**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.

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## 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 = 2 ^{ab} 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 = a ^{2} + b^{2} 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 = ab ^{2} 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 = a ^{b} 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.