RD Sharma Class 12 Solutions 2024-25 PDF Free Download

If you want to preparation for board examination so RD Sharma Class 12 Solutions is a great study tool to answer difficult questions. It is ideal for the intermediate or class 12 students who have taken Science stream and are referring to the RD Sharma textbooks to complete their class 12 Syllabus. The RD Sharma class 12 Maths Solutions are prepared by our subject experts having years of experience in teaching and mentoring students of JEE Mains, and several national level competitive exams for engineering. 

RD Sharma Class 12 Maths Solutions (Vol-1 & Vol-2 )

RD Sharma Class 12 Maths Solutions for Volume 1 and Volume 2 are undoubtedly very helpful study resources. It helps you to cover your Class 12 Maths Syllabus as well as helps you master the Mathematics topics of 12th class.

Solving the difficult questions of mathematics is quite a challenging task, however, RD Sharma Solutions for Class 12 assists you to answer all kinds of questions irrespective of their difficulties. Because, our maths experts have solved all the chapter’s questions in an easy to understand manner. 

Links to download RD Sharma Class 12 Solutions are given below.

The RD Sharma Class 12 Maths book has been splitted into two volumes: Volume 1 & Volume 2. Volume 1 has 19 chapters, starting from 1 to 19 where Volume 2 consists of chapters starting from 20 to 33. 

Every chapter of RD Sharma Class 12 Maths book contains illustrative examples, chapters’ end questions (Subjective and MCQs too) as well as Summary for quick revision. Also, the whole chapters of RD Sharma Class 12 Maths have two levels of difficulties and students learning from them need to face those levels of difficulties. Hence, to help students to tackle those difficulties, our experts have prepared RD Sharma Class 12 Solutions PDF.

Chapter Wise RD Sharma Class 12 Maths Solutions

Let’s dive into all the 33 chapters and explore what topics are there to cover.

RD Sharma Class 12 Solutions Maths Chapter 1 Relations

The very first chapter of RD Sharma Class 12 Maths is Relations that talks about properties of relations, types of relations, inverse of a relation, equivalence relation, reflexive relation, symmetric relation, and transitive relation. Apart from these subtopics, there are a few definitions of given topics. Also, there are some ways to represent types of relations, check them out - 

RD Sharma Class 12 Solutions Maths Chapter 2 Functions

The second chapter of Class 12 RD Sharma Maths covers topics such as what is function, types of functions such as constant function, identity function, modulus function, greatest integer function, and more. The major topics that are covered in this lesson are Function, Types of Function, & Inverse Function.

RD Sharma Class 12 Solutions Maths Chapter 3 Binary Operations

RD Sharma Class 12 Maths Chapter 3 Binary Operation helps students to understand Definition of a binary operation, the number of binary operations, types of binary operations, and more. There are 5 exercises in this lesson.

RD Sharma Class 12 Solutions Maths Chapter 4 Inverse Trigonometric Functions

A total of 14 exercises covering all the topics that are discussed in Chapter 4 Inverse Trigonometric Functions. There are inverse trigonometric functions such as sine function, cosine function, tangent function, secant function, cosecant, & cotangent function, etc.

Properties of Inverse Trigonometric Function

Property Set 1:

• Sin−1(x) = cosec−1(1/x), x∈ [−1,1] − {0}
• Cos−1(x) = sec−1(1/x), x ∈ [−1,1] − {0}
• Tan−1(x) = cot−1(1/x), if x > 0 (or) cot−1(1/x) −π, if x < 0
• Cot−1(x) = tan−1(1/x), if x > 0 (or) tan−1(1/x) + π, if x < 0

Property Set 2:

• 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)
• Cot−1(−x) = π − Cot−1(x)

RD Sharma Class 12 Solutions Maths Chapter 5 Algebra of Matrices

Matrices, Types of Matrices, & Transpose of Matrix are the main focus of RD Sharma Class 12 Chapter 5 Algebra of Matrices. Students will find a total of 5 exercises in this chapter.

RD Sharma Class 12 Solutions Maths Chapter 6 Determinants

Containing a total of 5 exercises that help students to develop a better understanding of the topic Determinants. The topics distributed across the chapter are determinants of a square matrix of order 1, 2, and 3, determinant of a square matrix of order 3 by using Sarrus diagram.

Properties of Determinants –

• Reflection Property
• All-zero property
• Proportionality property or Repetition Property
• Switching Property
• Sum Property
• Scalar multiple Property
• Factor Property
• Triangle Property
• Invariance Property
• The determinant of Cofactor matrix

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

Containing 2 exercises to practice but RD Sharma Class 12 Chapter 7 Adjoint and Inverse of a Matrix help learners to cover definition of the adjoint of a square matrix, the inverse of a matrix, verbal problems are also there in this chapter.

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

There are two types of linear equations: Homogeneous and Non-homogeneous equations. Hence, chapter 8 Solution of Simultaneous Linear Equations covers all the related topics along with their definition and a total of 2 exercises.

RD Sharma Class 12 Solutions Maths Chapter 9 Continuity

There are a total of 2 exercises in RD Sharma Class 12 Maths chapter 9 which examine student’s knowledge in definition of continuity, continuity at a point, algebra of continuous function, continuity on an interval. This whole lesson is very easy to solve and practice with the help of RD Sharma Class 12 Solutions Chapter 9 Continuity. Our experts have solved each and every lesson of this chapter. 

RD Sharma Class 12 Solutions Maths Chapter 10 Differentiability

RD Sharma Class 12 Chapter 10 Differentiability helps students to learn differentiability in a set, basic facts and formulae studied earlier in Class 11 and much more topics. Questions and solutions of RD Sharma Class 12 Chapter 10 are given here on this page. Questions are asked on the basis of Differentiability, & Differentiability formula; there are 2 exercises comprising the questions based on it.

RD Sharma Class 12 Solutions Maths Chapter 11 Differentiation

Differentiation of inverse trigonometric functions from first principles, differentiation of inverse trigonometric function by chain rule, differentiation of implicit functions, logarithmic differentiation, etc. are the topics that are discussed in RD Sharma Class 12 Chapter 11 Differentiation; based on it 8 exercises are given where students get to solve lots of differentiation problems.

RD Sharma Class 12 Solutions Maths Chapter 12 Higher Order Derivatives

The chapter 12 High order derivative includes topics where various relations are proved such as relations involving various order derivatives of parametric functions, relations involving various order derivatives via illustrations, involving various order derivatives of cartesian functions.

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

This chapter has a total of 2 exercises which is really worth practicing as this lesson contains more word problems which assist students to enhance their sentence formation. 

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

The chapter 14 Differentials, Errors and Approximations, Differentials help learners to learn about Absolute Error, Relative Error, Percentage Error & more. 

RD Sharma Class 12 Solutions Maths Chapter 15 Mean Value Theorems

A total of 81 questions across the 4 exercises are given. Thq questions are crafted on the basis of these topics: Graph of Maxima and Minima, Increasing and Decreasing Functions, Rate of Change of Bodies or Quantities, Simple Problems on Applications of Derivatives, etc..

RD Sharma Class 12 Solutions Maths Chapter 16 Tangents and Normals

Questions in RD Sharma Class 12 Chapter 16 have 3 exercises that are based on slope of a line, slopes of tangent and normal, finding slopes of tangent and normal at a given point, etc.

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

Containing 2 exercises based on Increasing and Decreasing Functions. Monotonic function is also explained within chapter 17 of RD Sharma Class 12 maths.

RD Sharma Class 12 Solutions Maths Chapter 18 Maxima and Minima

5 exercises that make students aware of the questions on point of inflection, properties of maxima and minima, maximum and minimum values in the closed interval. Practice to each question is advised to the class 12th students for higher understanding in chapter 18 Maxima and Minima.

RD Sharma Class 12 Solutions Maths Chapter 19 Indefinite Integrals

RD Sharma Class 12 chapter 19 Indefinite Integrals is a huge lesson and so their exercises are long too. A student has to solve a total of 32 exercises where Indefinite Integrals Formulas are used.

Indefinite Integrals Formula:

• ∫ 1 dx = x + C
• ∫ a dx = ax + C
• ∫ xndx = ((xn+1)/(n+1)) + C; n ≠ 1
• ∫ sin x dx = – cos x + C
• ∫ cos x dx = sin x + C
• ∫ sec2x dx = tan x + C
• ∫ cosec2x dx = -cot x + C
• ∫ sec x tan x dx = sec x + C
• ∫ cosec x cot x dx = -cosec x + C
• ∫ (1/x) dx = ln |x| + C
• ∫ exdx = ex + C
• ∫ axdx = (ax/ln a) + C; a > 0, a ≠ 1

RD Sharma Class 12 Solutions Maths Chapter 20 Definite Integrals

The topics of RD Sharma Class 12 Chapter 20 are antiderivative and indefinite integral of a function, change of limits, and such more topics that required a bit of practice to master. Hence the given 5 exercises will help students understand this lesson better.

RD Sharma Class 12 Solutions Maths Chapter 21 Areas of Bounded Regions

Area Between Two Curves, Area Under Simple Curves, Area of the Region Bounded by a Curve and a Line, etc. are covered in chapter 21 of RD Sharma Class 12 Maths. There are 4 exercises in this lesson that contain various types of questions including MCQs or Objective questions.

RD Sharma Class 12 Solutions Maths Chapter 22 Differential Equations

RD Sharma Class 12 Maths Chapter 22 has topics such as Degree of a differential equation, Formation of a Differential Equation, First Order, First Degree Differential Equations, and more. To help students in gathering the detailed knowledge of these topics the chapter 22 has a total of 11 exercises. And RD Sharma Class 12 Maths Solutions has answers to all the questions given in 11 exercises.

RD Sharma Class 12 Solutions Maths Chapter 23 Algebra of Vectors

RD Sharma Class 12 Maths Solutions is very helpful to learn about all the topics that are discussed in chapter 23 Algebra of Vectors. There are 9 exercises in this lesson that help students to assess their own learning from the topics Algebra of vectors and their types such as Zero Vectors, Unit Vectors, Equal, Negative, Position, etc.

RD Sharma Class 12 Solutions Maths Chapter 24 Scalar Or Dot Product

Chapter 24 Scalar or Dot product is a part of Vector. The topic is explained illustratively in RD Sharma Class 12 Maths Chapter 24. There are 2 exercises around this chapter which must be practiced by the class 12th students to deepen their knowledge of vectors. 

RD Sharma Class 12 Solutions Maths Chapter 25 Vector or Cross Product

Helping students to maintain their focus on each topic, the RD Sharma Class 12 maths has chapter 25 where Vector or Cross Product has been discussed in detail. Only one exercise is given there to help students to examine their basic understanding of the topic.

RD Sharma Class 12 Solutions Maths Chapter 26 Scalar Triple Product

Continuing the further lesson in RD Sharma Class 12 Maths the chapter 26 contains Scalar Triple Product that is also known as box product. Only one exercise is prepared for this topic where a few questions are asked. For each question, our maths experts have developed the RD Sharma Class 12 Solutions PDF.

RD Sharma Class 12 Solutions Maths Chapter 27 Direction Cosines and Direction Ratios

Selfstudys Maths experts have solved the chapter 27 of RD Sharma Class 12 Maths where one exercise is given on the topics of Direction Cosines and Direction Ratios. Each and every single question has been answered precisely and in an easy to understand manner.

RD Sharma Class 12 Solutions Maths Chapter 28 Straight line in space

Two-point form of the equation of a straight line, Parametric form equation of a straight line, The angle between two straight lines, Parallel lines, Perpendicular lines, The intersection of two lines in space, Parallel line and plane, etc. are the core topics of RD Sharma Class 12 Chapter 28 Straight line in space. There are 5 exercises in this lesson.

RD Sharma Class 12 Solutions Maths Chapter 29 The plane

Angle Between Two Planes, Coplanarity of Two Lines, Direction Cosines and Direction Ratios of a Line, Distance of a Point from a Plane, and such more subtopics are covered in RD Sharma Class 12 Maths Chapter 29 where 15 exercises are given.

RD Sharma Class 12 Solutions Maths Chapter 30 Linear programming

Graphical Method of Solving Linear Programming Problems, Introduction of Linear Programming, Mathematical Formulation of Linear Programming Problem, etc. have been covered in RD Sharma Class 12 Chapter 30. A total of 5 exercises are given in this lesson. As well as MCQs are also given. RD Sharma Class 12 MCQ Solutions PDF is ideal to answer all the MCQs questions of RD Sharma Class 12 Maths.

RD Sharma Class 12 Solutions Maths Chapter 31 Probability

The chapter 31 of RD Sharma Class 12 Maths teaches students about Bayes’ Theorem, Bernoulli Trials and Binomial Distribution, Random Variables and Its Probability Distributions, Variance of a Random Variable, and more. Probability of class 12 can be a bit challenging for students as it has a different level of difficulty so , here we have RD Sharma 12 Solutions that will assist students to discover various methods of answering the 7 exercises of RD Sharma Class 12 Maths Chapter 31.

RD Sharma Class 12 Solutions Maths Chapter 32 Mean and variance of a random variable

2 exercises containing questions on the topic of the mean of a discrete random variable, the variance of a discrete random variable, etc. helps students to deepen their fundamental knowledge of topic Probability.

RD Sharma Class 12 Solutions Maths Chapter 33 Binomial Distribution

Chapter 33 Binomial Distribution is an advanced level of the topic probability where students get to learn a lot of different things about the Bernoulli Trials and Binomial Distribution and more. A total of 2 exercises containing very short answer types of questions as well as MCQs are given in RD Sharma Class 12 Chapter 33. RD Sharma Class 12 Solutions PDF contains answers to all the questions asked.

Features of RD Sharma Class 12 Maths Solutions

Some of the amazing features of RD Sharma Class 12 Maths Solutions are discussed in this section.

• Questions with Step-wise Answers: A student who refers to our RD Sharma Solutions for Class 12 Maths need not carry their bulky books with them when solving the Maths questions. It is because the Maths experts have mentioned the questions followed by step-wise answers in the solutions booklet. Thus, students referring to the PDF file don’t have only access to the answers but their questions too.

• Easy to Understand Langauge and Techniques Used: Anyone who uses the PDF file of Class 12 Maths RD Sharma Solutions will have fun learning from the PDF file because the Maths questions are solved using simple and easy-to-understand language. The techniques that are used when answering the Maths questions are very easy and comfortable for students to practise whenever they want.

• Clear and Crisp Design: In order to keep the RD Sharma Class 12 Maths Solutions clear and crisp, the experts have maintained the cleanliness of the PDF file. Every single question, their answers, tips and tricks all are in a logical manner.

• PDFs are Available 24×7 Online: One of the most useful features of RD Sharma 12 Maths Solutions PDF is that it can be accessed 24×7 Online for free of cost.

Why Use RD Sharma Class 12 Solutions PDF?

Indeed, there are some reasons that ensure why a student should use RD Sharma Class 12 Maths Solutions PDF. In this section, we are discussing them one by one.

• 100% Accurate Answers: The answers prepared by Maths experts ensures 100% accuracy. Those who struggle to comprehend RD Sharma Maths questions should use the PDF file as it helps them understand the questions and answer them accurately. Higher the accuracy, higher the marks.

• Helpful for Self-study: Students who are solving RD Sharma Class 12 Maths when doing self-study may stuck on some questions. In that case, they won’t get instant help to solve that problem thus, the use of Class 12 Maths RD Sharma Solutions PDF is advised as it helps them access the answers to that particular question every time.

• Gives Confidence: Being able to answer the RD Sharma Class 12 Maths questions and having access to the Class 12 RD Sharma Maths Solutions PDF give students confidence. Students feel confident when solving RD Sharma 12 Maths questions regardless of their difficulty level.

How to Download RD Sharma Class 12 Solutions PDF?

To download RD Sharma Class 12 Solutions PDF from Selfstudys.com one needs to follow these steps:

• Visit the official website of Selfstudys
• Tap on the navigation icon available top-left-hand side. The navigation icon looks like this

• After tapping on the navigation icon, it shows various categories to choose from - Choose Books & Solutions

• The chosen category will expand further - Now, Choose RD Sharma Solutions

• Options to choose a class will be shown, tap on Class 12 to proceed further

• The page will quickly reload, tap on Maths - RD Sharma Solutions to access the PDF file in a chapter-wise manner

Why RD Sharma Class 12 Maths Solutions by Selfstudys Is a Good Choice?

RD Sharma Class 12 Maths Solutions available here at Selfstudys is a great choice for a learner here’s how -

• Maths experts of Selfstudys have prepared the solutions because of which the answers are highly accurate.

• Solutions are also easy to read and understand which promotes skills such as understanding context and analytics.

•  The Selfstudys team has kept in mind the necessity of tips and tricks so, the team has mentioned the tips separately in the PDF file.

How & When to Use RD Sharma Class 12 Solutions?

No specific time has been mentioned to use the RD Sharma Class 12 Solutions and one can use it however they want. Despite these, in this section, we are discussing some of the solid ways to use RD Sharma Class 12 Maths Solutions PDF.

• Attempt the Problems First: Ideally, students shouldn’t jump on the PDF file to answer RD Sharma Maths problems instead they should try to attempt the Maths problems by themselves. Doing this helps students use the concepts and skills they have learned earlier in theory classes. It also helps students know the areas of improvement.

• Check Your Answers: Those who struggle with verifying their answers can use the RD Sharma Class 12 Maths Solutions as the experts have already mentioned the answers in a PDF file.

• Identify Areas of Weakness: With the help of RD Sharma Class 12 Maths Solutions learners can identify areas of weakness in the subject. It is possible by trying to practice the questions and finding the problems they are unable to solve.

• Use the Solutions Booklet as a Learning Tool: The RD Sharma Class 12 Maths Solutions is one of the best learning tools for students relying on self-study. However, students who are solving and practising the RD Sharma Class 12 Maths can also learn a variety of techniques to solve the Maths questions.

About RD Sharma Class 12 Maths Solutions

RD Sharma Solutions for Class 12 is a well-known name in the field of maths because of its content, Easy explanation of various difficult concepts, the conceptual interlinking from different topics and a wide variety of questions for study and more. RD Sharma Solutions for Class 12 is a treasure for maths students. It is one of the best solutions that provides complete details about every chapter which helps students in their exam preparation. RD Sharma Solutions for Class 12 given by Selfstudys is one of the best solutions available on the whole internet. The solutions are created chapter wise and are further classified on the basis of exercises making it much simpler for students to navigate and select any chapters for which the solution is needed.

RD Sharma Solutions Class 12 Maths

Maths is the most important subject which not just decides the student's career but also grows their ability of analytical and rational thinking. RD Sharma Solutions Class 12 Maths includes a huge number of well-graded solved questions. Students are advised to study these resolved questions on their own without seeing the answers, they may look at the solutions if they are unable to determine them. This would help them in growing the confidence to attempt unsolved questions. This is very essential if one wants to obtain good marks in the final examination.

Maths has changed the face of the whole world by contributing to several advances in technology. Maths will no longer be a daunting subject when a student uses RD Sharma Solutions for Class 12. Guided diagrammatically, step-by-step, every chapter is explained to the letter and this helps students a big deal in preparing for their Class 12 board examinations.