NCERT Solutions for Class 12 Maths  PDF Download
JEE Mains & AdvancedFor students like you who are taking the JEE as well as several board exams, NCERT Solutions for Class 12 Math has been published by eSaral. It offers thorough knowledge and comprehension of all important concepts presented in each chapter of the NCERT textbook for class 12 Math. The NCERT textbook of class 12 math contains 13 major chapters. For a clear and precise understanding of the topics, eSaral presents NCERT Solutions for Class 12 Math. These solutions are created by our subject experts. In addition to the Class 12 Maths solutions for each chapter, There are problems and detailed solutions of these problems have been provided. The answers are developed by the top educators of eSaral to help students in better and quicker understanding of the concepts.The problems in these NCERT Class 12 Solutions are thoroughly explained stepbystep.
NCERT Solutions for Class 12 Math gives a strong conceptual foundation for each topic. For students to have a better conceptual understanding of the material, it thoroughly covers all the key theorems and formulas. Students can prepare for undergraduate engineering admission examinations like JEE Mains, BITSAT, VITEEE, and others with the help of NCERT Solutions for Class 12 Maths.
There are 13 chapter in class 12 Maths NCERT book which are listed below:
 Chapter 1 : Relations and Functions
 Chapter 2 : Inverse Trigonometric Functions
 Chapter 3 : Matrices
 Chapter 4 : Determinants
 Chapter 5 : Continuity and Differentiability
 Chapter 6 : Applications of Derivatives
 Chapter 7 : Integrals
 Chapter 8 : Application of Integrals
 Chapter 9 : Differential Equations
 Chapter 10 : Vector Algebra
 Chapter 11 : Three Dimensional Geometry
 Chapter 12 : Linear Programming
 Chapter 13 : Probability
Chapter 1: Relations and Functions
Chapter 1 of class 12 NCERT Maths textbook deals with Relations and Functions. Here, you will find exercise solution link for all the topics in this chapter.
Topics covered in chapter 1 are listed below:

Types of Relations: Reflexive, Symmetric, transitive and equivalence relations.

One to one and onto textbook

Composite functions

Inverse of a function

Binary operations
Chapter 2: Inverse Trigonometric Functions
Chapter 2 of class 12 NCERT Maths textbook deals with Inverse Trigonometric Functions. Here, you will find exercise solution link for all the topics in this chapter.
Topics covered in chapter 2 are listed below:

Definition

Range

Domain

Principle value branches

Graphs of inverse trigonometric functions
Chapter 3: Matrices
Chapter 3 of class 12 NCERT Maths textbook deals with matrices. Here, you will find exercise solution link for all the topics in this chapter.
Topics covered in chapter 3 are listed below:

Concept

Notation, order, equality

Types of matrices

Zero matrix

Transpose of a matrix

Symmetric and skew symmetric matrices

Addition, multiplication and scaler multiplication of matrices

Simple properties of addition, multiplication and scalar multiplication

Non Commutativity of multiplication of matrices

Concept of elementary row and column operations
Chapter 4: Determinants
Chapter 4 of class 12 NCERT Maths textbook deals with determinants. Here, you will find exercise solution link for all the topics in this chapter
Topics covered in chapter 4 are listed below:

Determinant of a square matrix

Properties of determinants

Minors and cofactors

Applications of determinants in finding the area of a triangle

Adjoint and inverse of a square matrix

Consistency, inconsistency and number of solutions of system in linear equations

Solving a system of linear equations in two or three variables using inverse of matrix.
Chapter 5: Continuity and Differentiability
Chapter 5 of class 12 NCERT Maths textbook deals with continuity and Differentiability. Here, you will find exercise solution link for all the topics in this chapter
Topics covered in chapter 5 are listed below:

Definition of continuity and differentiability

Derivative of composite functions

Chain rule

Derivatives of inverse trigonometric functions

Derivative of implicit functions

Concept of exponential and logarithmic functions and their derivatives

Logarithmic differentiation

Derivative of functions expressed in parametric forms

Second order derivatives

Rolle’s and lagrange’s mean value theorems
Chapter 6: Applications of Derivatives
Chapter 6 of class 12 NCERT Maths textbook deals with Application of derivatives.
Topics covered in chapter 6 are listed below:

Rate of change

Increasing and decreasing functions

Tangents and normals

Approximation

Maxima and minima
Chapter 7: Integrals
Chapter 7 of class 12 NCERT Maths textbook deals with Integrals.
Topics covered in chapter 7 of class 12 are listed below:

Definition of indefinite integral

Integration as an inverse process of differentiation

Geometrical interpretation of indefinite integral

Properties of indefinite integral

Comparison between differentiation and integration

Methods of integration such as integration by substitution

Integration using partial fractions

Integrations by parts

Integrations using trigonometric identities

Definite and meaning of definite integrals

Definite integrals as the limit of a sum

Fundamental theorem of calculus

Evaluation of definite integral by substitution
Chapter 8: Application of Integrals
Chapter 8 of class 12 NCERT Maths textbook deals with Application of derivatives.
Topics covered in chapter 8 are listed below:

Applications in finding the area under simple curves

Arcs of circles/parabolas/ellipses (in standard form only)

Area of the region bounded by a curve and a line
NCERT Solutions for Class 12 Maths Chapter 8  Application of Integrals All Exercises 

Exercise 8.1 
Chapter 9: Differential Equations
Chapter 9 of class 12 NCERT Maths textbook deals with Differential Equations.
Topics covered in chapter 9 are listed below:

Degree of a differential equation

Order of a differential equation

General and particular solutions of a differential equation.

Formation of differential solution whose general solution is given

Solution of differential equations by method of separation of variables

Homogeneous differential equations of first order and first degree
Chapter 10: Vector Algebra
Chapter 10 of class 12 NCERT Maths textbook deals with Vector Algebra.
Topics covered in chapter 10 of class 12 maths are listed below:

Vectors and scalars

Magnitude and direction of a vector

Direction cosines/ratios of vectors

Types of vectors (equal, unit, zero, parallel and collinear vectors)

Position vector of a point, negative of a vector, components of a vector

Addition of vectors, multiplication of a vector by a scalar

Position vector of a point dividing a line segment in a given ratio

Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.
Chapter 11: Three Dimensional Geometry
Chapter 11 of class 12 NCERT Maths textbook deals with Vector Algebra.
Topics covered in chapter 10 of class 12 are listed below:

direction cosines and direction ratios of a line

relation between the direction cosines of a line

direction cosines of a line passing through two points

equation of a line in space

equation of a line through a given point and parallel to a given vector

derivation of cartesian form from vector form

equation of a line passing through two given points

angle between two lines, shortest distance between two lines, distance between two skew lines

distance between two parallel lines, plane in cartesian form, equation of a plane in a normal form

equation of a plane perpendicular to a given vector and passing through a given point, equation of a plane passing through three non collinear points

intercept form of the equation of a plane, plane passing through the intersection of two given planes,

coplanarity of two lines

angle between two planes, distance of a point from a plane, angle between a line and a plane
Chapter 12: Linear Programming
Chapter 12 of class 12 NCERT Maths textbook deals with Linear Programming. It covers topics such as linear programming problems and their mathematical formulae, the mathematical formulae of the problem to be solved, the graphical approach to solving the linear programming problem, and various types of the linear programming problem with various examples. Furthermore, students can find exercises that adequately explain these concepts with solutions.
Topics covered in chapter 12 are listed below:

Introduction

related terminology such as constraints, objective function, optimization

different types of linear programming (L.P.) problems

mathematical formulation of L.P. problems

graphical method of solution for problems in two variables

feasible and infeasible regions

optimal feasible solutions (up to three nontrivial constrains).
NCERT Solutions for Class 12 Maths Chapter 12  Linear Programming 

Exercise 12.1 
Chapter 13: Probability
This chapter is all about probability. We'll go over the basics and formulas we looked at in class 11, and we'll do the same in this chapter with the new ideas we've learned.
Topics covered in chapter 13 are listed below:

Multiplication theorem on probability

Conditional probability

independent events

total probability

Baye’s theorem

Random variable and its probability distribution

mean and variance of haphazard variable

Repeated independent (Bernoulli) trials

Binomial distribution
Key Benefits of CBSE Class 12 Maths NCERT Solutions from eSaral
CBSE Class 12 Mathematics NCERT solutions from eSaral provide several advantages for students preparing for board and competitive exams. Some of the main advantages of NCERT solutions are:
Complete Coverage: All topics and chapters prescribed by CBSE Class 12 Syllabus are covered in NCERT solutions. Students will have access to a complete set of study material to help them prepare for their exams effectively.
Accurate & Verified Answers: NCERT solutions are provided by subject matter experts to ensure accuracy and reliability of answers. Students can depend on these solutions for getting the correct approach to solve problems.
Understanding Concepts: NCERT solutions provide step by step explanations for each problem to help students understand the basic concepts and improve their problem solving skills.
Save time and effort: Having a readymade solution saves students’ time since they don’t have to guess the answers themselves. They can use the extra time for revision and practicing.
Practice & revision: Using NCERT solutions helps students practice and revise. Students can try a variety of problems to strengthen their understanding of different concepts.
Exam preparation: CBSE board examinations are based on NCERT textbooks. Practicing with solutions helps students get familiar with the question format and marking system.
Homework & Assignments. NCERT solutions are useful for completing homework & assignments on time. Students can refer to NCERT solutions whenever they encounter challenging questions.
Higher Performance: With regular practice, students improve their problem solving skills, which helps them perform better in exams & other competitive tests
Frequently Asked Questions
Question 1: Why is a Class 12 maths book important for engineering exams?
Answer 1: The importance of a Class 12 Maths book for engineering exams can be summarised as follows:

Save Time & Effort: Students can save time and effort by having readymade solutions as they don’t have to work on their own. They can use the extra time to revise and practice.

Practice & revision: Using NCERT solutions helps students practice and revise. Students can try a variety of problems to strengthen their understanding of different concepts.

Exam preparation: CBSE board examinations are based on NCERT textbooks. Practicing with solutions helps students get familiar with the question format and marking system. Homework & Assignments NCERT solutions are useful for completing homework & assignments on time. Students can refer to NCERT solutions whenever they encounter challenging questions.

Clarification: Students may face doubts and misconceptions while studying independently. By using NCERT solutions, they can get clarity on their doubts. Higher Performance: With regular practice, students improve their problem solving skills, which helps them perform better in exams & other competitive tests
Question 2: How can students use NCERT solution effectively?
Answer: In order to effectively utilize NCERT Solutions, students must first solve the exercises on their own and then compare their answers to the solutions provided. Students should also analyse solution steps to understand the problem solving methods.
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