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# NCERT Solutions for Class 12 Maths

NCERT Solutions for Class 12 Maths are prepared by our experienced teachers, which are based on the latest syllabus approved by CBSE. As per the official syllabus, the Class 12 Maths comprises 13 chapters. Each of the chapters consists of comprehensive exercises that not only cover all concepts of the chapter but also cover all possible question types that can be asked in  the exam. Our NCERT Solutions for Class 12 answer all questions of all the exercises of all chapters simply, accurately, and logically in a step by step manner to help you learn quickly and effectively.

These chapters are Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives, Integrals, Application of Integrals, Vector Algebra, Probability, Linear programming, Three Dimensional Geometry, and Differential Equations.

Our NCERT Solutions make the best study companion for efficient learning, revising and practising sessions during your CBSE Class 12 Maths exam. They give ample practice to become thorough with the chapter and strengthen your conceptual base. With the facility to learn from anywhere and anytime, you can now perform well both in your board exams and various competitive exams. They have been devised to make learning fascinating, stimulating and highly productive.

Class 12

## Chapter-wise NCERT Solutions for Class 12 Maths

CBSE Class 12 Maths book solutions will cover all the major topics and subtopics of Class 12 Maths syllabus. Our experts have followed a well-structured format to explain all the concepts to save you a lot of time and effort. NCERT Class 12 Maths solutions consists of 13 chapters in total. They have been discussed below.

## NCERT Solutions for Class 12 Maths Chapter 1: Relations and Functions

Relations and Functions is the first chapter of NCERT Class 12 Maths syllabus. Chapter 1 talks about which are based on types of relations, types of functions, the composition of functions and invertible functions, equivalence classes, algebra of functions, and binary operations. This chapter also teaches you about the reflexive, symmetric, Bijective, surjective, and injective functions.

This chapter comprises 4 exercises. Our NCERT Solutions accurately answer all questions of all the exercises.

## NCERT Solutions for Class 12 Maths Chapter 2: Inverse Trigonometric Functions

Inverse Trigonometric Functions are the second chapter of CBSE Board Class 12 Maths Book. Here you will come across basic topics of trigonometric functions, properties of trigonometric functions, principal value branch, domain and range of inverse trigonometric functions, the graph of inverse trigonometric functions, trigonometric equation and solution or roots of trigonometric functions.

Chapter 2 of NCERT Class 12 Maths comprises 3 exercises in which the last exercise is miscellaneous exercise. The exercises have about 52 questions. The solutions to it are prepared as per the guidelines provided by CBSE and NCERT.

## NCERT Solutions for Class 12 Maths Chapter 3: Matrices

Matrices chapter discusses types of matrices, equality of matrices, operations on matrices, additions of matrices, multiplication of scalar matrices, transpose of a matrix, elementary operations and invertible matrices. Here, you will also come across the order of a matrix, notation of a matrix, equality matrix, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Further, you will learn about the properties of matrices like addition, multiplication and properties of the transpose of the matrices.

NCERT solutions of Maths chapter 3 has 4 exercises that contain about 62 questions. The solutions consist of answers to all questions in an easy to understand manner and in a well-structured way to help you learn effectively.

## NCERT Solutions for Class 12 Maths Chapter 4: Determinants

In the Determinants chapter of NCERT CBSE Class 12 Maths, you come across various interesting topics such as determinants of a matrix of order one, order two, order 3 * 3, properties of determinants, area of a triangle, minors and cofactors, adjoint and the inverse of a matrix and applications of determinants and matrices. Here, you will also learn about adjoint of a matrix, solutions of a system of linear equations using the inverse of a matrix, inconsistency and number of solutions of a system of linear equations with examples.

Chapter 4 consists of 6 exercises with 68 questions in total. Our accurate and step by step solutions to these questions are phrased in an easy and simple language.

## NCERT Solutions for Class 12 Maths Chapter 5: Continuity and Differentiability

Continuity and differentiability is one of the most important chapters of NCERT Class 12th Maths book. Chapter 5 covers the introduction of differentiability, continuity, algebra of continuous functions, derivatives of composite functions, derivatives of implicit functions, inverse trigonometric functions,  derivatives of functions in parametric forms, logarithmic differentiation, exponential and logarithmic functions, mean value theorem and second-order derivatives.

This chapter comprises 8 exercises, and it has 121 questions and our NCERT Solutions for Class 12 Maths answer all the questions accurately and precisely as per the guidelines of CBSE and NCERT.

## NCERT Solutions for Class 12 Maths Chapter 6: Applications of Derivations

Applications of Derivations are the sixth unit of NCERT Class 12 Maths syllabus. This chapter teaches you about the introduction of applications of derivations, rate of change of quantities, tangents and normals, increasing and decreasing functions, maxima and minima approximations, and maximum and minimum values of a function in a closed interval.

Chapter 6 of NCERT Class 12 Maths consists of 5 exercises which have 102 questions in total. These questions cover all parts of the chapter and help you gain a solid understanding of the various concepts of the chapter.

### NCERT Solutions for Class 12 Maths Chapter 7: Integrals

Integrals of NCERT Class 12 Maths solutions will teach you the inverse process of differentiation. Here you will also be introduced to integral calculus, integration as an inverse process of differentiation, methods of integrations, integrals of some particular functions, integration by parts, integration by partial fractions, definite integrals, fundamental theorem of calculus, the evolution of definite integrals by substitution and some properties of definite integrals.

Chapter 7 consists of 11 exercises and 1 miscellaneous exercise.  These exercises have about 270 questions, and they cover all the topics from the chapter. The NCERT Solutions for CBSE Class 12 Maths answer all questions accurately, precisely and in a step by step way to make it easy for you to learn.

## NCERT Solutions for Class 12 Maths Chapter 8: Applications of Integrals

Applications of Integrals of CBSE Class 12 Maths solutions. It teaches you about integrals used to find the area of a curved region, integrals used to find the area bounded by two curves, integrals used to find the area bounded by a curve and a line, and integrals used to find the area bounded by lines, between parabolas, between ellipses, between two lines, between a line and a parabola and between a line and an ellipse. Here you will also learn Walli’s formula and Leibnitz rule for differentiation under the integral sign.

This chapter 8 consists of 2 exercises which have 20 questions in total, and these questions cover the major topics of the chapter. The comprehensive NCERT Solutions for Class 12th Maths cover all concepts of the chapter in detail.

## NCERT Solutions for Class 12 Maths Chapter 9: Differential Equations

This chapter will teach you the introduction and basics of differential equations. Interesting parts of the chapter are an order of a differential equation, degree of a differential equation, the formation of a differential equation whose general solution is given, general and particular solutions of a differential equation, methods of solving first order, first-degree differential equations, the procedure to form a differential equation that will represent a given family of curves, differential equations with variables separable method, Inspection method, homogeneous differential equation and linear differential equations.

Here you will also learn about Differential Equation Reducible to Linear Form, Clairaut Form for Differential equation, Orthogonal trajectory, Differential Equation Reducible to Variables Separable Method, and Differential Equations Reducible to Homogeneous Equation.

This chapter consists of 6 exercises. Our NCERT Solutions for Class 12 Maths answer all questions of all exercises exhaustively yet precisely.

## NCERT Solutions for Class 12 Maths Chapter 10: Vector Algebra

Class 12 Maths Vector Algebra chapter discusses in details the meaning of vector, the types of vectors, the addition of vectors, components of a vector, multiplication of a vector by a scalar, vector joining two points, scalar or dot product of two vectors, section formula, a product of two vectors, projections of a vector on a line, vector or cross product of two vectors.

It comprises 4 exercises with 54 questions in total, and they comprehensively cover the whole unit. The solutions to these exercise questions are drafted from the examination point of view.

## NCERT Solutions for Class 12 Maths Chapter 11: Three Dimensional Geometry

Three Dimensional Geometry is one of the essential topics of NCERT Class 12 Maths textbook. Here you will gain knowledge of directions cosines and directions ratios of a line, direction cosines of a line passing through two points, the relation between the direction cosines of a line, equation of a line in space, the shortest distance between two lines, the angle between two lines, plane, coplanarity of two lines, a distance of a point from a plane, angle between two planes, and the angle between a line and a plane.

You will also learn about the equation of a plane in normal form, equation of a plane passing through three non-collinear points, intercept form of the equation of a plane and plane passing through the intersection of two given planes, and equation of a plane perpendicular to a given vector and passing through a given point.

Chapter 11 of NCERT CBSE Class 12 Maths consists of 3 exercises which have 36 questions in total, and these questions are answered in our solutions in an easy to understand language so that you can master even the most complex topics easily.

## NCERT Solutions for Class 12 Maths Chapter 12: Linear Programming

This chapter consists of a plethora of important linear programming related topics such as feasible region, optimal solution, theorems of linear programming, corner point method of solving linear programming problems, graphical method of solving linear programming problems, and Isom-profit or iso-cost method of solving a linear programming problem.

It consists of 2 exercises with 21 questions in total, and they cover all the topics and sub-topics from the chapter. Our NCERT Solutions answer all these questions and are phrased in an easy and simple language.

## NCERT Solutions for Class 12 Maths Chapter 13: Probability

NCERT Class 12 Maths Probability chapter will help you understand about the conditional probability, multiplication theorem on probability, independent events, Bayes theorem, the partition of a sample space, the theorem of total probability, random variables and its probability distributions, mean and variable of a random variable, Bernoulli’s trials and the binomial distribution.

The Probability chapter consists of 5 exercises with 81 questions. Our NCERT Solutions for Class 12 Maths prepared by expert Maths teachers answer all these questions accurately.