuff again and again.

**Helpful For Revisions during Examinations**

These all solutions are designed in such a way that Students can revise quickly during their Examinations.

**Save Your Preparation Time**

The well-defined solution saves your revision time by providing all the necessary logic and formulae in a proper way.

###### How are CBSE 12 Maths Solutions of NCERT Helpful for Board Exams?

CBSE 12 Maths Solutions help you secure marks in the 12 class Board exam as efficiently as they clear your conceptual doubts. The class 12 Maths NCERT solutions help students solve all the exercises given in the textbooks prescribed by the NCERT, which are easy to understand the concepts and get good marks in their board exam. If the students do practice and revise CBSE 12 Maths Solutions of NCERT in a proper way then you may surely passed your Class 12 Board Exams with above 90% marks in the subject Maths. It is seen that most of the student achieved a high score in math by learning CBSE 12 Maths Solutions of NCERT.

### Is NCERT Enough for Class 12 Maths Board Exams?

Yes, NCERT Class 12 Maths Books are enough to score maximum marks in the Class 12 Board exams. Just do practice all the exercise and learn the theorems. Also, do not skip any topic of CBSE 12th Maths syllabus and do revision 2-3 times before your class 12 board exam. The NCERT books for Class 12 are prescribed by the CBSE itself. So these NCERT books are known for their clear explanation of each topic and a good level of practice questions. It the best study material for Class 12 Board’s Maths. These NCERT textbooks are enough for you to score well in your CBSE Class 12 Maths board exam.

### Which Book is Best for Class 12 Maths Board Exam?

NCERT Book is the best and most trusted book for Class 12 board exam. Students can clear their concepts and logics through NCERT Class 12 Maths book by solving the examples and all exercise problems. Students are recommended to solve the NCERT book as this book follows the CBSE syllabus and pattern.

### Is Class 12 Maths Difficult?

No, Class 12 Maths is not difficult than class 11 in CBSE board. It is easier than the syllabus of class 11 Maths. By the practicing in perfectly you can score more marks in Class 12 Maths. The student who have cleared all concept of the early class 11 Maths syllabus, then no need to worry about the Class 12 Maths topic, they can easily understand all topics. If the student faces any doubt about the syllabus then they can learn and get solutions from Class 12 Maths NCERT solutions. It can help you to clear all doubts and concept of all topics.

### Which website is best for Class 12 maths NCERT solutions?

You can find many websites online which are providing Maths NCERT solutions for class 12. But tiwariacademy.com provides a solid conceptual base for all the topics included in CBSE Class 12 Maths Syllabus. All solutions cover all the important theorems and formulae with detailed explanations so that student can easily clear the concept. A detailed step-by-step explanations of problems given in the NCERT textbooks on tiwariacademy.com website. Apart from solutions for each chapter of CBSE Class 12 Maths are the best study materials for students who are preparing for their Class 12 board exams. From this website, you can get FREE Class 12 maths NCERT solutions with unlimited solution PDFs.