RD Sharma Solutions for Class 12 Maths – Chapter-wise Free PDF Download Updated for 2025-26

RD Sharma Solutions for Class 12 Maths PDF are now easily accessible for students aiming to prepare effectively for their upcoming exams. With the RD Sharma Solutions PDF download, students can confidently solve any problem from the RD Sharma textbooks by referring to detailed, step-by-step explanations. Crafted by subject matter experts at Infinity Learn, the solutions are presented in a simple and easy-to-understand manner, helping students approach problems more efficiently. These resources are designed to strengthen the fundamental concepts and assist CBSE Class 12 students in achieving excellent marks in their final exams.

Since Mathematics can often be challenging for Class 12 students, these RD Sharma Class 12 Solutions PDF download materials aim to transform their learning experience. They not only simplify complex topics but also make students realize how interesting and approachable the subject can be. Focused on building mathematical skills through various tricks and shortcuts, these solutions promote faster and more accurate calculations. 

Download the RD Sharma Class 12 PDF today and start practicing all the questions from the CBSE textbook. Regular practice with these solutions ensures students are well-prepared for all types of questions that may appear in the examination.

Download RD Sharma Chapter-wise Solutions for Class 12 Maths

RD Sharma Solutions for Class 12 Maths – Exercise-wise Solutions

Students can refer to the RD Sharma Class 12 solutions to strengthen their understanding of key concepts. For better guidance and exam preparation, practicing these solutions is highly recommended. Regularly solving the exercises from each chapter will help students build confidence and secure higher marks in their board exams.

RD Sharma Solutions for Class 12 Maths Chapter 1 – Relations

Chapter 1 of the RD Sharma Class 12 textbook introduces the concept of relations and explores their properties in detail. It covers various aspects such as the definition of relations, types of relations, inverse of a relation, equivalence relations, important results on relations, and the concepts of reflexive, symmetric, and transitive relations.

Relation: A relation defines the connection between two sets of information. If two non-empty sets are given, a relation is established when there is a meaningful association between the elements of these sets.

Types of Relations: Relations can be categorized into different types, including empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation.

RD Sharma Solutions for Class 12 Maths Chapter 2 – Functions

Chapter 2, Functions, from RD Sharma Class 12 Maths, offers an in-depth understanding of various key concepts such as the definition of functions, functions as correspondence, and functions as a set of ordered pairs. 

It also covers the graphical representation of functions, the vertical line test, and different types of functions including constant, identity, modulus, greatest integer function and its properties, smallest integer function and its properties, fractional part function, signum, exponential, logarithmic, reciprocal, square, square root, cube, and reciprocal squared functions. 

Students also learn about operations on real functions, kinds of functions like one-one, many-one, onto, bijection, and the composition of functions along with their properties. Furthermore, the chapter explains how to relate a function to its inverse graphically. 

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

Chapter 3 of the RD Sharma Class 12 Maths textbook focuses on the concept of binary operations. In this chapter, students will learn the definition of a binary operation, how to determine the number of binary operations possible on a set, and the different types of binary operations including commutativity, associativity, and distributivity. 

It also introduces important concepts like the identity element, the inverse of an element, the composition table, and explains operations like addition modulo 'n' and multiplication modulo 'n'. 

A binary operation is defined as an operation * performed on a set A, expressed by the function *: A × A → A, meaning that for any two elements a and b in A, the result a * b also belongs to A. The primary types of binary operations discussed are distributive, associative, and commutative operations.

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

Chapter 4 of RD Sharma Class 12 Maths Solutions focuses on the concept of inverse functions, specifically inverse trigonometric functions. In this chapter, students learn the definition and significance of inverse trigonometric functions along with detailed explanations of the inverse of the sine, cosine, tangent, secant, cosecant, and cotangent functions. 

The chapter also highlights the important properties of inverse trigonometric functions. Inverse trigonometric functions are the inverses of the basic trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant. They are also known as arcus functions, antitrigonometric functions, or cyclometric functions. 

The properties of inverse trigonometric functions are divided into two sets. Property Set 1 includes identities such as Sin⁻¹(x) = Cosec⁻¹(1/x) for x belonging to [−1,1] excluding 0, Cos⁻¹(x) = Sec⁻¹(1/x) for x in [−1,1] excluding 0, Tan⁻¹(x) = Cot⁻¹(1/x) if x > 0 or Cot⁻¹(1/x) − π if x < 0, and Cot⁻¹(x) = Tan⁻¹(1/x) if x > 0 or Tan⁻¹(1/x) + π if x < 0. 

Property Set 2 explains the behavior of inverse trigonometric functions with negative values, such as Sin⁻¹(−x) = −Sin⁻¹(x), Tan⁻¹(−x) = −Tan⁻¹(x), Cos⁻¹(−x) = π − Cos⁻¹(x), Cosec⁻¹(−x) = −Cosec⁻¹(x), Sec⁻¹(−x) = π − Sec⁻¹(x), and Cot⁻¹(−x) = π − Cot⁻¹(x). Mastering these properties helps students solve complex trigonometric problems efficiently.

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

Chapter 5 of the RD Sharma Class 12 Maths textbook introduces students to the concept of Matrices. The chapter begins with the definition of matrices and gradually moves on to cover important topics such as types of matrices, equality of matrices, addition of matrices, and properties related to matrix addition. 

It also discusses multiplication of a matrix by a scalar, properties of scalar multiplication, subtraction of matrices, multiplication of matrices, and the properties associated with matrix multiplication. 

Students also learn about positive integral powers of a square matrix, the transpose of a matrix, properties of transpose, and concepts of symmetric and skew-symmetric matrices with the help of examples. 

A Matrix is defined as a rectangular arrangement of m × n numbers (either real or complex) organized in m horizontal rows and n vertical columns, and is referred to as a matrix of order m × n. The types of matrices discussed in this chapter include symmetric matrices, skew-symmetric matrices, Hermitian and skew-Hermitian matrices, orthogonal matrices, idempotent matrices, involutory matrices, and nilpotent matrices. 

Additionally, the chapter explains the transpose of a matrix, which is obtained by interchanging the rows and columns of a given matrix A, and is denoted by Aᵀ or A′.

RD Sharma Solutions for Class 12 Maths Chapter 6 – Determinants

Chapter 6 of the RD Sharma Mathematics Class 12 textbook introduces the concept of determinants in detail. It covers the definition of determinants, the determinant of a square matrix of order 1, 2, and 3, and the method of finding the determinant of a 3×3 matrix using the Sarrus diagram. 

The chapter also explains related concepts such as singular matrices, minors, cofactors, and various important properties of determinants. Students learn about the evaluation of determinants and their practical applications in coordinate geometry as well as in solving systems of linear equations, including conditions for consistency. 

A determinant can be defined as an expression formed by the columns (or rows) of an n × n matrix arranged as column vectors. The chapter further discusses key properties of determinants such as the Reflection Property, All-zero Property, Proportionality (or Repetition) Property, Switching Property, Sum Property, Scalar Multiple Property, Factor Property, Triangle Property, Invariance Property, and the Determinant of the Cofactor Matrix. These properties are fundamental in simplifying calculations and understanding the behavior of matrices in higher-level mathematics.

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

In Chapter 7: Adjoint and Inverse of a Matrix from RD Sharma Class 12 Maths, students explore important concepts such as the definition of the adjoint of a square matrix, the inverse of a matrix, and key results related to invertible matrices. The chapter also covers elementary transformations and operations on matrices through detailed examples and word problems.

The adjoint of a matrix is defined as the transpose of the cofactor matrix. If A = [A_ij ]_n×n is a square matrix, then its adjoint is the transpose of the matrix formed by the cofactors A_ij of each element a_ij. In simple terms, the adjoint is obtained by taking the transpose of the cofactor matrix.

The inverse of a matrix exists for every non-singular square matrix. If A is a square matrix, then its inverse, denoted as A⁻¹, satisfies the property AA⁻¹ = A⁻¹A = I, where I is the identity matrix.

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

Chapter 8 of the RD Sharma Class 12 Maths textbook delves deeper into the topic of equations, starting with their definition and moving on to important concepts such as consistent systems, homogeneous and non-homogeneous systems, and the matrix method for solving non-homogeneous systems.

The chapter also discusses the final solutions of homogeneous systems of linear equations. Students will learn that there are two main types of linear equations: homogeneous and non-homogeneous.

A homogeneous equation has zero on the right-hand side of the equality sign, while a non-homogeneous equation includes a function of the independent variable on the right-hand side.

RD Sharma Solutions for Class 12 Maths Chapter 9 – Continuity

In this chapter, students focus on understanding the concept of continuity in depth. Key topics include the definition of continuity, continuity at a point, algebra of continuous functions, continuity over an interval, and specifically, continuity on open and closed intervals. Students also learn about continuous functions, functions that are continuous everywhere, and important properties of continuous functions.

Continuity is defined as follows: a function f is said to be continuous at a point “a” on the real line if the limit of f(x) as x approaches “a” is equal to f(a). A function is considered continuous if it is continuous at every point in its domain.

A continuous function is one that does not exhibit any sudden jumps, breaks, or unexpected changes in value. Regarding intervals, an open interval does not include its endpoints and is denoted by parentheses ( ), while a closed interval includes all its limit points and is denoted by brackets [ ].

RD Sharma Solutions for Class 12 Maths Chapter 10 – Differentiability

Differentiability is a fundamental concept in calculus that deals with the smoothness of functions and their ability to be differentiated at given points. Chapter 10 of RD Sharma Class 12 Maths introduces students to the formal definition of differentiability, explaining how it is closely linked to the existence of derivatives.

A function is said to be differentiable at a point if its derivative exists at that point and is continuous in the vicinity. This chapter revisits essential concepts from earlier studies and extends them to more advanced ideas such as differentiability at a point, differentiability over a set, and important results related to differentiability.

Through the RD Sharma Solutions for Class 12 Chapter 10, students gain a step-by-step understanding of solving problems based on differentiability. The solutions are designed to simplify complex topics, helping students master the techniques needed to determine whether a function is differentiable and how to apply differentiation rules effectively.

A solid grasp of differentiability is crucial not only for board exams but also for competitive exams like JEE, making this chapter an important milestone in a student's mathematical journey.