NCERT Solutions for Class 12 Maths - PDF Download

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Why NCERT Solutions for Class 12 Maths Matter for Boards and JEE 

Class 12 NCERT Mathematics is the single most important textbook for students preparing for both the CBSE Board exam and undergraduate engineering entrance exams like JEE Main, BITSAT, and VITEEE. Here is why:

For CBSE Boards: The entire Board exam question paper is set from the NCERT syllabus. Students who have solved every NCERT exercise thoroughly — and understood the solution method, not just the answer — consistently perform better in boards than those who rely solely on guidebooks.

For JEE Main: A significant portion of JEE Main Mathematics directly tests NCERT-level concepts, especially in chapters like Probability, Matrices, Determinants, Vector Algebra, and Three-Dimensional Geometry. Students who have solved NCERT exercises before moving to advanced JEE material build stronger conceptual foundations.

The critical distinction: Reading NCERT is not enough. Working through the exercises — and comparing your approach with verified, step-by-step solutions when you are stuck — is what builds the problem-solving skill that exams test.

💡 Expert Tip by eSaral Mathematics Faculty, IIT Kota: "Every year, students ask how to improve their Board Maths score. The answer is always the same: solve every NCERT exercise completely, understand each step, and then try the NCERT Exemplar. Students who do this reliably score 90+ in boards. The same NCERT foundation also carries them through JEE Main's direct concept questions — especially in Calculus, Vectors, and Probability."

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

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 non-trivial constrains).

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 ready-made 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

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