 # RS Aggarwal Class 12 Maths Solutions

Currently, BYJU’S does not provide RS Aggarwal Maths Solutions for Class 12. Stay tuned, while we are in the process of providing solutions.

RS Aggarwal Solutions for Class 12 are available in PDF format which can be downloaded by the students easily. The solutions are curated in a stepwise manner by the teachers at BYJU’S to boost the exam preparation of students. Students can analyse their areas of weakness and work on them based on the exam syllabus.
RS Aggarwal Solutions help students perform well in the board exam and design their career path.

The solutions PDF is a useful study material for students to solve problems and understand the topics. Students are advised to solve the exercise wise problems to get their doubts cleared instantly. RS Aggarwal Solutions for Class 12 Maths PDF are available here, which can be downloaded effortlessly.

## Chapter-wise Solutions for RS Aggarwal Class 12

Chapter 1 Relations
Chapter 2 Functions
Chapter 3 Binary Operations
Chapter 4 Inverse Trigonometric Functions
Chapter 5 Matrices
Chapter 6 Determinants
Chapter 7 Adjoint and Inverse of a Matrix
Chapter 8 System of Linear Equations
Chapter 9 Continuity and Differentiability
Chapter 10 Differentiation
Chapter 11 Applications of Derivatives
Chapter 12 Indefinite Integral
Chapter 13 Methods of Integration
Chapter 14 Some Special Integrals
Chapter 15 Integration Using Partial Fractions
Chapter 16 Definite Integrals
Chapter 17 Area of Bounded Regions
Chapter 18 Differential Equations and Their Formation
Chapter 19 Differential Equations with Variable Separable
Chapter 20 Homogeneous Differential Equations
Chapter 21 Linear Differential Equations
Chapter 22 Vectors and Their Properties
Chapter 23 Scalar, or Dot, Product of Vectors
Chapter 24 Cross, or Vector, Product of Vectors
Chapter 25 Product of Three Vectors
Chapter 26 Fundamental Concepts of 3-Dimensional Geometry
Chapter 27 Straight Line in Space
Chapter 28 The Plane
Chapter 29 Probability
Chapter 30 Bayes’s Theorem and its Applications
Chapter 31 Probability Distribution
Chapter 32 Binomial Distribution
Chapter 33 Linear Programming

Various online study materials are available at BYJU’S such as worksheets, question papers of previous years and sample papers. All the sample papers can be answered by students using RS Aggarwal Solutions for Class 12, which helps to get a clear idea about the CBSE syllabus and exam pattern.

### RS Aggarwal Solutions for Class 12 Maths

Chapter wise solutions curated by experts help students to improve their conceptual knowledge relevant to RS Aggarwal textbook of current syllabus. Practising problems on a daily basis improves confidence and reduces the fear of exams among students.

RS Aggarwal Solutions Class 12 Maths Chapter 1 – Relations

Cartesian product of sets is the concept discussed in previous classes. But here in Class 12, students understand the concept of relation in a set. Students can refer to the solutions PDF prepared by faculty at BYJU’S to ace the exam. This chapter includes concepts like relation in a set and domain and range of a relation. Students can find the shortcut methods in the PDF which can be used in solving problems relevant to the latest CBSE guidelines.

Here students can find the exercise solution links for the concepts discussed under this chapter.

➤ Exercise 1A

➤ Exercise 1B

RS Aggarwal Solutions Class 12 Maths Chapter 2 – Functions

Chapter 2 of RS Aggarwal textbook contains problems on concepts like domain, codomain and range of a function, types of functions, composition of functions and invertible function. The exercise wise problems are prepared in a stepwise manner to improve knowledge about the concepts among students.

Given below are the links of exercise wise solutions for the topics which are covered in this chapter.

➤ Exercise 2A

➤ Exercise 2B

➤ Exercise 2C

➤ Exercise 2D

RS Aggarwal Solutions Class 12 Maths Chapter 3 – Binary Operations

The faculty at BYJU’S prepare the exercise wise solutions with the aim of helping students perform well in the board exams. The exercise wise problems in this chapter are mainly based on topics like closure property, properties of a binary operation and new operations.

➤ Exercise 3A

➤ Exercise 3B

RS Aggarwal Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions

This chapter has problems based on invertible functions, properties of inverse functions and graphs of inverse trigonometric functions. The solutions are well structured in an interactive manner, as per the latest CBSE syllabus. Students can download the solutions PDF to prepare well for the Class 12 exams.

There are 4 exercises in this chapter and the solution links are given below for easy access of students.

➤ Exercise 4A

➤ Exercise 4B

➤ Exercise 4C

➤ Exercise 4D

RS Aggarwal Solutions Class 12 Maths Chapter 5 – Matrices

A rectangular array of numbers which can be written in the form of rows and columns is called a matrix. Matrix, types of matrices, operations on matrices, multiplication of matrices, transpose of matrices symmetric and skew symmetric matrices and elementary operations on matrices are the concepts covered in this chapter. Here the students can solve the problems by referring to RS Aggarwal solutions which is the best study material.

The solution links for the exercises covered in this chapter are as follows.

➤ Exercise 5A

➤ Exercise 5B

➤ Exercise 5C

➤ Exercise 5D

➤ Exercise 5E

➤ Exercise 5F

RS Aggarwal Solutions Class 12 Maths Chapter 6 – Determinants

A determinant is the arrangement of numbers in rows and columns where each determinant has a fixed value. The subject matter experts at BYJU’S design solutions after conducting a vast research on each concept covered in this chapter. Chapter 6 explains some of the important concepts like determinant of a square matrix, properties of determinants, value of a determinant, sum of two determinants and determinants on trigonometry.

This chapter has 3 exercises and the solution links are provided here.

➤ Exercise 6A

➤ Exercise 6B

➤ Exercise 6C

RS Aggarwal Solutions Class 12 Maths Chapter 7 – Adjoint and Inverse of a Matrix

Chapter 7 deals with adjoint of a matrix, invertible matrix and some results on invertible matrices. The stepwise explanations provided for the solutions improves problem solving abilities among students. Students who wish to score well in the board exam can download the solutions PDF based on their requirements. This chapter has only one exercise based on the topics covered.

RS Aggarwal Solutions Class 12 Maths Chapter 8 – System of Linear Equations

The method of solving a system of linear equations using matrix method is explained in brief under this chapter. There are two systems of equations discussed here namely, consistent and inconsistent system of equations. This chapter covers topics like solving problems using matrix method and illustrative examples based on them. Chapter 8 has only one exercise with answers designed by experienced teachers at BYJU’S.

RS Aggarwal Solutions Class 12 Maths Chapter 9 – Continuity and Differentiability

Students who find difficulties in solving the exercise wise problems can make use of solutions curated by teachers at BYJU’S available in PDF format. Chapter 9 explains real functions, some important functions, graphs, graphs on trigonometric functions, continuity and differentiability. The PDF of solutions is a major study material for students to garner a better academic score in Class 12.

Provided below are some of the exercise solution links designed by subject matter experts at BYJU’S.

➤ Exercise 9A

➤ Exercise 9B

➤ Exercise 9C

RS Aggarwal Solutions Class 12 Maths Chapter 10 – Differentiation

Students have learnt about the derivatives of algebraic and trigonometric functions in previous classes. Here they would be understanding about various topics like derivatives of some functions, derivatives of exponential and logarithmic functions, derivatives of inverse trigonometric functions, differentiation by trigonometric transformations etc. This chapter explains the steps to be followed in differentiation of various functions. These concepts are explained by the teachers at BYJU’S to help students score good marks in the board exam. Shortcut tips and important formulas required in solving problems are explained here in an interesting way.

10 exercises are present in this chapter and the links for the solutions are provided below

➤ Exercise 10A

➤ Exercise 10B

➤ Exercise 10C

➤ Exercise 10D

➤ Exercise 10E

➤ Exercise 10F

➤ Exercise 10G

➤ Exercise 10H

➤ Exercise 10I

➤ Exercise 10J

RS Aggarwal Solutions Class 12 Maths Chapter 11 – Applications of Derivatives

Applications of Derivatives in our daily lives is the topic discussed in brief under this chapter. Derivative as a rate measure, errors and approximation, Rolle’s and Lagrange’s theorem, Lagrange’s Mean-Value Theorem and maxima and minima are the important topics covered in this chapter. The solutions are prepared by experts to help the students in solving problems in a shorter duration.

➤ Exercise 11A

➤ Exercise 11B

➤ Exercise 11C

➤ Exercise 11D

➤ Exercise 11E

➤ Exercise 11F

➤ Exercise 11G

➤ Exercise 11H

RS Aggarwal Solutions Class 12 Maths Chapter 12 – Indefinite Integral

The inverse process of differentiation is called integration. The concepts on integration are explained in this chapter in an understandable manner. This chapter covers topics like integration, standard results on integration along with solved examples. Students can make use of PDF as a reference guide to score well in the exam. Chapter 12 has only one exercise in accordance with the topics covered in this chapter.

RS Aggarwal Solutions Class 12 Maths Chapter 13 – Methods of Integration

The methods of integration by substitution, using trigonometric identities and by parts are explained clearly in this chapter. Integration is one of the important topics in Class 12 as it will be continued in further education also. Chapter 13 has problems solved in a structured manner to help students during revision and exam preparation.

➤ Exercise 13A

➤ Exercise 13B

➤ Exercise 13C

RS Aggarwal Solutions Class 12 Maths Chapter 14 – Some Special Integrals

The concepts like three special integrals, three more special integrals and theorems based on them are explained in brief under this chapter. Various short cut tips used in solving tricky problems are provided to help students improve their logical approach. Students can download the PDF to solve exercise wise solutions in a shorter period of time.

3 exercises are present in this chapter and the PDF links are given here.

➤ Exercise 14A

➤ Exercise 14B

➤ Exercise 14C

RS Aggarwal Solutions Class 12 Maths Chapter 15 – Integration using Partial Fractions

Any proper fraction which can be expressed as the sum of rational fractions each having a simplest factor is known as a partial fraction. Students can download solutions PDF of RS Aggarwal textbook, as per current CBSE syllabus. This chapter mainly deals with partial fractions, integration using partial fractions and solved examples on each topic to improve a grip on solving problems among students.

The solution links for the problems of exercises solved by expert faculty at BYJU’S are as follows.

➤ Exercise 15A

➤ Exercise 15B

RS Aggarwal Solutions Class 12 Maths Chapter 16 – Definite Integrals

Fundamental theorem of integral calculus, evaluate a definite integral by substitution, properties of definite integrals and definite integral as the limit of a sum are the concepts explained in brief in this chapter. This chapter explains the methods of evaluating definite integrals in a stepwise manner as per CBSE exam pattern. The solutions contain explanations in simple language to make education interesting for students.

4 exercises are present in this chapter and the solutions PDF links are provided here.

➤ Exercise 16A

➤ Exercise 16B

➤ Exercise 16C

➤ Exercise 16D

RS Aggarwal Solutions Class 12 Maths Chapter 17 – Area of Bounded Regions

The steps to be followed in determining the areas of various bounded regions are explained in this chapter. The solutions are provided with graphical representation to make it interesting for the students during revision. Subject experts at BYJU’S prepare the solutions keeping in mind the current CBSE syllabus. Both tricky problems and simple problems are solved with ease to help students ace the exam. There is only one exercise in this chapter which covers the various topics.

RS Aggarwal Solutions Class 12 Maths Chapter 18 – Differential Equations and their Formation

Differential equation is an equation which contains an independent variable, dependent variable and the derivatives of the dependent variable. This chapter has problems on differential equation, solution and general solution of a differential equation and formation of a differential equation whose general solution is given. Step by step explanations help students understand concepts faster. It improves time management skills among students which is an important aspect for the board exam.

The exercise wise solution links for the 3 exercises in Chapter 18 are given here in PDF format.

➤ Exercise 18A

➤ Exercise 18B

➤ Exercise 18C

RS Aggarwal Solutions Class 12 Maths Chapter 19 – Differential Equations with Variable Separable

The steps to be followed in solving differential equations with variable separable is one of the important topics discussed in this chapter. The problems are based on determining the general solution for the given set of differential equations. The solutions created help students improve the overall idea about the chapter.

➤ Exercise 19A

➤ Exercise 19B

RS Aggarwal Solutions Class 12 Maths Chapter 20 – Homogeneous Differential Equations

A homogeneous differential equation consists of two or more functions of the same degree. Students here can obtain an idea about the method of solving a homogeneous differential equation. This chapter has one exercise in which problems are based on proving that the given set of differential equations are homogeneous.

RS Aggarwal Solutions Class 12 Maths Chapter 21 – Linear Differential Equations

Chapter 21 has problems on linear differential equations and the method of determining its solutions. In a subject like Mathematics, which contains numericals, regular practise is an important aspect. Solved examples are also present in the textbook to improve problems solving abilities among students. This chapter has one exercise to find the general solutions of the given set of differential equations.

RS Aggarwal Solutions Class 12 Maths Chapter 22 – Vectors and their Properties

In our daily life, we generally come across two types of quantities, namely scalars and vectors. A quantity which possesses both magnitude and direction is known as a vector. This chapter deals with vectors, law of addition of vectors, scalar multiplication of a vector and section formulae. Chapter 22 has only one exercise with problems based on vectors.

RS Aggarwal Solutions Class 12 Maths Chapter 23 – Scalar, or Dot, Product of Vectors

Chapter 23 covers topics like angle between two vectors, projection, properties of scalar product and solved examples based on them. Students who wish to obtain in-depth knowledge about the concepts can download the PDF of solutions. The doubts which arise while solving the exercise problems of RS Aggarwal textbook can be solved instantly. This chapter contains only one exercise with problems explaining the concepts clearly.

RS Aggarwal Solutions Class 12 Maths Chapter 24 – Cross, or Vector, Product of Vectors

This chapter deals with vector products of two vectors, properties of vector products, are of a parallelogram, triangle, quadrilateral and vector product in terms of components. The creativity of solutions in the PDF provides students with the importance of the subject. Only one exercise is present in this chapter which can be solved by students referring to the solved examples.

RS Aggarwal Solutions Class 12 Maths Chapter 25 – Product of Three Vectors

Some theorems on scalar triple product and problems based on them are explained in brief under this chapter. The solutions PDF is the best reference guide for students which helps in solving textbook problems easily. Various steps to be followed in solving problems along with important formulas are provided in order to help students ace the exam.

There are 2 exercises which cover all the topics present in this chapter.

➤ Exercise 25A

➤ Exercise 25B

RS Aggarwal Solutions Class 12 Maths Chapter 26 – Fundamental Concepts of 3-Dimensional Geometry

The chapter, Fundamental Concepts of 3-Dimensional Geometry, as the name indicates provides a proper understanding of 3-Dimensional Geometry among students. This chapter also covers coordinates of a point in space, some results on points in space and some results on lines in space. The chapter has one exercise which aids students in understanding basic concepts of 3-Dimensional Geometry.

RS Aggarwal Solutions Class 12 Maths Chapter 27 – Straight Line in Space

In this chapter, students will learn about the equation of line in various conditions in vector and Cartesian form. Collinearity of three given points, angle between two lines, shortest distance between two skew lines in the Cartesian form are the other topics of major importance in this chapter.

This chapter has 6 exercises which make students gain expertise on the concepts covered here.

➤ Exercise 27A

➤ Exercise 27B

➤ Exercise 27C

➤ Exercise 27D

➤ Exercise 27E

➤ Exercise 27F

RS Aggarwal Solutions Class 12 Maths Chapter 28 – The Plane

This chapter provides students with knowledge about the general equation of a plane in Cartesian and vector form. The other concepts discussed in this chapter are equations of a plane in various forms, distance of a point from a plane, equation of a plane parallel to given plane and plane passing through intersection of two planes.

Students get well versed in these concepts by solving problems using the PDF provided here.

➤ Exercise 28A

➤ Exercise 28B

➤ Exercise 28C

➤ Exercise 28D

➤ Exercise 28E

➤ Exercise 28F

➤ Exercise 28G

➤ Exercise 28H

➤ Exercise 28I

➤ Exercise 28J

RS Aggarwal Solutions Class 12 Maths Chapter 29 – Probability

The concept of probability and various results on it were discussed in the previous classes. This chapter deals with problems on conditional probability and probability of independent events. Students learn about the concepts and important steps to be followed in solving problems, as per CBSE syllabus.

There are 2 exercises in this chapter which deals with all the concepts explained here.

➤ Exercise 29A

➤ Exercise 29B

RS Aggarwal Solutions Class 12 Maths Chapter 30 – Bayes’s Theorem and its Applications

Theorem of total probability known as Bayes’s theorem and its applications in our day to day lives are covered in this chapter. The solved examples and problems in the exercise help us understand the uses of Bayes’s theorem in our daily activities. There is one exercise in this chapter which helps students understand the method of solving problems in a shorter period of time.

RS Aggarwal Solutions Class 12 Maths Chapter 31 – Probability Distribution

The chapter, Probability Distribution, provides students with basic knowledge of probability distribution of a random variable and mean and variance of a random variable, according to CBSE textbook. Students who are not able to analyse the tricky problems can use the solutions PDF to score well in the board exam. This chapter has one exercise which provides complete knowledge about probability distribution among students.

RS Aggarwal Solutions Class 12 Maths Chapter 32 – Binomial Distribution

In this chapter, students learn about Bernoulli’s Theorem, conditions for applicability and mean and variance of a binomial distribution. Students who aspire to score good marks in the board exam can solve problems using solutions PDF. By solving one exercise of this chapter, students gain expertise about the concepts covered here.

RS Aggarwal Solutions Class 12 Maths Chapter 33 – Linear Programming

The steps to be followed in the construction of graph of a linear inequation and linear programming are the topics which are covered in this chapter. The method which is used in decision making in business to obtain the maximum and minimum value of a linear expression which satisfies certain linear inequations.

➤ Exercise 33A

➤ Exercise 33B

RS Aggarwal Solutions for Class 12 are provided here to help students to understand and solve textbook questions. These solutions can be viewed online or downloaded for free by the students based on their needs. Solving sample papers and question papers help students improve time management skills and understand the weightage of each concept.

### Benefits of RS Aggarwal Solutions for Class 12 Maths

• The solutions are available for all the chapters present in the RS Aggarwal textbook of the current board.
• Step by step answers with explanations in simple language provide better understanding of concepts among students.