 # RD Sharma Class 12 Solutions

The RD Sharma Solutions Mathematics Class 12 PDF can be easily accessed by students to start adequate preparation for their upcoming exams. Students can now solve any problem from the RD Sharma textbooks by referring to RD Sharma Solutions. BYJU’S experts formulate these questions in an easy and understandable manner that helps students solve problems in the most efficient possible ways. We hope these solutions will help CBSE Class 12 students to build a strong foundation of the basics and secure excellent marks in their final exam.

As Mathematics is an intricate subject for Class 12 students, these solutions will change every student’s approach towards Mathematics and will definitely make them realize how interesting and easy the subject is. RD Sharma Solutions are focused on learning various Mathematics tricks and shortcuts for quick and easy calculations. Download the RD Sharma Solutions for Class 12 Maths now and practice all the questions. Practising these questions will ensure that students have a good practice of all types of questions that can be framed in the examination.

## RD Sharma Solutions for Class 12 Maths (Chapter-wise)

Chapter 1 – Relations

Chapter 2 – Functions

Chapter 3 – Binary Operations

Chapter 4 – Inverse Trigonometric Functions

Chapter 5 – Algebra of Matrices

Chapter 6 – Determinants

Chapter 7 – Adjoint and Inverse of a Matrix

Chapter 8 – Solutions of Simultaneous Linear Equations

Chapter 9 – Continuity

Chapter 10 – Differentiability

Chapter 11 – Differentiation

Chapter 12 – Higher Order Derivatives

Chapter 13 – Derivative as a Rate Measurer

Chapter 14 – Differentials, Errors and Approximations

Chapter 15 – Mean Value Theorems

Chapter 16 – Tangents and Normals

Chapter 17 – Increasing and Decreasing Functions

Chapter 18 – Maxima and Minima

Chapter 19 – Indefinite Integrals

Students are also given access to additional online study materials and resources, available at BYJU’S, such as notes, books, question papers, exemplar problems, worksheets, etc. Students are also advised to practice Class 12 Sample papers to get an idea of the question pattern in the final exam.

### RD Sharma Solutions for Class 12 Maths

Students can refer to these RD Sharma Solutions Class 12, which help in gaining knowledge and for better guidance, it is best to solve these solutions. Solving these exercises in each chapter will ensure that students score good marks in the exams.

RD Sharma Solutions for Class 12 Maths Chapter 1- Relations

Chapter 1 of the RD Sharma textbook deals with relations and their properties, types of relations, inverse of a relation, equivalence relation, some useful results on relations, reflexive relation, symmetric relation, and transitive relation. Here, you can find the exercises solution links for the topics covered in this chapter.

RD Sharma Solutions Class 12 Maths Chapter 1 – Relations Exercise 1.1

RD Sharma Solutions Class 12 Maths Chapter 1 – Relations Exercise 1.2

RD Sharma Solutions for Class 12 Maths Chapter 2 – Functions

Chapter 2, Functions of RD Sharma Class 12 Maths, gives an account of various topics such as the definition of functions, function as a correspondence, function as a set of ordered pairs, the graph of a function, vertical line test, constant function, identity function, modulus function, greatest integer function, properties of greatest integer function, smallest integer functions and its properties, fractional part function, signum function, exponential function, logarithmic function, reciprocal and square root function, square function, square root function, cube function, reciprocal squared function, operations on real function, kinds of functions such as one-one, many-one and onto function, bijection, the composition of functions and its properties and composition of real functions. Meanwhile, in this chapter, students get to learn how to relate between graphs of a function and its inverse.

RD Sharma Solutions Class 12 Maths Chapter 2 – Functions Exercise 2.1

RD Sharma Solutions Class 12 Maths Chapter 2 – Functions Exercise 2.2

RD Sharma Solutions Class 12 Maths Chapter 2 – Functions Exercise 2.3

RD Sharma Solutions Class 12 Maths Chapter 2 – Functions Exercise 2.4

RD Sharma Solutions for Class 12 Maths Chapter 3 – Binary Operations

In Chapter 3 of the RD Sharma textbook, we shall see the definition of a binary operation, the number of binary operations, types of binary operations such as commutativity, associativity and distributivity, an identity element, inverse of an element, composition table, addition modulo ‘n’ and multiplication modulo ‘n’. Here, you can find the exercises solution links for the topics covered in this chapter.

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations Exercise 3.1

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations Exercise 3.2

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations Exercise 3.3

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations Exercise 3.4

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations Exercise 3.5

RD Sharma Solutions for Class 12 Maths Chapter 4 – Inverse Trigonometric Functions

Chapter 4 of RD Sharma Solutions Maths discusses the topic of the inverse of a function. Students will get to learn about the definition and meaning of inverse trigonometric functions, the inverse of the sine function, inverse of the cosine function, inverse of the tangent function, inverse of secant function, inverse of cosecant function, inverse of cotangent function, and properties of inverse trigonometric functions. Below we have links provided to each exercise solution covered in this chapter.

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.1

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.2

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.3

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.4

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.5

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.6

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.7

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.8

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.9

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.10

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.11

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.12

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.13

RD Sharma Solutions Class 12 Maths Chapter 4 – Inverse Trigonometric Functions Exercise 4.14

RD Sharma Solutions for Class 12 Maths Chapter 5 – Algebra of Matrices

Chapter 5 of the RD Sharma textbook starts with the definitions of Matrices. Students go on to learn about types of matrices, equality of matrices, the addition of matrices, properties of matrix addition, multiplication of a matrix by a scalar, properties of scalar multiplication, subtraction of matrices, multiplication of matrices, properties of matrix multiplication, positive integral powers of a square matrix, transpose of a matrix, properties of transpose, symmetric and skew-symmetric matrices via examples. Here, students can see the exercises explaining these concepts properly with solutions.

RD Sharma Solutions Class 12 Maths Chapter 5 – Algebra of Matrices Exercise 5.1

RD Sharma Solutions Class 12 Maths Chapter 5 – Algebra of Matrices Exercise 5.2

RD Sharma Solutions Class 12 Maths Chapter 5 – Algebra of Matrices Exercise 5.3

RD Sharma Solutions Class 12 Maths Chapter 5 – Algebra of Matrices Exercise 5.4

RD Sharma Solutions Class 12 Maths Chapter 5 – Algebra of Matrices Exercise 5.5

RD Sharma Solutions for Class 12 Maths Chapter 6 – Determinants

Chapter 6 of the RD Sharma textbook, provides a definition of determinants, determinant of a square matrix of order 1, 2, and 3, determinant of a square matrix of order 3 by using Sarrus diagram, singular matrix, minors and cofactors, properties of determinants, evaluation of determinants, applications of determinants to coordinate geometry and applications of determinants in solving a system of linear equations and condition for consistency. Here, students can find exercises explaining these concepts properly.

RD Sharma Solutions Class 12 Maths Chapter 6 – Determinants Exercise 6.1

RD Sharma Solutions Class 12 Maths Chapter 6 – Determinants Exercise 6.2

RD Sharma Solutions Class 12 Maths Chapter 6 – Determinants Exercise 6.3

RD Sharma Solutions Class 12 Maths Chapter 6 – Determinants Exercise 6.4

RD Sharma Solutions Class 12 Maths Chapter 6 – Determinants Exercise 6.5

RD Sharma Solutions for Class 12 Maths Chapter 7 – Adjoint and Inverse of a Matrix

In Chapter 7, Adjoint and Inverse of a Matrix, we shall see the definition of the adjoint of a square matrix, the inverse of a matrix, some useful results on invertible matrices, elementary transformations of elementary operations of a matrix via examples and verbal problems related to it. Here, we have given exercises with solutions based on these topics from the chapter.

RD Sharma Solutions Class 12 Maths Chapter 7 – Adjoint and Inverse of a Matrix Exercise 7.1

RD Sharma Solutions Class 12 Maths Chapter 7 – Adjoint and Inverse of a Matrix Exercise 7.2

RD Sharma Solutions for Class 12 Maths Chapter 8 – Solutions of Simultaneous Linear Equations

In Chapter 8 of the RD Sharma textbook, we continue the discussions about equations starting with definition, consistent system, homogeneous and non-homogeneous systems, matrix method for the solution of a non-homogeneous system, and final solution of a homogeneous system of linear equations. From the below given links, students can access the exercises with solutions explaining the concepts from this chapter.

RD Sharma Solutions Class 12 Maths Chapter 8 – Solutions of Simultaneous Linear Equations Exercise 8.1

RD Sharma Solutions Class 12 Maths Chapter 8 – Solutions of Simultaneous Linear Equations Exercise 8.2

RD Sharma Solutions for Class 12 Maths Chapter 9 – Continuity

In this chapter, students concentrate on the definition of continuity, continuity at a point, algebra of continuous function, continuity on an interval, continuity on an open interval, continuity on a closed interval, continuous function, everywhere continuous function, and properties of continuous functions. Solutions to the exercises from this chapter can be accessed from here.

RD Sharma Solutions Class 12 Maths Chapter 9 – Continuity Exercise 9.1

RD Sharma Solutions Class 12 Maths Chapter 9 – Continuity Exercise 9.2

RD Sharma Solutions for Class 12 Maths Chapter 10 – Differentiability

This chapter deals with differentiability, by reviewing the basic facts and formulae studied earlier in Class 11, we shall implement those formulas again in this chapter along with the advance concepts mentioned i.e. differentiability at a point, differentiability in a set, and some useful results on differentiability. We have compiled here the solutions to exercises from this chapter, which have explained the concept thoroughly.

RD Sharma Solutions Class 12 Maths Chapter 10 – Differentiability Exercise 10.1

RD Sharma Solutions Class 12 Maths Chapter 10 – Differentiability Exercise 10.2

RD Sharma Solutions for Class 12 Maths Chapter 11 – Differentiation

Chapter 11 of RD Sharma Class 12 Maths constitutes topics related to differentiation, differentiation of inverse trigonometric functions from first principles, differentiation of a function, differentiation of inverse trigonometric function by chain rule, differentiation by using trigonometric substitutions, differentiation of implicit functions, logarithmic differentiation, differentiation of infinite series, differentiation of parametric functions and differentiation of a function with respect to another function via illustrations. Below we have listed links to the solutions for the exercises from this chapter.

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.1

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.2

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.3

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.4

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.5

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.6

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.7

RD Sharma Solutions Class 12 Maths Chapter 11 – Differentiation Exercise 11.8

RD Sharma Solutions for Class 12 Maths Chapter 12 – Higher Order Derivatives

In this chapter, students are introduced to higher-order derivatives. The concepts covered in this chapter are proving relations involving various order derivatives of cartesian functions, proving relations involving various order derivatives of parametric functions, and proving relations involving various order derivatives via illustrations.

RD Sharma Solutions for Class 12 Maths Chapter 13 – Derivative as a Rate Measurer

In this chapter, students are introduced to the derivative as a rate measurer. The concepts in this chapter cover how to find rate measurer of derivative and related rates in which the rate of change of one of the quantities involved is required, corresponding to the given rate of change of another quantity. This chapter contains more word problems that help the students to learn the sentence formation in an effective way.

RD Sharma Solutions Class 12 Maths Chapter 13 – Derivative as a rate measurer Exercise 13.1

RD Sharma Solutions Class 12 Maths Chapter 13 – Derivative as a rate measurer Exercise 13.2

RD Sharma Solutions for Class 12 Maths Chapter 14 – Differentials, Errors, and Approximations

Chapter 14 of RD Sharma Class 12 Maths deals with the topic of differentials and errors. The topics that are discussed include the definition of differentials, absolute error, relative error, percentage error, the geometrical meaning of differentials with algorithms, and finding the approximate value using differentials.

RD Sharma Solutions for Class 12 Maths Chapter 15 – Mean Value Theorems

In this chapter, we shall discuss theorems related to mean values. It also deals with Rolle’s theorem, geometrical interpretation of Rolle’s theorem, algebraic interpretation of Rolle’s theorem, the applicability of Rolle’s theorem, Lagrange’s mean value theorem, geometrical interpretation of Lagrange’s mean value theorem, verification of Lagrange’s mean value theorem, applications of Lagrange’s mean value theorem and proving inequalities by using Lagrange’s mean value theorem. From the below-given links, students can access the exercises with solutions explaining the concepts from this chapter.

RD Sharma Solutions Class 12 Maths Chapter 15 – Mean Value Theorems Exercise 15.1

RD Sharma Solutions Class 12 Maths Chapter 15 – Mean Value Theorems Exercise 15.2

RD Sharma Solutions for Class 12 Maths Chapter 16 – Tangents and Normals

Students can learn the concepts related to tangents and normals in this chapter. It also deals with the slope of a line, slopes of tangent and normal, finding slopes of tangent and normal at a given point, finding the point on a given curve at which tangent is parallel or perpendicular to a given line, equations of tangent, and normal with an algorithm, finding the equation of tangent and normal to a curve at a point, finding tangent and normal parallel or perpendicular to a given line, finding tangent or normal passing through a given point, angle of intersection of two curves and orthogonal curves. Solution links are provided below to each exercise, which is covered in this chapter.

RD Sharma Solutions Class 12 Maths Chapter 16 – Tangents and Normals Exercise 16.1

RD Sharma Solutions Class 12 Maths Chapter 16 – Tangents and Normals Exercise 16.2

RD Sharma Solutions Class 12 Maths Chapter 16 – Tangents and Normals Exercise 16.3

RD Sharma Solutions for Class 12 Maths Chapter 17 – Increasing and Decreasing Functions

Chapter 17 of RD Sharma textbook deals with the topic of increasing and decreasing functions, solution of rational algebraic inequations with algorithms, strictly increasing functions, strictly decreasing functions, monotonic functions, monotonic increasing, and monotonic decreasing functions, necessary and sufficient conditions for monotonicity, finding the intervals in which a function is increasing or decreasing and proving the monotonicity of a function on a given interval. Students can access the exercises solution links provided below, which cover all the topics discussed in this chapter.

RD Sharma Solutions Class 12 Maths Chapter 17 – Increasing and Decreasing Functions Exercise 17.1

RD Sharma Solutions Class 12 Maths Chapter 17 – Increasing and Decreasing Functions Exercise 17.2

RD Sharma Solutions for Class 12 Maths Chapter 18 – Maxima and Minima

In Chapter 18, Maxima and Minima of RD Sharma textbook deal with the maximum and minimum values of a function in its domain, definition of maximum, local maxima and local minima, definition and meaning of local maximum, first derivative test for local maxima and minima along with algorithm, higher-order derivative test, point of inflection, point of inflection, properties of maxima and minima, maximum and minimum values in the closed interval and applied problems on maxima and minima. Here, students can see the exercises explaining these concepts properly with solutions.

RD Sharma Solutions Class 12 Maths Chapter 18 – Maxima and Minima Exercise 18.1

RD Sharma Solutions Class 12 Maths Chapter 18 – Maxima and Minima Exercise 18.2

RD Sharma Solutions Class 12 Maths Chapter 18 – Maxima and Minima Exercise 18.3

RD Sharma Solutions Class 12 Maths Chapter 18 – Maxima and Minima Exercise 18.4

RD Sharma Solutions Class 12 Maths Chapter 18 – Maxima and Minima Exercise 18.5

RD Sharma Solutions for Class 12 Maths Chapter 19 – Indefinite Integrals

In this chapter, students concentrate on indefinite integral, primitive and antiderivative, fundamental integration formulae, some standard results on integration, integration of trigonometric functions, integration of exponential functions, geometrical interpretation of indefinite integral, comparison between differentiation and integration, methods of integration, integration by substitution, integration by parts, integration of rational algebraic functions by using partial fractions and integration of some special irrational algebraic functions. These concepts are explained very well through examples. Solutions to the exercises from this chapter can be accessed from here.

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.1

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.2

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.3

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.4

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.5

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.6

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.7

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.8

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.9

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.10

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.11

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.12

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.13

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.14

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.15

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.16

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.17

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.18

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.19

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.20

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.21

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.22

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.23

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.24

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.25

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.26

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.27

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.28

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.29

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.30

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.31

RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.32

We realize the importance of practising problems for a better understanding of concepts and their applications. For this reason, we, at BYJU’S bring to students an all-inclusive RD Sharma Solutions for Class 12 Maths. These solutions will help students to practice a variety of questions from different chapters to develop their analytical and reasoning skills. The solutions given here are in a well-structured format with different shortcut methods to ensure a proper understanding of the concept.

### Benefits of RD Sharma Solutions for Class 12 Maths

• RD Sharma Solutions provide an algorithmic approach to solve each problem.
• These solutions give more than one way to solve, with detailed illustrations and brief summaries, which consist of concepts and formulae.
• These solutions are prepared by our BYJU’S expert team, focusing completely on accuracy.
• Students get detailed study material on topics from Class 12 Maths.
• To make learning more interesting, each solution is provided with a pictorial representation to improve analysing skills among students.

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