CBSE has published the revised Class 12 Maths NCERT Solutions for 202122. Class 12 maths NCERT solutions PDF provides the conceptual foundation for all chapters of Class 12 Maths. The NCERT textbook has 13 major chapters. Each concept is explained clearly for students to understand. Going through the CBSE Maths NCERT Solutions will help students score well.
These Class 12 Maths solutions will also help clear the most challenging engineering entrance exams such as JEE Main, JEE Advanced, BITSAT etc. The top Maths teachers of Embibe solve all the NCERT Solutions for Class 12 Maths provided. Each question of CBSE NCERT Solutions for Class 12 Maths comes with detailed stepwise solutions. This article will provide you with the downloadable PDF of NCERT Solutions for Class 12 Maths for all the chapters.
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Table of Contents
 NCERT Solutions for Class 12 Maths Chapterwise PDF
 CBSE Class 12 Maths Unitwise Weightage for Term I
 Why Refer to NCERT Solutions for Class 12 Maths from Embibe?
 Maths Class 12 NCERT Solutions (Chapterwise)
 NCERT Solutions for Class 12 Maths: Chapter Descriptions
 How To Get Good Marks in Class 12 Maths?
 Some Important Questions for 12th Class Maths
 FAQs
NCERT Solutions for Class 12 Maths Chapterwise PDF
Students can download all the NCERT Solutions of Maths Class 12 provided on this page for free. Working on NCERT Class 12 Maths solutions will not only help clear your basics but will also help in improving your problemsolving abilities. Click on Class 12 Maths NCERT Chapterwise links/12th Maths Solution Book PDF.
To download the solutions as PDF, you can visit the chapterwise link and download the Class 12 Maths NCERT solutions PDF from there for free. For the 202122 academic session, CBSE has divided the curriculum into two terms – term I and term II. In the first term, there are 7 chapters, while there are only 6 chapters in the second term. The termwise NCERT solutions for 202122 are provided in the table below:
NCERT Solutions for Class 12 Maths Term – I 202122 
1st Chapter – Relations and Functions 
2nd Chapter – Inverse Trigonometric Functions 
3rd Chapter – Matrices 
4th Chapter – Determinants 
5th Chapter – Continuity and Differentiability 
6th Chapter – Application of Derivatives 
12th Chapter – Linear Programming 
NCERT Solutions for Class 12 Maths Term – II 202122 
7th Chapter – Integrals 
8th Chapter – Application of Integrals 
9th Chapter – Differential Equations 
10th Chapter – Vector Algebra 
11th Chapter – Three Dimensional Geometry 
13th Chapter – Probability 
CBSE Class 12 Maths Unitwise Weightage for Term I
No. 
Units 
Marks 
I 
Relations and Functions 
08 
II 
Algebra 
10 
III 
Calculus 
17 
V 
Linear Programming 
05 
Total 
40 

Internal Assessment 
10 

Total 
50 
Internal Assessment Class 12 Term I
Internal Assessment  Marks 
Periodic Tests  05 Marks 
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva  05 Marks 
Total Marks  10 Marks 
Unit 
Unit Name 
Marks 
III 
Calculus 
18 
IV 
Vectors and ThreeDimensional Geometry 
14 
VI 
Probability 
08 
Total 
40 

Internal Assessment 
10 

Total 
50 
Internal Assessment Class 12 Term II
Internal Assessment  Marks 
Periodic Tests  05 Marks 
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva  05 Marks 
Total Marks  10 Marks 
Why Refer to NCERT Solutions for Class 12 Maths from Embibe?
The advantages of using NCERT Solutions Class 12 Maths by Embibe are listed below:
 All CBSE NCERT Solutions for Class 12 Maths are provided in PDF form which can be downloaded for free by anyone, anywhere.
 Referring to the Class 12 Maths NCERT Solutions will help students understand all basic and fundamental concepts.
 As most of the engineering competitive exam syllabus such as JEE Main, JEE Advanced, BITSAT is almost the same as CBSE Class 11 and 12 Maths Syllabus. So, having a good command over the NCERT Solutions for Class 12 Maths will definitely help to clear the competitive exams easily.
 The CBSE NCERT Solutions will help students to solve their homework and assignments on time without any difficulty.
Maths Class 12 NCERT Solutions (Chapterwise)
Class 12 is a significant turning point in your life since it allows you to make crucial decisions about your future depending on your academic achievement. Indeed, mathematics is an important part of the Class 12 curriculum and the syllabus of all competitive exams. Whether you want to be an engineer or a doctor, you will have to deal with math in every aspect of your life. Making Class 12 concepts tangible will greatly assist you in achieving high results in the CBSE Class 12 board exam as well as other competitive examinations. CBSE NCERT Solutions for Class 12 Maths are essential for exam preparation since they include thorough chapterbychapter solutions to all problems.
First and foremost, you should remember that NCERT books are the most powerful tool you can use to learn the foundations. This will ensure that you do not overlook any important questions throughout your exam preparation.
The advantages of using Class 12 CBSE Maths NCERT Solutions are not limited to math performance; they also build the groundwork for other crucial courses. Understanding the derivations and concepts underlying the mathematics of Science may be greatly aided by having a firm grasp of the detailed details of specific math chapters such as calculus, differential equations, and so on. Every chapter of the CBSE Class 12th NCERT Maths Solutions PDF is available for free download.
Each exercise’s solutions have been chosen and approved by some of India’s top teachers. It contains all of the solutions to the problems from the NCERT Mathematics textbook’s 13 most significant chapters. Differentiation, Integration, Algebra, and other topics are covered in detail in Class 12 Maths NCERT Solutions. The chapters are organised in a logical and linear manner, allowing you to grasp the topics quickly.
NCERT Solutions for Class 12 Maths: Chapter Descriptions
All the Maths class 12 NCERT PDF solutions we have provided on this page are solved by the top Maths teachers of Embibe. Each Class 12 Maths NCERT Solution comes with a detailed stepwise explanation so that students get clarity on the topic. Download Maths Class 12 NCERT Solutions PDF for free and access them in offline mode as well.
Students can go through the description of each chapter to get an overview of the contents of the chapters. The chapterwise description has been included in the following sections. To download the NCERT Solutions PDF for each chapter, click on the link given at the end of the following sections.
Practice 12th CBSE Exam Questions
Chapter 1: Relations and Functions
The term ‘relation’ in Mathematics has been drawn from the meaning of relationships in the English language, according to which two objects or quantities are related if there is a recognizable connection or link between the two objects or quantities.
In Class 12 Chapter 1, you will learn about different types of relations and functions, the composition of functions, invertible functions, and binary operations. The subtopics along with the answer pdf are listed below:
 – 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
Exercise 1.1  16 Questions  Download Answers PDF 
Exercise 1.2  12 Questions  
Exercise 1.3  14 Questions  
Exercise 1.4  13 Questions 
Chapter 1: Relations and Functions – Download NCERT Solutions PDF
Chapter 2: Inverse Trigonometric Functions
In this chapter, you will study the restrictions on domains and ranges of trigonometric functions that ensure the existence of their inverses and observe their behaviour through graphical representations. Besides, some elementary properties will also be discussed. The inverse trigonometric functions play an important role in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions are used in science and engineering. The subtopics in this chapter are listed below:
 – 2.1 Introduction
 – 2.2 Basic Concepts
 – 2.3 Properties of Inverse Trigonometric Functions
Exercise 2.1  14 Questions  Download Answers PDF 
Exercise 2.2  21 Questions 
Chapter 2: Inverse Trigonometric Functions – Download NCERT Solutions PDF
Chapter 3: Matrices
In this chapter, you will learn about the fundamentals of matrix and matrix algebra. The subtopics in this chapter are listed below:
 – 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
Exercise 3.1 
10 Questions 

Exercise 3.2 
22 Questions 

Exercise 3.3 
12 Questions 

Exercise 3.4 
18 Questions 
Chapter 3: Matrices – Download NCERT Solutions PDF
Chapter 4: Determinants
The determinant is a scalar value that can be measured from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix A is denoted det(A), det A, or A. In the case of a 2 × 2 matrix, the determinant may be defined as:
Similarly, for a 3 × 3 matrix A, its determinant is:
So in this chapter, you will study determinants up to order three only with real entries. The subtopics in this chapter are listed below:
 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
Exercise 4.1 
8 Questions 

Exercise 4.2 
16 Questions 

Exercise 4.3 
5 Questions 

Exercise 4.4 
5 Questions 

Exercise 4.5 
18 Questions 

Exercise 4.6 
16 Questions 
Chapter 4: Determinants – Download NCERT Solutions PDF
Check CBSE Class 12 Detailed Syllabus Here
Chapter 5: Continuity And Differentiability
In this chapter, we will learn everything about the Continuity and Differentiability of a function. In this chapter, students will learn about the very important concepts of continuity, differentiability, and relations between them.
You will also learn the differentiation of inverse trigonometric functions. Further, this chapter introduces a new class of functions called exponential and logarithmic functions. The subtopics in this chapter are listed below:
 – 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
Exercise 5.1 
34 Questions 

Exercise 5.2 
10 Questions 

Exercise 5.3 
15 Questions 

Exercise 5.4 
10 Questions 

Exercise 5.5 
18 Questions 

Exercise 5.6 
11 Questions 

Exercise 5.7 
17 Questions 

Exercise 5.8 
6 Questions 
Chapter 5: Continuity and Differentiability – Download NCERT Solutions PDF
Chapter 6: Application of Derivatives
In the chapter Continuity and Differentiability, you have learned how to find a derivative of composite functions, inverse trigonometric functions, implicit functions, exponential functions, and logarithmic functions. In this chapter, you will study applications of the derivative in various disciplines, e.g., in engineering, science, social science, and many other fields.
You will also use the derivative to find intervals on which a function is increasing or decreasing. Finally, here you will use the derivative to find the approximate value of certain quantities. The subtopics in this chapter are listed below:
 – 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
Exercise 6.1 
18 Questions 

Exercise 6.2 
19 Questions 

Exercise 6.3 
27 Questions 

Exercise 6.4 
9 Questions 

Exercise 6.5 
29 Questions 
Chapter 6: Application of Derivatives – Download NCERT Solutions PDF
Chapter 7: Integrals
Differential Calculus is centred on the concept of the derivative. Integral Calculus is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions. The subtopics in this chapter are listed below:
 – 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
Exercise 7.1 
22 Questions 

Exercise 7.2 
39 Questions 

Exercise 7.3 
24 Questions 

Exercise 7.4 
25 Questions 

Exercise 7.5 
23 Questions 

Exercise 7.6 
24 Questions 

Exercise 7.7 
11 Questions 

Exercise 7.8 
6 Questions 

Exercise 7.9 
22 Questions 

Exercise 7.10 
10 Questions 

Exercise 7.11 
21 Questions 
Chapter 7: Integrals – Download NCERT Solutions PDF
Chapter 8: Application Of Integrals
In this chapter, you will study a specific application of integrals to find the area under simple curves, area between lines and arcs of circles, parabola, and ellipses (standard forms only). We shall also deal with finding the area bounded by the abovesaid curves. The subtopics in this chapter are listed below:
 – 8.1 Introduction
 – 8.2 Area under Simple Curves
 – 8.3 Area Between Two Curves
Exercise 8.1 
13 Questions 

Exercise 8.2 
7 Questions 
Chapter 8: Application of Integrals – Download NCERT Solutions PDF
Chapter 9: Differential Equations
In this chapter, we will study some basic concepts related to the differential equation, general and particular solutions of a differential equation, formation of differential equations, some methods to solve a firstorder – firstdegree differential equation, and some applications of differential equations in different areas. The subtopics in this chapter are listed below:
 – 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
Exercise 9.1 
12 Questions 

Exercise 9.2 
12 Questions 

Exercise 9.3 
12 Questions 

Exercise 9.4 
23 Questions 

Exercise 9.5 
17 Questions 

Exercise 9.6 
19 Questions 
Chapter 9: Differential Equations – Download NCERT Solutions PDF
Chapter 10: Vector Algebra
In this chapter, we will study some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties. When considered together, these two types of properties give a full realization to the concept of vectors and lead to their vital applicability in various areas. The subtopics in this chapter are listed below:
 – 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
Exercise 10.1 
5 Questions 

Exercise 10.2 
19 Questions 

Exercise 10.3 
18 Questions 

Exercise 10.4 
12 Questions 
Chapter 10: Vector Algebra – Download NCERT Solutions PDF
Chapter 11: Three Dimensional Geometry
In this chapter, we shall study the direction cosines and direction ratios of a line joining two points and also discuss the equations of lines and planes in space under different conditions, the angle between two lines, two planes, a line and a plane, the shortest distance between two skew lines and distance of a point from a plane. Most of the above results are obtained in vector form. The subtopics in this chapter are listed below:
 – 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
Exercise 11.1 
5 Questions 

Exercise 11.2 
17 Questions 

Exercise 11.3 
14 Questions 
Chapter 11: Three Dimensional Geometry – Download NCERT Solutions PDF
Chapter 12: Linear Programming
In this chapter, we shall apply the systems of linear inequalities/equations to solve some reallife problems. Also, we shall study some linear programming problems and their solutions by graphical method only, though there are many other methods to solve such problems. The subtopics in this chapter are listed below:
 – 12.1 Introduction to Linear Programming
 – 12.2 Linear Programming Problem and its Mathematical Formulation
 – 12.3 Different Types of Linear Programming Problems
Exercise 12.1 
10 Questions 

Exercise 12.2 
11 Questions 
Chapter 12: Linear Programming – Download NCERT Solutions PDF
Chapter 13: Probability
In this chapter, we shall discuss the important concept of the conditional probability of an event given that another event has occurred, which will help understand the Bayes’ theorem, multiplication rule of probability, and independence of events.
We shall also learn an important concept of a random variable, its probability distribution, and the mean and variance of a probability distribution. The subtopics in this chapter are listed below:
 – 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
Practice 12th CBSE Exam Questions
Exercise 13.1 
17 Questions 

Exercise 13.2 
18 Questions 

Exercise 13.3 
14 Question 

Exercise 13.4 
17 Questions 

Exercise 13.5 
15 Questions 
Chapter 13: Probability – Download NCERT Solutions PDF
How To Get Good Marks in Class 12 Maths?
Students can follow the tips listed below to get better at the subject and improve their score:
 First and most important is the regular practice of problems and exercises. You cannot get good marks in Maths if you do not practice regularly.
 You should be thorough with the syllabus of CBSE Class 12 Maths. You should be familiar with all the concepts and topics in every chapter.
 Start your preparation with the NCERT Class 12 Maths textbook. Once you are done with the NCERT textbook, you can pick up a reference book of your choice for practice.
 Solve all the exercises at the end of each chapter. Refer to the NCERT solutions for Class 12 Maths if you are stuck on a problem.
 Give special attention to the chapters/concepts that you find difficult. Do not skip any chapter or topic.
 Take timed mock tests to improve your speed and accuracy.
 Solve previous years’ question papers to understand what kind of questions are asked in the final exam.
Some Important Questions for 12th Class Maths
Below we have provided some important questions that will aid you in understanding the chapters as well as help you in scoring better:
1. Let f : N → Y be a function defined as f (x) = 5x + 2, where, Y = {y ∈ N: y = 5x + 2 for some x ∈ N}. Show that f is invertible. Find the inverse. 
2. Find the value of cos^{1} (1/2) + 2 sin^{1} (1/2) 
3. Verify the mean value theorem for the following function f (x) = (x – 4) (x – 8) (x – 12) in [4, 6] 
4. Using matrix method, solve the system of equations 2x + 3y – 2z = 3, x + 3y + 2z = 6 and 3x – 2y + z = 2. 
5. A circular disc of radius 4 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 5.2 cm. 
6. Find the value of ∫tan^{8}x sec^{4} x dx 
7. Determine the area of the region bounded by y^{2} = 8x, x = 3, x = 2 and the xaxis in the first quadrant. 
8. Find the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constants. 
9. Find the vector joining the points P(3, 4, 0) and Q(– 2, – 4, – 5) directed from P to Q. 
10. If a line makes an angle of 80°, 120°, 65° with the x, y, and zaxes, respectively, determine its direction cosines. 
11. There are 5 cards numbered 1 to 5 with one number on each card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on two cards drawn. Find the mean and variance of X. 
12. The probability of solving a specific problem independently by persons A and B are 1/2 and 1/3, respectively. If both of them try to solve the problem independently, then calculate the probability that the problem is solved. 
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Learn & Practice Lessons Online With Embibe
At Embibe, you can solve free Class 12 Practice Questions for Science and Maths or take free Class 12 Mock Tests. These tests and practice questions will help you to strengthen your concepts and problemsolving abilities. Students can follow the steps listed below to take a Class 12 mock test or practice questions:
 – 1st Step: Visit embibe.com. To have the best experience, log in to your account. If you are visiting the site for the first time, register yourself.
 – 2nd Step: At the time of registration, you need to select your goal. Choose your board for example, “CBSE” then “12th CBSE”, and click on “Done”.
 – 3rd Step: To practice questions for Class 12 CBSE, click on “Practice” option at the top. If you want to take a mock test, click on “Test” option.
 – 4th Step: Select the subject as “Mathematics” as you want to take the test/practice questions for Maths.
 – 5th Step: Click on the chapter name for which you want to practice questions. Then click on ‘Practice Now’ to start practising questions.
 – 6th Step: If you want to take mock tests for any subject, you have the option to take chapterwise tests or full subject tests. Click on any test link and then click on “Start Test” to start the test.
FAQs
Some of the frequently asked questions on NCERT Solutions for Class 12 Maths are listed below:
Q1. How NCERT Solutions for Class 12 Maths can help me in improving my score?
A1. The NCERT solutions include all the details in an easy and stepwise manner. Hence, you will easily understand the problems. With the help of these solutions, you can revise the syllabus quickly. They are available both offline and online and thus, you can access them anytime you want.
Q2. Is NCERT enough for Class 12 boards?
A2. As per CBSE guidelines, NCERT books and NCERT solutions for Class 12 are enough for the board exam, but students can still practice from other reference books to widen their level of understanding.
Q3. Is the NCERT Mathematics textbook enough for Class 12 exam preparation?
A3. According to many teachers and experts, the NCERT Mathematics textbook is sufficient to clear Class 12 Maths exams. However, students can also refer to other textbooks if they are aiming for the top marks.
Q4. Which book is the best for the Class 12 Maths exam preparation?
A4. Many experts consider the NCERT Mathematics textbook the best book for the Class 12 exam preparation.
Q5. How many chapters are there in Class 12 Maths?
A5. There are a total of 13 chapters in Class 12 Maths.
Q6. Which is the best app for NCERT Solutions?
A6. Embibe’s app is the best app for NCERT Solutions where students can get access to all chapterwise and termwise study material to pass the NCERT exams with flying colours.
Attempt 12th CBSE Exam Mock Tests
So, now you have all the NCERT Solutions for Class 12 Maths. Make the best use of these resources. It will help you in your board exam as well as in engineering entrance exams like JEE Main and Advanced.
We hope this article has been helpful to you. If you have any queries/doubts, leave them in the comment section below, and we will get back to you at the earliest.
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