Classical

Set Theory and Algebra MCQ - Algebra

11:  

If a, b are positive integers, define a * b = a where ab = a (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is

A.

3

B.

1

C.

5

D.

4

 
 

Option: C

Explanation :

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12:  

Which of the following is TRUE ?

A.

Set of all rational negative numbers forms a group under multiplication

B.

Set of all non-singular matrices forms a group under multiplication

C.

Set of all matrices forms a group under multipication

D.

Both (b) and (c)

 
 

Option: B

Explanation :

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13:  

The set of all nth roots of unity under multiplication of complex numbers form a/an

A.

semi group with identity

B.

commutative semigroups with identity

C.

group

D.

abelian group

 
 

Option: D

Explanation :

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14:  

 Which of the following statements is FALSE ?

A.

The set of rational numbers is an abelian group under addition

B.

The set of rational integers is an abelian group under addition

C.

The set of rational numbers form an abelian group under multiplication

D.

None of these

 
 

Option: C

Explanation :

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15:  

In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is

A.

6

B.

8

C.

4

D.

2

 
 

Option: A

Explanation :

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