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 = 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 = 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 = 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

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