# RS Aggarwal Class 12 Solutions Chapter 3

## RS Aggarwal Solutions for Class 12 Chapter 3 â€“ Binary Operations Solutions PDF Download

### RS Aggarwal Solutions Class 12 Maths Chapterwise â€“ Free PDF Download

The CBSE Class 12 students can find the **RS Aggarwal class 12 Solutions Chapter 3 Binary Operations** Maths on the Utopper website. All of the exercise questions from Maths Class 12 Chapters are answered, which will help students a lot as they study for exams and review. Utopper is Indiaâ€™s most popular online learning platform. The details for each chapter of these solutions are given to you for free in PDF format.

You will also be able to download all of the RS Aggarwal class 12 Solutions Chapter 3 in PDF format, which will help you study for exams in the school year 2022. our experts teachers have put together the RS Aggarwal Solutions for Class 12 Chapter 3 on Utopper. Also, use the updated CBSE textbook solutions we give you to review and answer the important questions for the Class 12 Maths (RS Aggarwal) exam.

In this chapter, we will learn about the three properties of binary operations: that they are commutative, associative, and distributive. You will also learn about the identity element and the invertible element of a binary operation. You will also learn how to use a composition table to describe a binary operation on a finite set.

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**RS Aggarwal class 12 Solutions Chapter 3 Math â€“ Binary OperationsÂ **

**RS Aggarwal class 12 Solutions Chapter 3 Math â€“ Binary OperationsÂ**

**RS Aggarwal Class 12 Solutions**

## Chapter-1 Relation Solutions

## Chapter-2 Functions Solutions

## Chapter-3 Binary Operations Solutions

## Chapter-4 Inverse Trigonometric Functions Solutions

## Chapter-5 Matrices Solutions

## Chapter-6 Determinants Solutions

## Chapter-7 Adjoint and Inverse of a Matrix Solutions

## Chapter-8 System of Linear Equations Solutions

## Chapter-9 Continuity and Differentiability Solutions

## Chapter-10 Differentiation Solutions

## Chapter-11 Applications of Derivatives Solutions

## Chapter-12 Indefinite Integral Solutions

## Chapter-13 Method of Integration Solutions

## Chapter-14 Some Special Integrals Solutions

## Chapter-15 Integration Using Partial Fractions Solutions

## Chapter-16 Definite Integrals Solutions

## Chapter-17 Area of Bounded Regions Solutions

## Chapter-18 Differential Equations and Their Formation Solutions

## Chapter-19 Differential Equations with Variable Separable Solutions

## Chapter-20 Homogeneous Differential Equations Solutions

## Chapter-21 Linear Differential Equations Solutions

## Chapter-22 Vectors and Their Properties Solutions

## Chapter-23 Scalar, or Dot, Product of Vectors Solutions

## Chapter-24 Cross, or Vector, Product of Vectors Solutions

## Chapter-25 Product of Three Vectors Solutions

## Chapter-26 Fundamental Concepts of 3-Dimensional Geometry Solutions

## Chapter-27 Straight Line in Space Solutions

## Chapter-28 The Plane Solutions

## Chapter-29 Probability Solutions

## Chapter-30 Bayesâ€™s Theorem and its Applications Solutions

## Chapter-31 Probability Distribution Solutions

## Chapter-32 Binomial Distribution Solutions

## Chapter-33 Linear Programming Solutions

#### RS Aggarwal class 12 Solutions Chapter 3 Binary Operations covers the following topics:

In the two exercises 3A and 3B of RS Aggarwal class 12 Solutions Chapter 3, there are a total of 14 questions that cover each topic in the course outline in depth. The questions range from ones with very short answers to ones where you have to show that a certain binary operation has a certain property or not. You will also get to try harder problems where you have to define operations for functions that have already been given.

- Introduction to Binary Operations
- Commutative Property of Binary Operations
- Associative Property of Binary Operations
- Distributive Property of Binary Operations
- Identity Element Inverse Element

#### Summary of RS Aggarwal class 12 Solutions Chapter 3 : Binary Operations

In a binary operation, the cartesian product of two sets is the same as the given set.

A binary operation

- has commutative property if a * b = b * a for every a, b âˆˆ S;Â
- has associative property if (a * b)* c = a*(b*c) for every a, b, c âˆˆ S;
- has distributive property over binary operation if a*(b âŠ™ c)=(a*b) âŠ™ (a*c) and (b âŠ™ c)*a=(b*a) âŠ™ (c*a)for all a, b, c âˆˆ S.
- The identity element: a * e = a = e * a When * is a binary operation for the set S, which statement is true?
- Inverse element: a * b = e = b * aÂ

#### Why you should use Utopper

Utopper is one of Indiaâ€™s best and most affordable digital learning platforms. It offers free study materials, lectures, and video classes to all of its users and students. Students can get free PDFs of all the chapters and other materials that help them study better from Utopper. The Utopper website and app have notes, solutions, sample papers, and copies of NCERT textbooks for classes 1 through 12. Utopperâ€™s solutions and review notes are made by subject experts and teachers who want to make it easier for students to study for exams and understand the concepts well.Â

## FAQ ( Frequently Asked Questions )

**1. How many questions are in Chapter 3 of Class 12 RS Aggarwal?**

Ans â€“ In RS Aggarwal class 12 Solutions chapter 3, there are a total of 14 full-length questions, which are split between two exercises, 3A and 3B. Both exercises have a wide range of questions that cover a lot of different ideas that students can use. Students are eased into the chapter with the first 3A exercise, which has questions about the binary operations and their properties. In the second activity, students have to figure out which binary operations are commutative, associative, and distributive.

**2. Where can I find the Chapter 3 Binary Operations solutions for Class 12 RS Aggarwal?**

Ans â€“ Students who want to access Class 12 Math RS Aggarwal Solutions can do so through the Utopper website. Since their solutions are made by experts in the field, Utopper has the best study materials of any online digital learning platform. All of the answers and exercises for all 33 chapters can be found on the Utopper website. On the website, you can also find revision notes and NCERT solutions, among other things.

**3. What are the advantages of using RS Aggarwal Class 12 Solutions for Mathematics?**

Ans â€“ Â Students who want to study for and do well on their board exams can get a lot out of the Utopper solutions for Class 12 RS Aggarwal. These solutions are helpful for students because they are written in a way that is easy for them to understand and can help them clear up their doubts.

The answers are written in a step-by-step format, which makes it easy to follow and also lets students see where they went wrong. The solutions can also be downloaded for free from the Utopper website, so students can use them whenever they want, whether they are online or not.Â