# RD Sharma Solutions For Class 12 Maths Exercise 3.2 Chapter 3 Binary Operations (Updated for 2021-22)

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2: The types of binary operations are the focus of this exercise. The question in RD Sharma Solutions for Class 12 Chapter 3 Exercise 3.2 are based on binary operations’ commutativity and associativity. Students may download the free PDF of RD Sharma Solutions for Class 12 Chapter 3 Binary Operations Exercise 3.2 from this article.

## Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2 PDF

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2

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### Access RD Sharma Solutions For Binary Operations Exercise 3.2 Class 12 Maths Chapter 3 Important Questions

1. Let ‘*’ be a binary operation on N defined by a * b = l.c.m. (a, b) for all a, b ∈ N
(i) Find 2 * 4, 3 * 5, 1 * 6.

(ii) Check the commutativity and associativity of ‘*’ on N.

Solution:

2. Determine which of the following binary operation is associative and which is commutative:

(i) * on N defined by a * b = 1 for all a, b ∈ N

(ii) * on Q defined by a * b = (a + b)/2 for all a, b ∈ Q

Solution:

3. Let A be any set containing more than one element. Let ‘*’ be a binary operation on A defined by a * b = b for all a, b ∈ A Is ‘*’ commutative or associative on A?

Solution:

4. Check the commutativity and associativity of each of the following binary operations:

(i) ‘*’ on Z defined by a * b = a + b + a b for all a, b ∈ Z

Solution:

(ii) ‘*’ on N defined by a * b = 2ab for all a, b ∈ N

Solution:

(iii) ‘*’ on Q defined by a * b = a – b for all a, b ∈ Q

Solution:

(iv) ‘⊙’ on Q defined by a ⊙ b = a2 + b2 for all a, b ∈ Q

Solution:

(v) ‘o’ on Q defined by a o b = (ab/2) for all a, b ∈ Q

Solution:

(vi) ‘*’ on Q defined by a * b = ab2 for all a, b ∈ Q

Solution:

(vii) ‘*’ on Q defined by a * b = a + a b for all a, b ∈ Q

Solution:

(viii) ‘*’ on R defined by a * b = a + b -7 for all a, b ∈ R

Solution:

(ix) ‘*’ on Q defined by a * b = (a – b)2 for all a, b ∈ Q

Solution:

(x) ‘*’ on Q defined by a * b = a b + 1 for all a, b ∈ Q

Solution:

(xi) ‘*’ on N defined by a * b = ab for all a, b ∈ N

Solution:

(xii) ‘*’ on Z defined by a * b = a – b for all a, b ∈ Z

Solution:

(xiii) ‘*’ on Q defined by a * b = (ab/4) for all a, b ∈ Q

5. If the binary operation o is defined by a0b = a + b – ab on the set Q – {-1} of all rational numbers other than 1, show that o is commutative on Q – [1].

6. Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative?

7. On the set Z of integers a binary operation * is defined by a 8 b = ab + 1 for all a, b ∈ Z. Prove that * is not associative on Z.

Binary Operations Ex 3.2 Q8

Binary Operations Ex 3.2 Q9

Binary Operations Ex 3.2 Q10

Binary Operations Ex 3.2 Q11

Binary Operations Ex 3.2 Q12

Binary Operations Ex 3.2 Q13

We have provided complete details of RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2. If you have any queries related to CBSE Class 12 Exam, feel free to ask us in the comment section below.

## FAQs on RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2

### How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2?

There are a total of 13 questions in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2.

### Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free?

Yes, You can get RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free.

### Where can I download RD Sharma Solutions for Chapter 3 Exercise 3.2 Class 12 Maths free PDF?

You can download RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 free PDF from the above article.