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RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.5) Exercise 3.5

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RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.5) Exercise 3.5 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 3 - Binary Operations Exercise 3.5 solved by Expert Mathematics Teachers on All Chapter 3 - Binary Operations Ex 3.5 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

Competitive Exams after 12th Science

Introduction to the Chapter

‘Binary Operations’ is the third chapter of class 12 Maths in which students learn about calculations that combine two elements to produce another element, Examples of binary operations are also the common arithmetic operations addition, subtraction, division, and multiplication. Binary Operation is one of the vital chapters in Class 12 since the topic has lots of applications and it is an important topic for higher studies as well, therefore it is very important to go thoroughly through the chapter.

Topics of RD Sharma Class 12 Chapter 3- Binary Operations

  1. Relation

  2. Function

  3. Types of Relation

  4. Empty Relation

  5. Universal Relation

  6. Trivial Relation

  7. Reflexive Relations

  8. Symmetric Relations

  9. Transitive Relations

  10. Equivalence Relations

  11. Equivalence Class

  12. Types of functions

  13. Injective

  14. Non-Injective

  15. Surjective

  16. Non onto

  17. Bijective

  18. Composition of functions

  19. Invertible functions

  20. Theorems

  21. Binary Operations

  22. Commutative Binary Operations

  23. Associative Binary Operations

  24. Identity Binary Operations

  25. Invertible Binary Operations

Exercises and their Page Numbers RD Sharma Class 12 Chapter 3- Binary Operations

Exercise Number

Page Number











Very Short Answer


Multiple Choice Questions


FAQs on RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.5) Exercise 3.5

1. What are equivalence relations in Binary Operations?

An equivalence relation on a set S is a relation on S which is reflexive, transitive, and symmetric, and the equivalence relation is denoted by.

Example- On the set X=a,b,c, the relation R=(a,a),(b,b),(c,c),(b,c),(c,b)is an equivalence relation.

The equivalence classes of the above relation are- 


All equivalence classes for R are ab,c.

The relations that have “is equal to”, “is similar to”, “is congruent to”, “has the absolute value as”, “has the same cosine as” are all equivalence relations.

2. What are the properties of binary relations?

There are 4 properties of binary relations.

Let R be relation on a set, then:

  1. If aRa, aA , R is reflexive.

  2. If a,bA, if aRB then bRa, R is symmetric.

  3. If a,b,cA, if aRb and bRc, then aRc, R is transitive.

  4. If a,bA, if aRb and bRa, then a=b, R is anti-symmetric.

3. Are Vedantu’s solutions helpful for practicing Maths questions in Class 12?

Vedantu’s solutions are designed by subject experts and in accordance with the CBSE Board pattern in a step-by-step manner.  The solutions are easy to understand as the students find the language familiar and easy to understand. Students can also refer to the revision notes provided by Vedantu to have a better understanding of the concept before solving the question since it is very important for the students to understand the concepts to the core in Class 12 as it lays a foundation for higher-level studies. 

4. Can a student rely completely on Vedantu’s study materials if he wants to score good grades in Maths in Class 12 Boards?

Vedantu has lots of study materials available on its website which includes, syllabus for the subjects, revision notes for CBSE, ICSE, and other state boards, solved questions of various books, previous year question papers. So for the theoretical and conceptual part students should go through the chapter in textbooks first and then go for the revision notes. But the students can definitely rely on Vedantu for textbook solutions and previous year question papers.

5. Is binary operations an important Chapter for class 12 boards?

Binary Operations is the third chapter of RD Sharma Class 12 Maths and the first chapter of NCERT Maths with the name Functions and Relations. The whole chapter is very important for Class 12 and for National and State level competitive and entrance exams as well. In Boards, the weightage of the Chapter itself is a total of 8 marks. Therefore, students should not miss topics in this chapter. Students who want to focus on boards can refer to the NCERT Maths book and the student who wishes to study the concepts in-depth can refer to RD Sharma as detailed explanations of all concepts are there.