# NCERT Solution for class 12 Maths

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The NCERT Solution for **12 maths** PDF are as per the sullabus and helps students solve the exercises given in the textbooks.

**NCERT Solution for class 12 Maths**

### Chapter 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

### Chapter 2: Inverse Trigonometric Functions

- 2.1 Introduction and Basic Concepts or Inverse Trigonometric Functions

- 2.3 Properties of Inverse Trigonometric Functions

### Chapter 3: Matrices

- 3.1 Introduction

- 3.2 Matrix

- 3.3 Types of Matrices

- 3.4 Operation on Matrices

- 3.5 Transpose of a Matrix

- 3.6 Symmetric and Skew Symmetric Matrices

- 3.7 Elementary Operation (Transformation) of a Matrix

- 3.8 Invertible Matrices

### Chapter 4: Determinants

- 4.1 Introduction

- 4.2 Determinant

- 4.3 Properties of Determinants

- 4.4 Area of a Triangle

- 4.5 Minors and Cofactors

- 4.6 Adjoint and Inverse of a Matrix

- 4.7 Applications of Determinants and Matrices

### Chapter 5: Continuity and Differentiability

- 5.1 Introduction to Continuity and Differentiability

- 5.2 Exponential and Logarithmic Functions

- 5.3 Logarithmic Differentiation

- 5.4 Derivatives of Functions in Parametric Forms

- 5.5 Second Order Derivative

- 5.6 Mean Value Theorem

### Chapter 6: Applications of Derivatives

- 6.1 Introduction

- 6.2 Rate of Change of Quantities

- 6.3 Increasing and Decreasing Functions

- 6.4 Tangents and Normals

- 6.5 Approximations

- 6.6 Maxima and Minima

### Chapter 7: Integrals

- 7.1 Introduction to Integral Calculus

- 7.2 Integration as an Inverse Process of Differentiation

- 7.3 Methods of Integration

- 7.4 Integrals of Some Particular Functions

- 7.5 Integration by Partial Fractions

- 7.6 Integration by Parts

- 7.7 Definite Integral

- 7.8 Fundamental Theorem of Calculus

- 7.9 Evolution of Definite Integrals by Substitution

- 7.10 Some Properties of Definite Integrals

### Chapter 8: Application of Integrals

- 8.1 Introduction

- 8.2 Area under Simple Curves

- 8.3 Area Between Two Curves

### Chapter 9: Differential Equations

- 9.1 Introduction to Differential Equations

- 9.2 Basic Concepts

- 9.3 General and Particular Solutions of a Differential Equation

- 9.4 Formation of a Differential Equation whose General Solution is given

- 9.5 Methods of Solving First Order, First Degree Differential Equations

### Chapter 10: Vector Algebra

- 10.1 Introduction to Vectors

- 10.2 Some Basic Concepts

- 10.3 Types of Vectors

- 10.4 Addition of Vectors

- 10.5 Multiplication of a Vector by a Scalar

- 10.6 Product of Two Vectors

### Chapter 11: Three Dimensional Geometry

- 11.1 Introduction

- 11.2 Direction Cosines and Direction Ratios of a Line

- 11.3 Equation of a Line in Space

- 11.4 Angle between Two Lines

- 11.5 Short 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

### Chapter 12: Linear Programming

- 12.1 Introduction to Linear Programmin

- 12.2 Linear Programming Problem and its Mathematical Formulation

- 12.3 Different Types of Linear Programming Problems

### Chapter 13: Probability

- 13.1 Probability Introduction

- 13.2 Conditional Probability

- 13.3 Multiplication Theorem on Probability

- 13.4 Independent Events

- 13.5 Bayes’ Theorem

- 13.6 Random Variables and its Probability Distributions

- 13.7 Bernoulli Trials and Binomial Distribution

**Class 12 Maths Chapterwise NCERT Solutions Free PDF Download**

**NCERT Solutions of Class 12 Maths Chapter 1 Relations and Functions**

In this chapter, you will learn about the Relations between two items and other topics like the Cartesian product of set. You will get more than 40 problems solved in this chapter in this free NCERT solutions PDF.

**NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions**

We covered trigonometric functions in Class 11. Now it is time to learn about Inverse Trigonometric functions. In this chapter, you will learn how to measure the angles between the two sides of the right angle and properties of angle. We have solved more than 40 problems in NCERT solutions for inverse trigonometric functions.

**NCERT Solutions for Class 12 Maths Chapter 3 Matrices**

Matrix is one of the most important applications of Maths. Understand matrices will also help you in further courses. In this chapter, you will learn different topics on matrices like transpose of matrices, multiplication of matrices, etc. Download NCERT Solutions for Matrices here.

**NCERT Solutions for Class 12 Maths Chapter 4 Determinants**

Learning matrices is not complete without learning Determinants. The inverse of the matrix depends upon the Determinants. In this chapter, Determinant of a matrix, properties of determinants and more. We have solved more than 100 problems for this chapter. Download NCERT solution for Class 12 Maths Determinants here.

**NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability**

Continuity and differentiability are all about derivates and its algebra. You will get more than 100 problems solved in this NCERT Solutions for Continuity and Differentiability.

**NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives**

Tangents and normal, Maxima and minima and some more applications of derivatives you will learn in this chapter. Download NCERT Solutions free PDF for applications of derivates here.

**NCERT Solutions for Class 12 Maths Chapter 7 Integrals**

Integrals are the most important and toughest topic in mathematics. It is very important to understand integrals very clearly and NCERT solutions will definetly help you in that. Our team of experts has solved more than 200 problems in this chapter for you. Download NCERT Solutions for Class 12 Integrals here.

**NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals**

Integrals have a lot of applications in Engineering. In this chapter, we will learn how to measure how to find area under simple curves, area between two curves, area bounded by curve and line. We have solved more than 50 problems in this chapter. Download NCERT Solutions for this chapter here.

**NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations**

In this chapter, you will learn about Linear and homogenous Differential equations and how to find the order of differential equations. We have solved more than 50 problems solved in this chapter. Download NCERT Solutions for Differential equations here.

**NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra**

Vector algebra is a really important topic for cracking exams like JEE Main and Advanced. This topic can be helpful in real life scenarios too. In this chapter, you will learn different types of vectors, product, and addition of vectors. We have solved more than 50 problems solved in this chapter. Download NCERT Solutions of Vector algebra here.

**NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry**

Three Dimensional Geometry is an interesting topic. In this chapter, you will learn to measure the distance between parallel lines, the distance between skew lines, etc. Download NCERT Solutions for three-dimensional geometry here.

**NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming**

Linear programming problems have wide applications in business mathematics, economics, and statistics. In this chapter, you will learn about types of linear programming, graphical method of linear programming and more. Download NCERT Solutions for Linear programming here.

**NCERT Solutions for Class 12 Maths Chapter 13 Probability**

Probability is one of the most important topics in Mathematics which helps in real life applications as well. In this chapter, we will learn about Baye’s theorem, Bernoulli trials and more. Download NCERT Solutions for this chapter here.