**Class 12 CBSE Board exams** are just around the corner which means students are spending their days and nights preparing for it. It is a widely accepted fact that among the various subjects, the majority of students consider maths to be the toughest. Given that it is 12th standard maths, the highest grade in a school curriculum, the syllabus is pretty intricate. With introduction to concepts like Set Theory, Dimensional Geometry, Permutations & Combinations, Calculus and Trigonometric Functions among several others. So it is obvious that students dedicate most of their preparation time in Maths i.e. practice solving as many problems as they can and getting thorough with the concepts.

While students refer to various study materials during this period, it is often seen that experts also recommend **NCERT Solutions**. **NCERT Solutions** basically are solved exercises from the NCERT Textbook with a thorough explanation of concepts in a simple manner. A lot of students refer to **NCERT Solutions** as they near the board exams. And especially more so for maths. If you are still doubtful about referring to **NCERT Solutions** here are a few reasons why you should in fact hurry and refer to them.

**Benefits of NCERT Solutions**

CBSE Curriculum & Exam Questions

CBSE curriculum is totally based on NCERT i.e. the concepts given by the NCERT are the only ones asked in the exams. This means that the questions asked in the paper are all from NCERT textbook and majority of them are from NCERT Solutions. So it is most likely that the questions which you practiced a number of times come in the paper. All this potentially results in scoring high.

**In-Depth Understanding of the concept**

As mentioned above one of the major aims of the **NCERT Solutions** are to explain the concepts in the easiest way possible. So the **NCERT Solutions** provide an easy to understand description for even the complex mathematical concepts. It is a huge help when clearing any last minute doubts a student may have.

**Free Availability**

NCERT Solutions can be found everywhere and in anyform; hard copy or soft copy. With the internet, it is in fact available at the tip of your fingers. There are plenty of websites which offer NCERT Solutions that too, in-depth. On top of that, these study materials are free of cost. While most offer solutions from class 6th to 12th, some even offer solutions from class 1st to 12th. These solutions are given exercise wise for each chapter.

**Solutions by Experts**

If you are worried about the credibility of the solutions, you don’t have to, as these are given by experts. Mathematics experts i.e. teachers, professors, IITians and various other mathematical gurus solve these problems which makes it authentic. So as far as the answers being correct is concerned be rest assured.

**Preparation for Entrance Exams**

A fair number of students appear for Entrance Exams after 12th standard. The questions asked in these are mainly from the NCERT apart from current affairs and general knowledge. Getting hands on with NCERT Solutions for class 12 maths helps a student for being prepared for competitive exams like IIT-JEE, NDA, BITSAT, IPU-CET etc. as Maths is a crucial subject in engineering many engineering colleges also conduct entrance exams where NCERT Solutions for **class 12 maths** proves to be useful.

**NCERT Solutions for Class 12 Maths All Chapters**

*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*

*Chapter 1* – NCERT Solutions Class 12 Maths (Relations and Functions)

*Chapter 1*– NCERT Solutions Class 12 Maths (Relations and Functions)

This chapter is an expansion and ascension of the concepts of Relations and Functions introduced in Class 11. This chapter talks more about domain, codomain, real valued functions and their graphs. It includes four exercises which unify the concepts explained in the chapter.

NCERT Solutions for Class 12 Maths All Chapters Mathematics is indubitably the most easy to score yet one of the toughest subjects in Class 12. And the subject only demands practice. While there are a lot of study materials out there to practice class 12 maths, NCERT solutions is one of the most essential one. NCERT Solutions for class 12 maths has not only proven to be useful in CBSE Board examinations but also helps when appearing for various engineering and other entrance exams like JEE.

NCERT has divided class 12 mathematics in two books, Part I and Part II with a total of 13 chapters. Mathematics Part I comprises 6 chapters and Mathematics Part II has 7 chapters. Most of these chapters pick up the concepts introduced in class 11 with addition of introduction to some new concepts and tools of mathematics. We have given chapter wise details and NCERT Solutions below.

**Relations and Functions**

This chapter is an expansion and ascension of the concepts of Relations and Functions introduced in Class 11. This chapter talks more about domain, codomain, real valued functions and their graphs. It includes four exercises which unify the concepts explained in the chapter.

**Topics and Sub Topics Class 12 Maths Chapter 1- Relations and Functions:**

*1 – Relations and Functions**1.1 Introduction**1.2 Types of Relations**1.3 Types of Functions**1.4 Composition of Functions and Invertible Function**1.5 Binary Operations*

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**Chapter 2 – ****NCERT Solutions Class 12 Maths (****Inverse Trigonometric Functions)**

As the name of the chapter suggests, this chapter focuses on the inverse trigonometric functions. Exploring the inverse trigonometric functions, the chapter also talks about behavior of the functions, their graphical representations, and other elementary properties.

**Inverse Trigonometric Functions**

As the name of the chapter suggests, this chapter focuses on the **inverse trigonometric functions**. Exploring the inverse trigonometric functions, the chapter also talks about behavior of the functions, their graphical representations, and other elementary properties. There are two exercises.

In simple terms inverse trigonometric functions are the inverse of the basic trigonometric functions Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (Cot), Secant (Sec) and Cosecant (Csc). These are used mainly to get the angle from any of the angle’s trigonometric ratios. This concept of mathematics is mainly used in real world professions like Engineering, Navigation, Physics and Geometry.

**Topics and Sub Topics Class 12 Maths Chapter 2 – Inverse Trigonometric Functions:**

*• 2 – Inverse Trigonometric Functions**• 2.1 Introduction**• 2.2 Basic Concepts**• 2.3 Properties of Inverse Trigonometric Functions*

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**Chapter 3 – ****NCERT Solutions Class 12 Maths (****Matrices)**

This chapter is fully dedicated to matrices, one of the most vital tools of mathematics. It explains the concept of matrix, it’s types, order of matrix, equality of matrices, operations and properties. There are a total of 4 exercises.

Matrices a plural of matrix which is a table of numbers, symbols or expressions, arranged in rows and columns. If they have the same dimensions i.e each matrix has the same number of columns and rows as the other, these matrices can be added or subtracted by an element. However, for matrix multiplication, only when the number of columns in the first equals the number of rows in the second i.e. the inner dimensions are the same, n for an (mxn)-matrix times an (nxp)-matrix, resulting in an (mxp)-matrix.

**Topics and Sub Topics Class 12 Maths Chapter 3 – Matrices:**

• 3 – Matrices

• 3.1 Introduction

• 3.2 Matrix

• 3.3 Types of Matrices

• 3.4 Operations on Matrices

• 3.5 Transpose of Matrix

• 3.6 Symmetric and Skew Symmetric Matrices

• Elementary Operation (Transformation) of Matrix

• Invertible Matrices

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**Chapter 4 – ****NCERT Solutions Class 12 Maths ****(Determinants)**

Determinants is an important part of Matrices and this chapter focuses on determinants of orders upto 3. It also explains their cofactors and inverses, applications of determinants such as calculation of area of triangles, adjoint of matrices, consistency of a set of linear equations.

Determinants is an important part of Matrices and this chapter focuses on determinants of orders upto 3. It also explains their cofactors and inverses, applications of determinants such as calculation of area of triangles, adjoint of matrices, consistency of a set of linear equations. The chapter is one of the most important for students.

The determinant of a matrix A is signified as det(A), det A, or |A|. In Linear algebra it is a scalar value which can be computed from the elements of a square matrix. It encrypts specific properties of the linear transformation described by the matrix. The determinant is either positive or negative with respect to if the linear transformation preserves or reverses the orientation of a real vector space.

**Topics and Sub Topics Class 12 Maths Chapter 4 – Determinants:**

*• 4 – Determinants**• 4.1 Introduction**• 4.2 Determinant**• 4.3 Properties of Determinants**• 4.4 Area of a Triangle**• 4.5 Adjoint and Inverse of a Matrix**• Applications of Determinants and Matrices*

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**Chapter 5 – ****NCERT Solutions Class 12 Maths ****(Continuity and Differentiability)**

This chapter is a build up of a chapter introduced in class 11, Differentiation of Functions. It talks about continuity, differentiability and states the relationship between them. The chapter further deals with continuity and differentiability of Inverse Trigonometric Functions and introduces logarithm and exponential functions.

This chapter is a build up of a chapter introduced in class 11, Differentiation of Functions. It talks about continuity, differentiability and states the relationship between them. The chapter further deals with continuity and differentiability of Inverse Trigonometric Functions and introduces logarithm and exponential functions.

**Topics and Sub Topics Class 12 Maths Chapter 5 – Continuity and Differentiability:**

*• 5 – Continuity and Differentiability**• 5.1 Introduction**• 5.2 Algebra of continuous functions**• 5.3 Differentiability**• 5.4 Derivatives of composite functions**• 5.5 Derivatives of implicit functions**• 5.6 Derivatives of inverse trigonometric functions**• 5.7 Exponential and Logarithmic Functions**• 5.8 Logarithmic Differentiation**• 5.9 Derivatives of Functions in Parametric Forms**• 5.10 Second-Order Derivative**• 5.11 Mean Value Theorem**• 5.12 Summary*

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**Chapter 6 – ****NCERT Solutions Class 12 Maths ****(Application of Derivatives)**

This chapter continues on with differentiability and talks about the differentiability of functions, and introduction to derivatives. It focuses on derivatives of specific functions, and their applications, particularly tangents and normal to curves, the rate of change in some quantities and increasing & decreasing functions.

**Application of Derivatives**

This chapter continues on with differentiability and talks about the differentiability of functions, and introduction to derivatives. It focuses on derivatives of specific functions, and their applications, particularly tangents and normal to curves, the rate of change in some quantities and increasing & decreasing functions.

**Topics and Sub Topics Class 12 Maths Chapter 6**

*• 6 – Application of Derivatives**• 6.1 Introduction**• 6.2 Rate of Change of Quantities**• 6.3 Increasing and Decreasing Functions**• 6.4 Tangent and Normals**• 6.5 Approximations**• 6.6 Maxima and Minima**• 6.7 Maximum and Minimum Values of a Function in a Closed Interval*

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**Chapter 7 – ****NCERT Solutions Class 12 Maths ****(Integrals)**

This chapter is the introduction to integral calculus and it is one of the most important chapters in class 12 mathematics. The chapter mainly focuses on This integration of functions, and its applications in terms of calculation of areas. There are a total of 11 exercises in this chapter which means it can be really time consuming.

**Integrals**

This chapter is the introduction to integral calculus and it is one of the most important chapters in class 12 mathematics. The chapter mainly focuses on This integration of functions, and its applications in terms of calculation of areas. There are a total of 11 exercises in this chapter which means it can be really time consuming.

**Topics and Sub Topics Class 12 Maths Chapter 7 – Integrals:**

- 7 – Integrals
- 7.1 Introduction
- 7.2 Integration as an Inverse Proportion of Differentiation
- 7.3 Methods of Integration
- 7.4 Integrals of Some Particular Functions
- 7.5 Integration by Partial Functions
- 7.6 Integration by Parts
- 7.7 Definite Integral
- 7.8 Fundamental Theorem of Calculus
- 7.9 Evaluation of Definite Integrals by Substitution
- 7.10 Some Properties of Definite Integrals

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**Chapter 8 – ****NCERT Solutions Class 12 Maths ****(Application of Integrals)**

As the title of this chapter goes, it deals with the applications of integrals in calculating areas under simple curve, lines, parabolas and ellipses. There are two exercises in this chapter.

**Application of Integrals**

As the title of this chapter goes, it deals with the applications of integrals in calculating areas under simple curves, lines, parabolas and ellipses. There are two exercises in this chapter.

**Topics and Sub Topics Class 12 Maths Chapter 8 – Application of Integrals:**

- 8 – Application of Integrals
- 8.1 Introduction
- 8.2 Area Under Simple Curves
- 8.3 Area between Two Curves

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**Chapter 9 – ****NCERT Solutions Class 12 Maths ****(Differential Equations)**

It is the introductory chapter to concepts of Differential equations, the general and particular solutions, and the order and degree of an equation. The chapter also deals with the applications of differential equations and there are a total of six exercises in the chapter

**Differential Equations**

It is the introductory chapter to concepts of Differential equations, the general and particular solutions, and the order and degree of an equation. The chapter also deals with the applications of differential equations and there are a total of six exercises in the chapter.

**Topics and Sub Topics Class 12 Maths Chapter 9 – Differential Equations:**

- 9 – Differential Equations
- 9.1 Introduction
- 9.2 Basic Concepts
- 9.3 General and Particular Solutions of Differential Equations
- 9.4 Formation of a Differential Equation whose General Solution is Given
- 9.5 Methods of Solving First Order, First Degree Differential Equations

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**Chapter 10 – ****NCERT Solutions Class 12 Maths ****(Vector Algebra)**

The chapter talks about vector vector quantities i.e. the quantities with both magnitude and direction. Vector algebra plays a big role in physics and this chapter summarises the rules of addition of vector quantities, and other important properties

The chapter talks about vector vector quantities i.e. the quantities with both magnitude and direction. Vector algebra plays a big role in physics and this chapter summarises the rules of addition of vector quantities, and other important properties.

**Topics and Subtopics Class 12 Maths Chapter 10 – Vector Algebra:**

- 10 – Vector Algebra
- 10.1 Introduction
- 10.2 Some Basic Concepts
- Types of Vectors
- Addition of Vectors
- Multiplication of a vector by a Scalar
- Product of Two Vectors

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**Chapter 11 – ****NCERT Solutions Class 12 Maths ****(Three Dimensional Geometry)**

This chapter uses vectors to calculate the distance between lines, a point and a line, and a line and a plane, along with the angles between them.It also introduces the concept of direction cosines.

This chapter uses vectors to calculate the distance between lines, a point and a line, and a line and a plane, along with the angles between them.It also introduces the concept of direction cosines.

**Topics and Subtopics Class 12 Maths Chapter 11 – Three Dimensional Geometry:**

- 11 – Three Dimensional Geometry
- 11.1 Introduction
- 11.2 Direction Cosine and Direction of Ratios of a Line
- 11.3 Equation of a Line in Space
- 11.4 Angle between Two Lines
- 11.5 Shortest Distance between Two Lines
- 11.6 Plane
- 11.7 Coplanarity of Two Lines
- 11.8 Angle Between Two Planes
- 11.9 Distance of a Point from a Plane
- 11.10 Angle between a Line and a Plane

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**Chapter 12 – ****NCERT Solutions Class 12 Maths ****(Linear Programming)**

This chapter talks about the concept of linear programming problems, and their solutions using graphical methods only

**Linear Programming**

This chapter talks about the concept of linear programming problems, and their solutions using graphical methods only.

**Topics and Subtopics Class 12 Maths Chapter 12 – Linear Programming:**

- 12 – Linear Programming
- 12.1 Introduction
- 12.2 Linear Programming Problem and its Mathematical Formulation
- 12.3 Different Types of Linear Programming Problems

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**Chapter 13 – ****NCERT Solutions Class 12 Maths ****(Probability)**

This chapter focuses on Conditional Probability and how we encounter it in our daily lives. It talks about Bayes’ Theorem, the multiplication rule, and the independence of events.

This chapter focuses on Conditional Probability and how we encounter it in our daily lives. It talks about Bayes’ Theorem, the multiplication rule, and the independence of events.

**Topics and Subtopics Class 12 Maths Chapter 13 – Probability:**

- 13 – Probability
- 13.1 Introduction
- 13.2 Conditional Probability
- 13.3 Multiplication Theorem on Probability
- 13.5 Bayes’ Theorem
- 13.6 Random Variables and its Probability Distributions
- 13.7 Bernoulli Trials and Binomial Distribution

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**Also Read**

*Top 5 Websites For NCERT Solutions**List of Integral Formulas**Complete List of Trigonometric Formulas**CBSE Board Exams 2021 Class 12th: 5 Benefits of Solving Previous Year Questions Papers**How To Prepare For Board Exam 2021 – Tips By Expert**9 Effective Study Tips For Scoring 95% In Class 12th Board Exam*

## FAQs NCERT Solutions Class 12 Maths

## Which site is best for Ncert solutions?

Ans: The internet is filled with websites providing NCERT Solutions but some of the best websites among them are Byju’s, Vedantu, LearnCBSE and TopperLearning. They not only provide NCERT Solutions from elementary levels to higher secondary but they also provide other study materials.

## What are NCERT solutions?

Ans: NCERT Solutions are basically solved exercises from the NCERT Textbook. The exercises given at the end of each chapter is solved by experts and the study material is provided to the students. These question-answers are very important in terms of the CBSE board exams.

## Which app is best for NCERT solutions?

Apps like NCERT Books & Solutions and Byju’s some of the best. NCERT Books & Solutions provides all NCERT textbooks from class 1 to 12 and on top of that provides solutions for all the exercises. Byju’s gives a similar experience to it’s website with additional materials.

## Where Can I Download NCERT Solutions PDF?

NCERT Solutions can be downloaded from the websites like Byju’s, Vedantu, LearnCBSE and TopperLearning.

## Where can I get the solutions for the NCERT books?

Solutions for the NCERT books i.e. NCERT Solutions are available in websites like yju’s, Vedantu, LearnCBSE and TopperLearning.

## Which one is the best NCERT solution book for class 12 MATHS?

Ans: While there are many online options such as Byju’s, Vedantu, LearnCBSE and TopperLearning if you are more about hard copies, Chapter Wise NCERT by Disha Publication is one of the most referred to by experts.