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# CBSE Class 12 Maths NCERT Solutions 2022-23

## NCERT Solutions for Class 12 Maths - Free PDF Download all Chapters

Last updated date: 28th Jan 2023
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Are you looking for the most accurate NCERT Solutions for Class 12 Maths, then Vedantu.com is the perfect website to download it in PDF format free of cost. You might be aware that the curriculum for all schools that follow the Central Board of Secondary Education (CBSE) is set by The National Council of Education Research and Training (NCERT) across the nation. The NCERT Solutions for Class 12 Maths are created by our Maths experts as per the CBSE syllabus to students solve the exercises given in the textbooks.

Knowing the basic formulas and concepts in Mathematics will definitely help you to score better marks in your Class 12 Maths exam. NCERT Solutions for Class 12 Maths has been provided in PDF format for all the chapters.

## NCERT Solutions for Class 12 Maths | Chapter-wise List

Given below are the chapter-wise NCERT Solutions for Class 12 Maths. These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## NCERT Solutions for Class 12 Maths Exercises | All Chapters

Maths as a subject is considered difficult by most of the students. But clearing the basic concepts and practising all the formula-based questions regularly makes it easy to score high marks in this subject. Class 12 Maths is an important subject of the CBSE Class 12 Syllabus as it helps you prepare for various entrance exams such as JEE Main, BITSAT and many other engineering entrance exams.

## Class 12 Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions of NCERT Class 12 Maths Syllabus deals with types of relations and functions along with a few miscellaneous examples.

Here is the list of topics covered in Class 12 Maths Chapter 1 Relations and Functions.

1. Types of relations

• Symmetric

• Reflexive

• Transitive

• Equivalence.

1. Types of functions

• One to one functions

• Onto functions

• Composite functions

• Invertible functions.

1. Binary operations.

NCERT Solutions for Class 12 Maths Chapter 1 Exercises are given in the table below:

 Chapter 1 - Relations and Functions Exercises in PDF Format Exercise 1.1 Type of Relations 16 Questions & Solutions (3 Short Answers, 13 Long Answers) Exercise 1.2  Types of Functions 12 Questions & Solutions (5 Short Answers, 7 Long Answers) Exercise 1.3 Invertible Function 14 Questions & Solutions (4 Short Answers, 10 Long Answers) Exercise 1.4 Binary Operations 13 Questions & Solutions (6 Short Answers, 7 Long Answers)

## Class 12 Maths Chapter 2 Inverse Trigonometric Functions

In CBSE Class 12 Inverse Trigonometric Functions, there are only two exercises where you will study the restrictions on domains and ranges of trigonometric functions which enables the visibility of their inverses and observe their behaviour through graphical representations.

The inverse trigonometric functions hold great value in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions are applied vastly in science and engineering.

 Chapter 2 - Inverse Trigonometric Functions Exercises in PDF Format Exercise 2.1 Basic Concepts 14 Questions & Solutions (14 Short Answers) Exercise 2.2 Inverse Trigonometric Functions 20 Questions & Solutions (4 Short Answers, 16 Long Answers)

## CBSE Class 12 Maths Chapter 3 Matrices

Chapter 3 of NCERT Class 12 Maths covers the following topics:

• What are Matrices?

• Types of Matrices

• Properties of scalar multiplication

• Multiplication of matrices

• Properties of multiplication of matrices

• Symmetric and skew-symmetric matrices

• Elementary operation or transformation of a matrix

• Inverse of a matrix by elementary operations

There are 4 exercises included in this chapter. The links to these exercises are provided in the table below.

 Chapter 3 - Matrix Exercises in PDF Format Exercise 3.1 Matrix 10 Questions & Solutions (5 Short Answers, 5 Long Answers) Exercise 3.2 Operations on Matrices 22 Questions & Solutions (3 Short Answers, 19 Long Answers) Exercise 3.3 Transpose of a Matrix 12 Questions & Solutions (4 Short Answers, 8 Long Answers) Exercise 3.4 Elementary Operation of a Matrix 18 Questions & Solutions (18 Short Answers)

## CBSE Class 12 Maths Chapter 4 Determinants

There are six exercises which are included in the NCERT Class 12 Maths Chapter 4 Determinants. By solving these exercises, students will be familiar with the concepts of determination, cofactors and the application of determinants in finding the area of a triangle, minors, adjoint and inverse of a square matrix.

The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 4 exercises can be downloaded from the links provided below:

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

Class 12 Maths Chapter 5 Continuity and Differentiability explains the definition of continuity and meaning of differentiability.

The important concepts that students will get to learn from NCERT Solutions for Class 12 Maths Chapter 5 are as follows:

• Algebra of continuous function

• Derivatives of composite functions, Implicit functions, Inverse trigonometric functions, Exponential and logarithmic functions

• Logarithmic differentiation

• Derivatives of functions in parametric forms

• Second order derivatives

•  Rolle’s and Lagrange’s Mean Value Theorems

The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 5 exercises can be downloaded from the links provided below:

Here are the links for some important study materials that are available on our website for CBSE Class 12 Maths Chapter 5.

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

In this chapter, you will study the applications of the derivative in various disciplines such as engineering, science, and many other fields. For instance, you will learn how the derivative can be used to determine the rate of change of quantities and to find the equations of tangent and normal to a curve at a point. You will also learn the use of derivatives to find intervals of increasing or decreasing functions, maxima and minima, along with a few simple problems based on all these concepts.

 Chapter 6 - Application of Derivatives Exercises in PDF Format Exercise 6.1 Rate of Change of Quantities 18 Questions & Solutions (6 Short Answers, 10 Long Answers, 2 MCQs) Exercise 6.2 Increasing and Decreasing Functions 19 Questions & Solutions (7 Short Answers, 10 Long Answers, 2 MCQs) 27 Questions & Solutions (25 Short Answers, 2 MCQs) Exercise 6.4 Approximations 9 Questions & Solutions (7 Short Answers, 2 MCQs) 29 Questions & Solutions (11 Short Answers, 15 Long Answers, 3 MCQs)

## NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Topics in this chapter include an introduction to indefinite integrals, integration as inverse to differentiation, its geometrical interpretation, and properties. Other topics that are discussed in this chapter are the following:

• Comparison of integration and differentiation

• Integration methods including substitution, partial fraction, by parts, and trigonometric identities.

• Definite integrals

• Fundamental theorem of calculus

• How to evaluate definite integrals by substitution

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

Here, in this chapter, you will study some specific applications of integrals to find the area given under the simple curves, also, the area between lines and arcs of circles, parabolas and ellipses (standard forms only). There are two exercises in this chapter in which you will also deal with finding the area bounded by the above-said curves.

 Chapter 8 - Application of Integrals Exercises in PDF Format Exercise 8.1 Area under Simple Curves 13 Questions & Solutions (11 Short Answers, 2 MCQs) 7 Questions & Solutions (5 Short Answers, 2 MCQs)

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

In Differential Equations, you will be studying some basic concepts related to the differential equation, general and particular solutions of a differential equation, formation of differential equations, number of methods to solve a question based on first order - first-degree differential equations and some applications of differential equations in different areas.

 Chapter 9 - Differential Equations Exercises in PDF Format Exercise 9.1 Order/Degree of a differential equation 12 Questions & Solutions (10 Short Answers, 2 MCQs) Exercise 9.2 General and Particular Solutions of a Differential Equation2 12 Questions & Solutions (10 Short Answers, 2 MCQs) Exercise 9.3 Formation of a Differential Equation 12 Questions & Solutions (5 Short Answers, 5 Long Answers, 2 MCQs) Exercise 9.4 Methods of Solving First Order, First Degree Differential Equations 23 Questions & Solutions (10 Short Answers, 12 Long Answers, 1 MCQs) Exercise 9.5 Homogeneous Differential Equations 17 Questions & Solutions (15 Short Answers, 2 MCQs) 19 Questions & Solutions (15 Short Answers, 2 Long Answers, 2 MCQs)

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

In Class 12 Maths Chapter 10  Vector Algebra, you will be studying some basic concepts of vectors, various operations on vectors, and the algebraic as well as geometric properties. You will also learn about the types of vectors such as zero, unit, equal and collinear vectors.

Other topics discussed in this chapter include the negative of a vector, operations of vectors such as addition, its properties, components and how to multiply a vector by a scalar. You will also learn about section formulae, vector joining two points, dot product of two vectors, product of two vectors, cross product of two vectors, and projection of a vector on a line.

 Chapter 10 - Vector Algebra Exercises in PDF Format Exercise 10.1 Types of Vectors 5 Questions & Solutions (5 Short Answers) Exercise 10.2 Addition of Vectors 19 Questions & Solutions (5 Short Answers, 14 Long Answers) Exercise 10.3 Product of Two Vectors 18 Questions & Solutions (5 Short Answers, 13 Long Answers) Exercise 10.4 Vector (or cross) product of two vectors 12 Questions & Solutions (4 Short Answers, 8 Long

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

CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry deals with the direction cosines and direction ratios of a line joining two points and also about the equations of lines and planes in space under different conditions. Along with that, you will also get to know about the angle between two lines, a line and a plane, two planes, the shortest distance between two skew lines and the distance of a point from a plane.

You will also learn about cartesian equations and vector equations of a line, skew and coplanar lines, and the cartesian and vector equations of a plane.

 Chapter 11 - Three Dimensional Geometry Exercises in PDF Format Exercise 11.1 Vector (or cross) product of two vectors 5 Questions & Solutions (5 Short Answers) Exercise 11.2 Equation of a Line in Space 17 Questions & Solutions (9 Short Answers, 8 Long Answers) Exercise 11.3 Plane 14 Questions & Solutions (5 Short Answers, 9 Long Answers)

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

This chapter has only two exercises in which you will study some linear programming problems and their solutions by graphical method. Other concepts in this chapter are the mathematical formulation of linear programming problems, different types of linear programming problems, terms such as objective function, optimization and constraints, as well as feasible and infeasible regions and solutions.

 Chapter 12 - Linear Programming Exercises in PDF Format Exercise 12.1 Linear Programming Problem and its Mathematical Formulation 10 Questions & Solutions (10 Long Answers) Exercise 12.2 Different Types of Linear Programming Problems 11 Questions & Solutions (11 Long Answers)

## NCERT Solutions for Class 12 Maths Chapter 13 Probability

Class 12 Maths Chapter 13 Probability will teach you the important concepts of the conditional probability of an event given that another event has occurred, which will, in turn, clarify the Bayes' theorem, multiplication rule of probability and independence of events. You will also learn the concept of a random variable and its probability distribution, mean and variance of a probability distribution, total probability theorem, Bernoulli trials and binomial distribution.

 Chapter 13 - Probability Exercises in PDF Format Exercise 13.1 Conditional Probability 17 Questions & Solutions (4 Short Answers, 13 Long Answers) 18 Questions & Solutions Exercise 13.3 Bayes' Theorem 14 Questions & Solutions 17 Questions & Solutions Exercise 13.5 Binomial Distribution 15 Questions & Solutions

## CBSE Class 12 Maths Weightage (2022-23)

Given below is the unit-wise mark distribution for CBSE Class 12 Maths exam for session 2022-23.

 Unit Unit Name Marks 1 Relations and Functions 08 2 Algebra 10 3 Calculus 35 5 Vectors and Three - Dimensional Geometry 14 6 Linear Programming 5 7 Probability 8 Internal Assessment Marks 20 Total Marks 100

The Class 12 Maths NCERT Solutions provided on Vedantu have been written to help you understand all the chapter-wise problems in the latest and updated textbooks prescribed by NCERT. Being the most preferred study material, NCERT Solutions will help the students in various ways. Let us look into this.

## Key Benefits of CBSE Class 12 Maths NCERT Solutions from Vedantu

• You can easily clear your doubts by accessing this PDF anytime and also be able to learn some important tips to answer some complex questions in a detailed manner.

• You no longer have to turn in several pages for revision before the examination. The NCERT Maths class 12 PDF Download is available on our website for FREE, which you can access anytime, anywhere.

• Also, all the CBSE Class 12 Maths solutions are arranged in a sequential manner which enables smooth learning. Maths is a sequential subject, and it is important that it is studied in the right manner.

• The solutions are explained in a detailed manner. Step by step solutions provided for all the exercise questions helps you to know the subject in a detailed manner.

• The topic-wise detailed solutions will help you to take your preparation to the next level. Vedantu’s NCERT Solutions for Class 12 Maths will definitely help you in improving your mathematical skills as well.

Go through these Chapter-wise Exercise Solutions that are provided for CBSE Class 12 Maths and begin your preparation for the Class 12 Board exam confidently. For any more information and study materials, visit Vedantu’s website.

## FAQs on CBSE Class 12 Maths NCERT Solutions 2022-23

1.  Is NCERT Maths Textbook a Good Study Material for Cracking JEE Main Exam?

NCERT Maths textbook is the best book to get your concepts cleared regarding the subject. For many students, the Maths paper of JEE Main is considered one of the toughest subjects to clear. NCERT book is a good book to start your preparations for the exam. However, it is not just sufficient to clear the exam as students need to have enough practice of the concepts. Referring to other books that are specialized for JEE preparation would give students an idea of different types of questions. If a student practices NCERT books enough, they will have a strong grip on the subject to start with. For any assistance regarding JEE preparation, students can log in to Vedantu’s platform.

2. Which is the Best Book Available in the Market for NCERT Maths Class 12 Board Exam Preparation?

NCERT textbook is considered the most valuable resource for board exam preparation. If a student concentrates well on the concepts given in NCERT textbook chapters and practices the exercise and example problems regularly, he/she can get good marks in the Class 12 Board exam. CBSE students must have a clear concept of the NCERT books before referring to other books for revision.

3. Where Can I Get Free to Download NCERT Solutions for Class 12 Maths?

The one-stop solution where you can get all the free materials for Class 12 board exam preparation is Vedantu. On Vedantu’s site, you can find the best NCERT Solutions for Class 12 Maths for free in PDF format. Vedantu is a trusted name when it comes to availing of the most authentic study materials. NCERT Solution of Maths Class 12 is designed by expert teachers who are well versed in the exam pattern and syllabus and have years of experience in the field of teaching.

4. How many chapters are there in NCERT Class 12 Maths Textbook?

NCERT Class 12 Maths Textbook consists of 2 parts. Part 1 of the NCERT Textbook includes 6 chapters, i.e., chapter 1 to chapter 6, whereas part 2 contains 7 chapters, i.e., chapter 7 to chapter 13. Therefore, a total of 13 chapters are included in the NCERT Class 12 Maths Textbook, which includes the following:

• Matrices

• Inverse Trigonometric Functions

• Relations and Functions

• Determinants

• Applications of Derivatives

• Continuity and Differentiability

• Applications of Integrals

• Vector Algebra

• Differential Equations

• Three Dimensional Geometry

• Probability

• Linear Programming.

5. Are NCERT Exemplar Solutions available online?

Yes, NCERT Exemplar Solutions are available online. Students can also download the NCERT Exemplar Solutions for all classes and subjects from Vedantu in free PDF format. SHARE TWEET SHARE SUBSCRIBE