RD SHARMA Solutions for Class 12-science Maths Chapter 3 - Binary Operations

Chapter 3 - Binary Operations Exercise Ex. 3.1

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 1(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 1(vi)

Determine whether the following operation defines a binary operation on the

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 1(vi)

We have,

A b = ab + ba for all a, b, ϵ N

Let a ϵ N and b ϵ N

ab ϵ N and ba ϵ N

ab + ba ϵ N

a b ϵ N

Thus, the operation ‘’ defines a binary relation on N

Question 1(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 3

Let * be a binary opeartor o the set I of integers, defined by a*b = 2a + b - 3.

find the value of 3*4

Solution 3

It is given that, a*b = 2a + b - 3

now,

3*4 = 2 × 3 + 4 - 3

      = 10 - 3

      = 7

Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 9

The binary operation & : R × R → R is defined as a * b = 2a + b.

Find (2*3)*4.

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise Ex. 3.2

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(iv)

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

 

 

'' on Q defined by ab = a2 + b2 for all a, b ϵ Q.

Solution 4(iv)

'' on Q defined by ab = a2 + b2 for all a, b ϵ Q

 

Commutativity:

For a, b ϵ Q

ab = a2 + b2 = b2 + a2 = ba

So, '' is commutative on Q.

 

Associativity:

For a, b, c ϵ Q

(ab) ⊙c = (a2 + b2) ⊙c = (a2 + b2)2 + c2

a⊙(b ⊙c) =a ⊙( b2 +c2)= a2 +(b2 + c2 )2

(ab) ⊙c ≠ a⊙(b ⊙c)

So, '' is not associative on Q.

 

 

Question 4(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4(viii)

Check the commutativity and associativity of the following binary operation :

'*' on R defined by a*b = a + b - 7 for all a, b ε Q

Solution 4(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(ix)

Check the commutativity and associativity of the following binary operation :

'*' on Q defined by a*b = (a - b)2 for all a, b ε Q.

Solution 4(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(X)

Check the commutativity and associativity of the following binary operation :

'*' on Q defined by a*b = ab + 1 for all a, b ε Q

 

Solution 4(X)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(xi)

Check the commutativity and associativity of the following binary operation :

'*' on N, defined by a*b = ab for all a, b, ε N.

Solution 4(xi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(xii)

Check the commutativity and associativity of the following binary operation :

'*' on Z, a*b = a - b for all a, b, ε Z.

Solution 4(xii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(xiii)

Check the commutativity and associativity of the following binary operation :

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 4(xiii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4(xiv)

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

 

 

'*' on Z defined by a * b = a + b - ab for all a, b ϵ Z.

Solution 4(xiv)

'*' on Q defined by a*b = a + b - ab for all a, b ϵ Z

 

Commutativity:

For a, b ϵ Z

a*b = a + b - ab = b + a - ba = b*a

So, '*' is commutative on Z.

 

Associativity:

For a, b, c ϵ Z

(a*b) *c = (a + b - ab) *c

= a + b - ab + c + ac + bc - abc

 

a*(b*c )= a*( b + c - bc)

= a + b +c - bc + ab + ac + - abc

 

(a*b) *c ≠ a*(b*c )

So, '*' is not associative on Z.

 

Question 4(xv)

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

 

 

'*' on Q defined by a * b = gcd (a, b) for all a, b ϵ N.

Solution 4(xv)

'*' on Q defined by a*b = gcd (a, b) for all a, b ϵ N

 

Commutativity:

For a, b ϵ Q

a*b = gcd (a, b) = gcd (b, a) = b*a

So, '*' is commutative on N.

 

Associativity:

For a, b, c ϵ N

(a*b) *c = (gcd (a, b)) *c

= gcd (a, b, c)

=a*( gcd (b, c))

=a*(b*c)

 

(a*b) *c = a*(b*c )

So, '*' is associative on N.

 

Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Now consider (a * b) * c.

Thus, we have, (a * b) * c = (a + b + ab) * c

                                               = a + b + ab + c +(a + b + ab)c

                                     = a + b + ab + c + ac + bc + abc

                                    = a + b + c + ab + ac + bc + abc   ---(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 14

Let S be the set of all rational numbers except 1 and be defined on S by a b = a + b - ab, for all a, b s.

Prove that:

(i) is a binary operation on S

(ii) is commutative as well as associative.

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise Ex. 3.3

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise Ex. 3.4

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise Ex. 3.5

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise MCQ

Question 1

If a*b = a2 + b2, then the value of (4*5) * 3 is

 

a. (42 + 52) + 32

b. (4 + 5)2 + 32

c. 412 + 32

d. (4 + 5 + 3)2

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 2

If a*b denote the bigger among a and b and if a. b = (a * b) + 3, then 4.7 =

 

a. 14

b. 31

c. 10

d. 8

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 3

On the power set p of a non-empty set A, we define an operation Δ by

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Then which are the following statements is true about Δ

 

a. Commutative and associative without an identity

b. Commutative but not associative with an identity

c. Associative but not commutative without an identity

d. Associative and commutative with an identity

 

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4

If the binary operation* on Z is defined by a*b = a2 - b2 + ab + 4, then value of (2*3)  * 4 is

 

a. 233

b. 33

c. 55

d.  - 55

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 5

For the binary operation * on Z is defined by a*b = a + b + 1 the identity element is

 

a. 0

b. -1

c. 1

d. 2

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 6

If a binary operation * is defined on the set Z of integers as a * b = 3a - b, then the value of (2*3) * 4 is

 

a. 2

b. 3

c. 4

d. 5

Solution 6

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 7

Q+ denote the set of all positive rational numbers. If the binary operation on Q+ is defined as Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations then the inverse of 3 is

 

a. 4/3

b. 2

c. 1/3

d. 2/3

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 8

If G is the set of all matrices of the form Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations , where x R - {0}, then the identity element with respect to the multiplication of matrices as binary operation, is

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 8

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 9

Q+ is the set of all positive rational numbers with the binary operation * defined by Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations for all a, b Q+. Then inverse of an element a Q+ is

 

a. A

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 10

If the binary operation is defined on the set Q+ of all positive rational numbers by

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 11

Let * be a binary operation defined on set Q - {1} by the rule

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations 

a*b = a + b - ab. Then, the identity element for * is

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 12

Which of the following is true?

 

a. * defined by a * b = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations is a binary operation on Z

b. * defined by a * b = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations is a binary operation on Q

c. All binary commutative operations are associative

d. Subtraction is a binary operation on N.

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 13

The binary operations * defined on n by a * b = a+ b + ab for all a, b N is.

 

a. Commutative only

b. Associative only

c. Commutative and associative both

d. None of these

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 14

If a binary operation * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is equal to

 

a. 20

b. 40

c. 400

d. 445

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 15

Let * be a binary operation on R defined by a * b = ab + 1. Then, * is

 

a. Commutative but not associative

b. Associative but not commutative

c. Neither commutative nor associative

d. Both commutative and associative

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 16

Subtraction of integers is

 

a. Commutative but not associative

b. Commutative and associative

c. Associative but not commutative

d. Neither commutative nor associative

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 17

The law a + b = b + a is called

 

a. Closure law

b. Associative law

c. Commutative law

d. Neither commutative nor associative

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 18

An operation * is defined on the set Z of non-zero integers by Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations for all a, b Z. Then the property satisfied is

 

a. Closure

b. Commutative

c. Associative

d. None of these

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 19

On Z an operation * is defined by a * b = a2 + b2 for all a, b Z. Then operation * on Z is

 

a. Commutative and associative

b. Associative but not commutative

c. Not associative

d. Not a binary operation

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 20

A binary operation * on Z defined by a * b = 3a + b for all a, b Z, is

 

a. Commutative

b. Associative

c. Not commutative

d. Commutative and associative

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 21

Let * be a binary operation on Q+ defined by a * b = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations for all a, b Q+. The inverse of 0.1 is

 

 

a. 105

b. 104

c. 106

d. None of these

 

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 22

Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b N. The identify element for * in N is

 

a. -10

b. 0

c. 10

d. Non-existent

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 23

Consider the binary operation * defined on Q - {1} by the rule a * b = a + b - ab for all a, b Q - {1}. The identity element in Q - {1} is

 

a. 0

b. 1

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

d. -1

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 24

For the binary operation * defined on R - {- 1} by the rule a * b = a + b + ab for all a, b R - {1}, the inverse of a is

 

a. -a

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

d. a2

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 25

For the multiplication of matrices as a binary operation on the set of all matrices of the form Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations , a, b R the inverse Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations  is

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 25

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 26

On the set Q+ of all positive rational numbers a binary operation * is defined by a * b = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations for all a, b Q+. The inverse of 8 is

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

c. 2

d. 4

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 27

Let * be a binary option defined on Q+ by the rule a * b = Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations for all a, b, Q+. The inverse of 4 * 6 is

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

d. None of these

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 28

The number of binary operations that can be defined on a set of 2 element is

 

a. 8

b. 4

c. 16

d. 64

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 29

The number of commutative binary operations that can be defined on a set of 2 elements is

 

a. 8

b. 6

c. 4

d. 2

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Chapter 3 - Binary Operations Exercise Ex.3VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 9

Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, ..., 10}.

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Binary Operations