NCERT Solutions for Class 12 Maths

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

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 Solution for Class 12 Maths PDF is as per the syllabus and helps students solve the exercises given in the textbooks.

The NCERT (National Council of Educational Research and Training) is an autonomous institution founded by the Government of India as a Literary, Scientific and Charitable Society under the Societies Registration Act, in 1961. Headquartered at Sri Aurobindo Marg in New Delhi, this body is responsible for setting up the curriculum for CBSE schools in India. To prepare for their CBSE class 12 board exams as well as entrance exams, students should refer to the NCERT Solutions for all subjects of Class 12.

Vedantu has prepared NCERT Solutions for Class 12 Maths so that students can refer to them while preparing for their board exams as well as competitive entrance exams. By referring to them while preparing, students can understand all the concepts in their Class 12 Maths Textbook thoroughly. There are 13 chapters in the Class 12 Maths textbook. Vedantu is your one-stop-shop for students who are looking for Class 12 Maths NCERT Solutions. We offer precise and accurate CBSE Class 12 Maths solutions that are written in simple language and curated by subject experts who are highly experienced. Our solutions are made according to the NCERT textbooks because these books are prescribed by CBSE.

For getting admission into good colleges, students must perform well in their class 12 board exams. They might be under pressure and get stressed and demotivated due to this, however, students don’t need to worry as Vedantu can help them achieve their target scores and get admission into their dream colleges. They can download the NCERT books, previous year question papers as well as sample papers of Class 12 Maths for their practice.

Click on the following chapters to download chapter wise Solutions for Class 12 Maths -

NCERT Solutions Class 12 Maths - Free PDF Download

Class 12 Maths NCERT Solutions PDF Download

Class 12 is an important milestone in your life as you take some serious decisions about your future based on your performance. Indeed, Mathematics forms a vital component of Class 12 as well as every competitive exams’ syllabus. Whether you choose to be an engineer or a doctor, you will have to deal with Mathematics in every area. Making the concepts of Class 12 concrete can immensely help you in securing good marks in the CBSE Class 12 board exam as well as in various competitive exams. CBSE NCERT Solutions for Class 12 Maths plays a vital role in your exam preparation as it has detailed chapter-wise solutions for all exercises. First and foremost, you should imprint in your mind that NCERT books are the biggest tool that you can have to get well-versed with the fundamentals. This will help you not leave out any important questions in your exam preparation.

NCERT Solutions for Class 12 Maths Solutions contain detailed explanations of all the key concepts, theorems and formulas, to aid students to get a better understanding on a foundational and conceptual level. It will also help them in their preparation for undergraduate-level engineering admission exams such as VITEEE, JEE Mains, BITSAT and others.

The benefits of accessing Class 12 CBSE Maths NCERT Solutions are not only confined to your success in Maths, but it also lays a foundation for other super important subjects. Getting a good grip over exhaustive details of some chapters of Maths like Calculus, differential equations etc can be of great help while understanding the derivations and concepts behind the numerical of Science. You can easily download the Class 12 Maths NCERT solutions PDF of every Chapter of Mathematics. The solutions for each exercise have been curated and reviewed by some of the best teachers across India. It covers all the answers to the questions from 13 important chapters from the NCERT Mathematics textbook. Class 12 Maths NCERT Solutions covers crucial and intricate chapters such as Differentiation, Integration, Algebra, and others. The chapters are designed sequentially and logically, which allows you to understand the concepts easily.

Maths is one of the most important subjects in Class 12 as well as competitive exams such as JEE Main and Advance. At Vedantu, Class 12 Maths Solutions have been designed with this in mind. The solutions are simple and clear and alternative techniques for all questions have also been given for each chapter. Our priority is to provide students with the maximum study resources to aid their preparation and help them score excellent marks. Along with the solutions, Vedantu also provides other study material including sample papers, previous year question papers, NCERT Exemplar solutions, revision notes, important questions and formulas, for Class 12 Maths and other subjects.

Let us look into the Class 12 Maths chapters in detail.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

The first chapter of CBSE Class 12 deals with the notion of relations and functions, domain, co-domain and range which have already been introduced in the Class 11 syllabus along with various types of specific real-valued functions and their respective graphs. In this chapter, topics that are covered include types of relations including reflexive, symmetric, transitive and equivalence and one to one and onto functions. In this chapter, you will be solving a total of four exercises’ questions entailing all the essential topics in them. 

Chapter 1 - Relations and Functions Exercises in PDF Format

Exercise 1.1

16 Questions & Solutions (3 Short Answers, 13 Long Answers)

Exercise 1.2

12 Questions & Solutions (5 Short Answers, 7 Long Answers)

Exercise 1.3

14 Questions & Solutions (4 Short Answers, 10 Long Answers)

Exercise 1.4

13 Questions & Solutions (6 Short Answers, 7 Long Answers)

 

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NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

There are many functions which are not one-one, onto or even both and hence we cannot talk of their inverses. Class 11 studied that trigonometric functions are not one-one and onto over their natural domains and ranges and hence their inverses do not exist. 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. Besides, some elementary properties will also be discussed. The concept of the principal value branch will also be talked about in this chapter. The inverse trigonometric functions hold great value in calculus for they serve to define many integrals. Inverse trigonometric functions’ concepts are applied vastly in science and engineering. 

Chapter 2 - Inverse Trigonometric Functions Exercises in PDF Format

Exercise 2.1

14 Questions & Solutions (14 Short Answers)

Exercise 2.2

20 Questions & Solutions (4 Short Answers, 16 Long Answers)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 3 Matrix

You need to know about Matrices as it is instrumental in various branches of mathematics. Matrices are considered one of the most powerful tools in mathematics. It simplifies our work to a great extent when compared with other methods. In this chapter, students will learn about matrices, their notations, order, equality and types of matrices. They will also learn about zero and identity matrix, and symmetric as well as skew-symmetric matrices. They will learn how to find the transpose of a matrix and operations including addition, multiplication and multiplication with a scalar, on matrices. Apart from this, topics including non-commutativity of multiplication of matrices and invertible matrices will also be covered in this chapter.

There are a total of 62 questions in the 4 exercises of this chapter. In this chapter, you will be delving deeper into the fundamentals of matrix and matrix algebra.

Chapter 3 - Matrix Exercises in PDF Format

Exercise 3.1

10 Questions & Solutions (5 Short Answers, 5 Long Answers)

Exercise 3.2

22 Questions & Solutions (3 Short Answers, 19 Long Answers)

Exercise 3.3

12 Questions & Solutions (4 Short Answers, 8 Long Answers)

Exercise 3.4

18 Questions & Solutions (18 Short Answers)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

In chapter 3, matrices and the algebra of matrices will be explained. Whereas, in this chapter, you will be studying determinants up to order three only with real entries. Also, the six exercises are distributed in a way that you will study various properties of determinants, cofactors and applications of determinants in finding the area of a triangle, minors, adjoint and inverse of a square matrix, consistency and inconsistency of system of linear equations and solution of linear equations in two or three variables using the inverse of a matrix in these exercises. 

Chapter 4 - Determinants Exercises in PDF Format

Exercise 4.1

8 Questions & Solutions (3 Short Answers, 5 Long Answers)

Exercise 4.2

10 Questions & Solutions (4 Short Answers, 10 Long Answers)

Exercise 4.3

5 Questions & Solutions (2 Short Answers, 3 Long Answers)

Exercise 4.4

5 Questions & Solutions (2 Short Answers, 3 Long Answers)

Exercise 4.5

18 Questions & Solutions (4 Short Answers, 14 Long Answers)

Exercise 4.6

16 Questions & Solutions (3 Short Answers, 13 Long Answers)

 

Students can also download the following additional study material -

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

This chapter is the extension of the differentiation of functions that you have studied in Class XI. You must have learnt to differentiate certain functions like polynomial functions and trigonometric functions. This chapter explains the very important concepts of continuity, differentiability and relations between them. You will be learning about the differentiation of inverse trigonometric functions. Furthermore, you will be getting acquainted with a new class of functions called exponential and logarithmic functions. You will also learn about the derivatives of exponential and logarithmic functions, as well as logarithmic differentiation. The concepts of derivatives of functions in terms of parametric forms and second-order derivatives are also discussed in this chapter. There are a total of eight exercises in this chapter so you will have to dedicate some extra time and effort to get well-versed with this chapter.

Chapter 5 - Continuity and Differentiability Exercises in PDF Format

Exercise 5.1

34 Questions & Solutions (10 Short Answers, 24 Long Answers)

Exercise 5.2

10 Questions & Solutions (2 Short Answers, 8 Long Answers)

Exercise 5.3

15 Questions & Solutions (9 Short Answers, 6 Long Answers)

Exercise 5.4

10 Questions & Solutions (5 Short Answers, 5 Long Answers)

Exercise 5.5

18 Questions & Solutions (4 Short Answers, 14 Long Answers)

Exercise 5.6

11 Questions & Solutions (7 Short Answers, 4 Long Answers)

Exercise 5.7

17 Questions & Solutions (10 Short Answers, 7 Long Answers)

Exercise 5.8

6 Questions & Solutions (2 Short Answers, 4 Long Answers)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

In Chapter 5, you will learn how to find the derivative of composite functions, implicit functions, exponential functions, inverse trigonometric functions, and logarithmic functions. In this chapter, you will study the applications of the derivative in various disciplines such as engineering, science, and many other fields. For instance, we 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 and many more uses of derivatives. We will also use the derivative to find intervals of increasing or decreasing functions. You will also learn about maxima and minima and simple problems based on all these concepts. There are five exercises in total where you will get a detailed insight into the Application of Derivatives. Finally, the derivative is used to find an approximate value of certain quantities.

Chapter 6 - Application of Derivatives Exercises in PDF Format

Exercise 6.1

18 Questions & Solutions (6 Short Answers, 10 Long Answers, 2 MCQs)

Exercise 6.2

19 Questions & Solutions (7 Short Answers, 10 Long Answers, 2 MCQs)

Exercise 6.3 

27 Questions & Solutions (25 Short Answers, 2 MCQs)

Exercise 6.4

9 Questions & Solutions (7 Short Answers, 2 MCQs)

Exercise 6.5 

29 Questions & Solutions (11 Short Answers, 15 Long Answers, 3 MCQs)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Differential Calculus is based on the idea of a derivative. Derivatives came into existence for the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines. Integral Calculus eases the problem of defining and calculating the area of the region bounded by the graphs of the function. 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 comparison of integration and differentiation, integration methods including substitution, partial fraction, by parts, and trigonometric identities. Students will also learn about definite integrals, the fundamental theorem of calculus and how to evaluate definite integrals by substitution as well as their properties, accompanied by miscellaneous examples. With a total of eleven exercises, you will have to learn every topic and their related questions with sheer concentration.

Chapter 7 - Integrals Exercises in PDF Format

Exercise 7.1

22 Questions & Solutions (21 Short Answers, 1 MCQs)

Exercise 7.2

39 Questions & Solutions (37 Short Answers, 2 MCQs)

Exercise 7.3

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.4

25 Questions & Solutions (23 Short Answers, 2 MCQs)

Exercise 7.5

23 Questions & Solutions (21 Short Answers, 2 MCQs)

Exercise 7.6

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.7

11 Questions & Solutions (9 Short Answers, 2 MCQs)

Exercise 7.8

6 Questions & Solutions (6 Short Answers)

Exercise 7.9

22 Questions & Solutions (20 Short Answers, 2 MCQs)

Exercise 7.10

10 Questions & Solutions (8 Short Answers, 2 MCQs)

Exercise 7.11

21 Questions & Solutions (19 Short Answers, 2 MCQs)

 

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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

13 Questions & Solutions (11 Short Answers, 2 MCQs)

Exercise 8.2 

7 Questions & Solutions (5 Short Answers, 2 MCQs)

 

Students can also download the following additional study material -

 

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. There are a total of six exercises in this chapter for the students. Differential equations are implemented in a plethora of applications in all the other subjects and areas. Hence, if you study the Differential equations chapter in a detailed manner, it will help you to gain a detailed insight into all modern scientific investigations.

Chapter 9 - Differential Equations Exercises in PDF Format

Exercise 9.1

12 Questions & Solutions (10 Short Answers, 2 MCQs)

Exercise 9.2

12 Questions & Solutions (10 Short Answers, 2 MCQs)

Exercise 9.3

12 Questions & Solutions (5 Short Answers, 5 Long Answers, 2 MCQs)

Exercise 9.4

23 Questions & Solutions (10 Short Answers, 12 Long Answers, 1 MCQs)

Exercise 9.5

17 Questions & Solutions (15 Short Answers, 2 MCQs)

Exercise 9.6 

19 Questions & Solutions (15 Short Answers, 2 Long Answers, 2 MCQs)

 

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

Did you know those quantities that involve only one value (magnitude), which is a real number, are called scalars? Whereas, quantities that involve magnitude and direction are called Vectors. In chapter 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

5 Questions & Solutions (5 Short Answers)

Exercise 10.2

19 Questions & Solutions (5 Short Answers, 14 Long Answers)

Exercise 10.3

18 Questions & Solutions (5 Short Answers, 13 Long Answers)

Exercise 10.4

12 Questions & Solutions (4 Short Answers, 8 Long Answers)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

Chapter Three Dimensional Geometry will take you through the study of 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, as well as skew and coplanar lines. Other topics in this chapter include the cartesian and vector equations of a plane.

Chapter 11 - Three Dimensional Geometry Exercises in PDF Format

Exercise 11.1

5 Questions & Solutions (5 Short Answers)

Exercise 11.2

17 Questions & Solutions (9 Short Answers, 8 Long Answers)

Exercise 11.3

14 Questions & Solutions (5 Short Answers, 9 Long Answers)

 

Students can also download the following additional study material -

 

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 only, though there are many other methods also available to solve such problems. 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

10 Questions & Solutions (10 Long Answers)

Exercise 12.2

11 Questions & Solutions (11 Long Answers)

 

Students can also download the following additional study material -

 

NCERT Solutions for Class 12 Maths Chapter 13 Probability

The probability will take you through 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. With a total of five exercises, you will also learn an important concept of a random variable and its probability distribution and the mean and variance of a probability distribution. You will also learn about the partition of a sample space, total probability theorem, Bernoulli trials and binomial distribution.

Chapter 13 - Probability Exercises in PDF Format

Exercise 13.1

17 Questions & Solutions (4 Short Answers, 13 Long Answers)

Exercise 13.2 

18 Questions & Solutions

Exercise 13.3

14 Questions & Solutions

Exercise 13.4 

17 Questions & Solutions

Exercise 13.5

15 Questions & Solutions

 

Students can also download the following additional study material -

Unit wise weightage of CBSE Class 12 First Term

Unit

Unit Name

Marks

1

Relations and Functions

08

2

Algebra

10

3

Calculus

17

5

Linear Programming

05


Total

40


Internal Assessment Marks

10


Total Marks

50

 

Unit wise weightage of CBSE Class 12 Second Term

Unit

Unit Name

Marks

3

Calculus

18

4

Vectors and Three-Dimensional Geometry

14

6

Probability

08


Total

40


Internal Assessment Marks

10


Total Marks

50

 

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 grasp some crucial tips to answer some particular 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 shortcuts help you to take your preparation to the next level. Vedantu NCERT Solutions will help you in improving your mathematical skills as well.

Mathematics is a subject that has been relevant to humanity since ancient times. Archaeologists have discovered that a numbering system was even used by the Indus Valley civilization. They used this mainly for trade and commerce purposes with different parts of the world. Today, Math holds a very important place in almost all aspects of our daily life. For instance, at the supermarket billing counter, we inevitably use the computerized numerical system to calculate our total bill. The CBSE class 12 Maths solution has been curated and reviewed by some of the best Maths teachers in the country to help students grasp all the fundamental concepts. It is a great guide that can be used to prepare for the CBSE Board exams, as well as engineering entrance examinations like JEE. The Class 12 Maths NCERT Solutions are very helpful during individual or group studies, teaching students how to best approach a problem. The Maths NCERT Solutions Class 12 is an aid that should complement the students' school textbook and help them understand the problems in a much better manner. It helps the students to get good marks in their Maths board exams 2019-20. One of the best advantages of NCERT Solutions is it acts as an expert tool that can be used as a gateway to the mind of the examiner.

 

Vedantu Gives You the Competitive Edge

Students who need additional guidance while solving Class 12 Maths Questions can avail the online tutoring option that is available at Vedantu. The 12th board exam can be the stepping stone that can ensure admission into a good college. Due to the intense pressure, students may get demotivated quickly if they get ‘stuck’ with any particular problem. The professional help extended by the Vedantu faculty will help the students become more confident as any doubt they have while solving questions with the help of NCERT Class 12 Maths Solutions can be immediately addressed.

 

About Vedantu.com

Vedantu.com, being the No.1 online tutoring company in India, provides you free NCERT Maths class 12 PDF option for all the NCERT Solutions that help you in your exam preparation. You can find NCERT books and NCERT Solutions of all the subjects on our website from Class 6-12. The Vedantu Learning App will give you access to attend free live masterclasses and conceptual videos, access to all the PDFs of study materials and solutions. Additionally, you will be provided FREE Online Tests. You will have all the required standard study materials handy and this will make the process of learning easier for you. Also, your problem-solving speed will be improved as you practice. The more you practice, the more you will have a good command of the subject. Register for our free webinar class with the best Mathematics tutor in India.

FAQs (Frequently Asked Questions)

Q1. Is NCERT Maths Textbook a Good Study Material for Cracking JEE Main Exam?

Ans: 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 number of times, 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.

Q2. Which is the Best Book Available in the Market for NCERT Maths Class 12 Board Exam Preparation?

Ans: 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 enough number of times, he/she can get good marks in the Class 12 Board exam. CBSE students must have a good grip on NCERT books before referring to other books for revision or practising more number of questions. NCERT books are designed in such a way that it covers most of the important topics in fair detail. Problems given in the book are also of standard types which are asked frequently in exams.

Q3. Where Can I Get Free to Download NCERT Solutions for Class 12 Maths?

Ans: 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 in free to download PDF format. Vedantu is a trusted name when it comes to availing 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.

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