CBSE Class 12 Maths NCERT Solutions 2022-23

CBSE Class 12 Maths is thought to be a difficult subject as one should have a robust basis for know-how the idea of mathematics. One can't imagine a profession in Engineering if one does not recognizes the NCERT class 12 maths. Maths learnt in Class eleven and Class 12 forms the fundamentals of Engineering. Students who want to make a career in engineering have to study this subject with incredible passion as Mathematics is the language of all engineering applications.

Class 12 results can have a substantial effect on a student's future. If a student aspires to crack the entrance examination, similarly to getting in-depth information about the situation, she or he needs to recognize all of the hints to solve the problems. Class 12 Maths NCERT Solutions of Extramarks can show to be an aid of an incredible application for the scholars to solve the hassle and achieve good marks in the exams. Solutions to all the textbook issues specified in the syllabus of the NCERT Maths Class 12 are to be had on Extramarks and college students can flip to those solutions anytime they encounter trouble with any problem.

The course of Mathematics includes- Relations and Functions, Inverse Trigonometric Functions, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, and Probability. Most of the chapters are interrelated. Questions withinside the entrance examination are asked by blending concepts from unique chapters. A scholar has to absolutely recognize all of the principles from every chapter. Mathematics NCERT answers designed on our page will certainly help the scholars in achieving these learning objectives.

What could be better if you get the simpler and readymade solutions of your Class 12 NCERT textbook exercises? Moreover, all these are created by an experienced subject matter expert. Can you imagine how beneficial these could be? Sounds amazing, right! You must opt for these Class 12 Maths NCERT Solutions in Hindi right away. You can download NCERT Maths Book Class 12 Solutions Pdf in Hindi from Vedantu’s official website (vedantu.com) by registering yourself with your phone number/ email address. You can also access the same study materials from the Vedantu app as well. In that case, you need to download the Vedantu app first from Google play store.

You will get Class 12 Maths in Hindi NCERT solutions written in a simple and lucid manner. Solve all the problems/ questions given in the exercises and evaluate your performance with these 100% accurate solutions so that you can learn how to write answers to the questions from any perspective during the final exam. Each of the answers in the Maths in Hindi NCERT solutions Class 12 is student-friendly and customized by the experts. 

These NCERT solutions Class 12 Maths in Hindi contain step-by-step answers to all the questions from the exercise which are considered as an invaluable aid to the students when it comes to regular study, exam preparation or doing homework. Class 12 Maths in Hindi NCERT solutions will clear all your doubts in very less time. Hence your confidence will be boosted. By practising the questions from these books, you will be able to improve your time management skills. That will help you in solving all the questions in the stipulated time frame during the final exam. 

Class 12th Maths NCERT Solutions are designed as per the latest CBSE curriculum and guidelines. Vedantu’s study materials are updated regularly as per the latest changes. Hence students of Class 12 who are referring to these materials will be able to score the best marks in the final exam. Once you start using these Math NCERT Solutions Class 12, the preparation for Class 12 exam and scoring the highest percentile amongst your peers will seem like a cakewalk at the end of the day.

With Class 12 Maths NCERT Solutions, you will have a solid foundation of all the topics that are included in the Class 12 Maths Syllabus. These solutions cover all the important formulae and theorems along with detailed explanations so that you have a better conceptual understanding. These solutions will help you prepare for your undergraduate level engineering entrance exams like BITSAT, JEE Mains, VITEEE, etc.

Vedantu Class 12th Maths NCERT Solutions have been designed by top subject matter experts of the field that facilitates a precise and smooth understanding of the concepts. With these solutions, you will have access to detailed and step-by-step explanations of all the problems given in the NCERT textbooks. Apart from the Maths NCERT Solutions Class 12 for all the chapters, we also provide you with solved example problems, previous year question papers, notes, and worksheets as study materials so that you are able to prepare for your board exams.

Chapter 1 - Relations and Functions

In this chapter, you will be learning about Relations and Functions. It is among the most important topics in Algebra. In the mathematical sense, these are two different words that have different meanings. There are many students who get confused with these terms. Relations refer to the set of inputs and outputs whereas Function is a relation where each input has one output. It is important to remember that all functions are relations, but all relations are not functions. In this chapter, you will find definition of relations and functions, their special functions, different types of relations - symmetric, reflexive, equivalence, and transitive relations, composite functions, one to one and onto functions, binary operations, and the inverse of a function.

Chapter 2 - Inverse Trigonometric Functions

The NCERT Maths Book Class 12 Solutions Pdf in Hindi Maths Chapter 2 will cover Inverse Trigonometric functions. This can be defined as inverse functions of basic trigonometric functions including sine, cosine, secant, cosecant, tangent, and cotangent functions. In this chapter, you will learn how to use inverse functions in trigonometry for getting the angle with any trigonometric ratio. Trigonometric functions is an important concept and is mostly used in the field of physics, engineering, navigation, and geometry.

Also known as Arc Functions, Inverse trigonometric functions produce the arc’s length that is needed to get a particular value. These are especially applicable to a right-angled triangle. There are six inverse trigonometric functions which include Arcsine, Arcsecant, Arccosine, Arccosecant, Arctangent, and Arccotangent. The chapter will cover definition, domain, range, principal value branch, elementary properties of inverse trigonometric functions, and graphs of inverse trigonometric functions.

Chapter 3 - Matrices

In this chapter, you will learn about Matrices and Matrix operations. The Chapter 3 Matrices in Class 12 Maths NCERT Solutions covers matrix, the rectangular array of real and complex numbers presented in the form of n vertical lines known as columns and m horizontal lines known as rows. You will also learn about the types of matrices - symmetric matrix, Hermitian and skew matrix, skew-symmetric matrix, idempotent matrix, orthogonal matrix, nilpotent matrix, and involuntary matrix. It is important to note that matrix is an arrangement of certain quantities.

There can be real or complex numbers as elements in the matrix. A real matrix is one where the matrix’ elements are real. The chapter will cover topics like concept, order, notation, types of matrices, equality, zero and identity matrix, symmetric and skew symmetric matrices, transpose of a matrix, etc. You will also learn operation on matrices - Addition, multiplication, and multiplication with a scalar. Existence of non-zero matrices where products are the zero matrix and non-commutativity of multiplication of matrices is covered as well.

Chapter 4 - Determinants

In this chapter, the NCERT Solutions for Class 12 Maths Chapter 4 Determinants will introduce you to Determinants. Determinant is a scalar value that you can calculate from a square matrix’s elements. When you solve a system of simultaneous linear equations, the development of determinants takes place, the shape of which will be square. A determinant of order n will contain n columns and n rows. A square matrix of order m x n will have a number associated with it called the determinant of a square matrix. The number of elements in the determinant of order n will be n2.

The concepts covered in this chapter will include determinants of a square matrix, minors, properties of determinants, applications and cofactors of determinants that can be used to find the area of a triangle, inverse and adjoint of a square matrix, etc. You will learn about consistency, inconsistency, solving a system of linear equations using the inverse of a matrix, and number of solutions of a system of linear equations.

Chapter 5 - Continuity and Differentiability

Chapter 5 of NCERT Solutions for Class 12 Maths is about Continuity and Differentiability. This is one of the most important chapters as you will be learning the concepts such as continuity on an interval, continuity at a point, etc. Learning differentiability of functional parameters can be very difficult. The value of function x = 0 changes suddenly. Once you find that left hand limit ≠ right hand limit, it means that the function is not continuous when x = 0. If you are able to graph it without lifting your pen, you will see that the function is continuous at a point. The function will be discontinued when the function is undefined.

The concepts covered in this chapter include continuity and differentiability, chain rule, a derivative of composite functions, derivative of implicit functions, and derivatives of inverse trigonometric functions. In these Maths NCERT Solutions Class 12, you will also learn the concept of logarithmic and exponential functions, derivatives of exponential and logarithmic functions, derivative of functions that are expressed in parametric forms, logarithmic differentiation, Lagrange’s and Rolle’s Mean Value Theorems and their geometric interpretation, and second-order derivatives.

Chapter 6 - Applications of Derivatives

In this chapter, you will be learning about the different applications of derivatives that are used in a wide range of fields like Science, Engineering, etc. Derivative is the rate of change one quantity has with respect to another. The rate of change of function can be defined as dy/dx - f(x) = y’. The ratio of dy/dx is one of the derivatives’ applications in real life. There are a lot of ways in which the concept of derivatives can be used such as for rate of change of sizes and shapes or change of temperature.

If you use the derivative function for calculating the lowest and highest point of the curve in a graph, you will know its turning point as well. The chapter will cover increasing/decreasing functions, rate of change of bodies, normals and tangents, maxima and minima (first derivative test that is motivated geometrically and second derivative test as a provable tool), use of derivatives in approximation, and simple problems that illustrative the basic understanding and principle of the subject and real-life situations.

Chapter 7 - Integrals

In this chapter, you will be learning about Integration, calculation of an integral which can be used for finding out useful quantities like displacement, areas, volumes, etc. one of the major calculus in Mathematics, Integrals are related to definite integrals in this chapter. The idea of limit is used while implementing algebra and geometry. In simple terms, Integration is a step of summing up or adding the parts to find the whole. Differentiation is the opposite of that.

There are two types of integrals - Definite and Indefinite Integrals. Indefinite integrals are defined without lower and upper limits whereas definite contains lower and upper limits. The concepts covered in this chapter are integration as inverse of differentiation, evaluating simple integrals of the types, integration of several functions by substitution, definite integrals as a limit of a sum, evaluation of definite integrals, basic properties of definite integrals, and Fundamental Theorem of Calculus.

Chapter 8 - Applications of the Integrals

This chapter from Class 12 Maths NCERT Solutions will cover differentiation and integrations, methods of calculations functions, and applications of the integrals. This concept can be applied in a wide range of fields to calculate areas like science, engineering, etc. An integral can be used for finding areas of 2-D objects and volumes of 3-D objects. Also known as the antiderivative, the integral has the opposite process of differentiation. The concepts covered in this chapter are applications in finding areas under the simple curves like lines, circles, ellipses, and parabolas in standard forms, areas bounded between any two curves where the region is clearly identifiable.

Chapter 9 - Differential Equations

In this chapter, you will be learning about differential equations, an equation containing one or more functions along with its derivatives. The function of a differential equation is the function’s rate of change at a point. This concept is used in physics, biology, engineering, and several other fields. The derivatives represent the rate of change whereas the differential equation describes the relationship between the speed of change and the quantities.

The Class 12th Math NCERT Solutions covers concepts like definition, particular and general solutions of a differential equation, order and degree, formation of differential equations when a general solution is given. You will also learn how to solve differential equations using the method of separation of variable solutions of homogeneous differential equations that are of the first degree and first order. The solutions of linear differential equations are covered in the syllabus as well.

Chapter 10 - Vector Algebra

In this chapter, you will be learning about vectors and scalars. There are certain numbers of quantities that involve magnitude and direction. Such quantities with magnitude as well as direction are known as vectors. The main use of vectors is describing physical quantities that have directions as well as magnitude. There are different types of vectors which will be covered in this chapter including Zero Vector, unit Vector, Collinear Vectors, Coinitial Vectors, Negative of a Vector, and Equal Vectors.

This chapter covers different concepts like vectors and scalars, direction and magnitude of a vector, direction ratios and direction cosines of a vector, types of vectors, negative or a vector, position vector of a point, multiplication of a vector with a scalar, addition of vectors, and vector of a point that divides the line segment in a ration. You will also learn the definition, properties, application of scalar product, and geometrical interpretation of vectors along with a scalar triple product and vector (cross) product of vectors.

Chapter 11 - Three-Dimensional Geometry

In this chapter, you will be learning about topics like direction ratios and direction cosine of a line that joins two points. Dimensional Geometry is about the angle between two lines, between a line and a plane, etc. In order to understand dimensional geometry, you must have an understanding of the different types of figures and shapes. The concepts that are covered in this chapter include direction ratios and direction cosines of a line that is joining two points, vector equation and cartesian equation of a line, skew and coplanar lines, vector and cartesian equation of a plane, the shortest distance between two lines, the angle between two planes, two lines, and a line and a plane, and the distance of a point from a plane.

Chapter 12 - Linear Programming

This is the second last chapter of Class 12 Maths NCERT Solutions where you will learn about Linear Programming. Linear Programming refers to the method of optimizing operations using some constraints. The main use of linear programming is maximizing or minimizing the numerical value. Today, linear programming is used in a wide range of Mathematical fields as well as other fields like business, manufacturing, telecommunication, and economics.

You can define Linear Programming as the problem of minimizing and maximizing a linear function. The concepts covered in this chapter include introduction, related terminology like constraints, optimization, objective function, different types of linear programming problems, graphical method of finding a solution for problems in two variables, the mathematical formulation of linear programming problems, feasible and infeasible regions (bounded and unbounded) along with feasible and infeasible solutions, and optimal feasible solutions for up to three non-trivial constraints.

Chapter 13 - Probability

This is the last chapter in Class 12 Maths NCERT Solutions where you will be learning probability and its properties. Probability can be defined as the extent to which an event is likely to occur. Probability is the number of events that can occur divided by the total number of events that occur. Its formula can be defined as the likelihood of an event to occur which is equal to the ratio of the number which results and total number of outcomes. Conditional probability can be defined as the likelihood of an outcome or an event as an occurrence of a previous outcome or event.

This chapter will cover a wide range of concepts including conditional probability, independent events, multiplication theorem on probability, total probability, random variable and its probability distribution, Bayes’ theorem, mean and variance of a random variable, Binomial distribution, and repeated independent trials (also known as Bernoulli trials).

Importance of Studying From Vedantu’s NCERT Maths Book Class 12 Solutions PDF in Hindi

If you learn and practice with Vedantu’s Class 12 Maths NCERT Solutions, you will be able to enjoy several benefits. The concepts that you study in Class 12 Maths will play an important role in helping you prepare for your board exams as well as undergraduate competition exams. With the detailed and well-described NCERT Maths Class 12 Pdf Free Download from Vedantu, you will be able to get a thorough understanding of the concepts and clear all your doubts.

It is among the best study materials available for use that will help you score better in your board exams as well as competitive exams. There are a total of 13 chapters which contain a multitude of problems. All the solutions are provided by expert math teachers and are extensively reviewed. If you learn properly and practice using this Class 12th Maths NCERT Solutions, you will be able to score good marks in your board exams. Here are the key benefits you will be able to enjoy by referring to Vedantu’s NCERT Solutions for Class 12 Maths:

1. Get Authentic Information

All the solutions that are provided in Vedantu’s Class 12 Maths NCERT Solutions have been created by experienced Maths teachers after conducting an extensive research on all the chapters. This way, they are able to provide accurate information to you.

2. Follows the CBSE Curriculum

NCERT textbooks are the best study material to prepare for your board exams. That is why we have created solutions that strictly follow the CBSE curriculum.

3. Prepare for the Board Exams

When you are giving your board exams, it is important that you write your answers in a format that can be comprehended easily by the person who is correcting them. All the Class 12th Maths NCERT Solutions provided by Vedantu have a clear, stepwise explanation that will give you an insight into solving any sum. There are certain marks allotted to each step. So, if you follow the pattern given in these NCERT Maths Book Class 12 Solutions Pdf in Hindi, you will score better.

4. Clear Your Concepts and Logic

With Vedantu’s NCERT Maths Class 12 Pdf Free Download, you will be able to make your concepts crystal clear. Once you have an in-depth understanding of the concepts, you won’t have to read the same stuff over and over again.

5. Easy Revision

The solutions have been designed in a way that will help you quickly revise before your examination. During your exam days, you already have a cramped schedule and there is no way you can solve the questions from your textbook. In such situations, these solutions can help you get a way of having a quick overview of the different types of problems and their solutions. It will help you save a lot of time.

6. Save Some Preparation Time

These are well-defined solutions and if you prepare with them, you will be able to save some revision time as you will have all the necessary formulae and logic in a proper way.

Tips to Prepare Better for Class 12 Maths Exam

1. Know the Exam Pattern

Before you start preparing, you should know the exam pattern as it will help you know what chapters you have to focus on more. You should visit the official website of CBSE to get the latest information. 

2. Go Through the Entire Syllabus

If you have the right preparation strategy that works for you, you will be able to ace your mathematics exam. Apart from learning about the exam pattern, you should also review the syllabus provided by the CBSE. Then, you can start working on a study plan that covers all the topics and concepts. If you want to score well, you have to go through the complete NCERT textbook. Remember that CBSE sets the paper based on the concepts given in the NCERT book and all the questions will be directly or indirectly from it.

3. Check out the Sample Papers

Every academic year, CBSE publishes a few sample papers. You can use these sample papers not only for practice, but also for determining how you will be writing in the actual exam. You can download these papers from the official website of CBSE and practice from them regularly. You can also practice from the sample papers provided by CBSE.

4. Create Hand-Written Notes

In order to master the subject, it is important that you learn and remember all the theories, formulae, and concepts by heart. Apart from the concepts that you learned in this class, you should also know the formulae from previous classes as they are equally relevant. Make a separate copy that contains all the theories, formulae, and methods using the NCERT Maths Class 12 Pdf Free Download you might need for your last-minute revision.

5. Create a Personalized Time Table

You have to give time to all the subjects in your time table. Focusing on one subject for a long time will become boring and monotonous for you. You have to mix and match all the subjects. Solve different kinds of questions every day. Remember that in order to score well in Maths, you have to not only get the right answer, but also show your work. Only then will you get the full marks.

6. Clear Your Doubts

Write all the difficult concepts and mathematical doubts you have. As long as you are able to solve questions efficiently, maths will be very interesting. But, if you get stuck, you might start to lose interest. To clear your concepts, you have to practice all kinds of questions. Self-evaluate to find your weak points and it will help you improve your marks.

7. Take Breaks Between Sessions

After every 2 to 3 hours, you should take a break. During this time, avoid playing games, using your phone, or watching television as it will strain your eyes. Instead, you can play some indoor or outdoor games that will refresh your body and mind. Don’t give up on activities you like as it will help you concentrate better.

8. Practice as Much as You Can

The key to scoring better in Maths is practice. As your exam approaches, increase the frequency of solving sample papers, previous years’ question papers, and mock tests. You should solve at least one question paper every day within the time frame of 3 hours. It will not only increase your speed but also make you familiar with the kind of questions that are asked in the exam. You will get insights on the important topics for the board exams and your preparation level. Once you have solved the paper, go through the details of the answer. Check the subject toppers’ answer sheets as it will help you know what the correct way of writing the answers is. Remember that the more you practice, the better score you will be able to get.

Significance of NCERT Maths Book Class 12 in Hindi Solutions

There are 13 chapters in the Class 12 Maths syllabus that will need the utmost attention from the students. All the chapters are important to study to cover the syllabus and to score well in the exams.

To make the preparations better, the study material will need the exercise solutions too. This is where the experts of Vedantu have designed the solutions in a Chapter Wise List of Class 12 Maths in Hindi. Students can find the solutions for respective chapters easily and follow the solutions given by the subject experts.

These solutions can be used as the ideal study material to complete solving all the exercises of chapters included in the syllabus. The precise and easy language of the answers will explain how to attempt to solve certain questions in a stepwise method. Hence, these solutions will act as the perfect guide for the complete preparation of the chapters.

Referring to the 12th Maths in Hindi Book Answers will also aid students to understand the concepts easily and learn how to apply them to frame accurate answers.

Benefits of NCERT Maths Book Class 12 in Hindi Solutions

• The exercises of each chapter have been addressed to formulate an individual file for the convenience of the students.

• The files can be downloaded from the given list according to your academic requirements. Once downloaded, you can access the files according to your study sessions.

• Use the solutions files to find the right answers to study and complete preparing a chapter before time.

• Resolve doubts related to the chapter exercises faster and make your preparation more efficient. Find out which chapters need more attention from your end to take your preparation to the next level.

• Assessing your answering skills will become a lot easier when you can compare your answers to the solutions. Learn to answer maths questions accurately from the solutions.

Download NCERT Maths Book Class 12 in Hindi Solutions PDF

Perform the NCERT Maths Book Class 12 in Hindi Solutions PDF free download easily and add them to your study material. Follow how the exercise questions have been answered following the ideal techniques to practise and score more in the exams. Develop your mathematics skills and stay ahead of the competition. 

NCERT Solutions for Class 12 Books

• NCERT Solutions for Class 12 Maths

• NCERT Solutions for Class 12 Physics

• NCERT Solutions for Class 12 Chemistry

• NCERT Solutions for Class 12 Biology

• NCERT Solutions for Class 12 English

• NCERT Solutions for Class 12 Business Studies

• NCERT Solutions for Class 12 Economics

• NCERT Solutions for Class 12 Accountancy