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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

3

1

5

4

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12. Which of the following is TRUE ?

Set of all rational negative numbers forms a group under multiplication

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

Set of all matrices forms a group under multiplication

Both (b) and (c)

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

semi group with identity

commutative semigroups with identity

group

abelian group

14. Which of the following statements is FALSE ?

The set of rational numbers is an abelian group under addition

The set of rational integers is an abelian group under addition

The set of rational numbers form an abelian group under multiplication

None of these

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

6

8

2

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