SEQUENCE QUESTIONS

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SEQUENCE QUESTIONS

1) The set of all positive rational number's forms an abelian group under the composition defined by

2 points

a*b=ab/2

a*b=a+b/2

a*b=2a/b

a*b=a-b/2

Clear selection

2)In a group G, if ab=a and ba=a ,e be the identity element of G, then

2 points

a=e

a^2=e

b=e

b^2=e

Clear selection

3) In an abelian group ,if o(a)=5 & o(b)=6 then (ab)^14 =

2 points

a^2b^-1

ab^-1

a^-1b^2

Clear selection

4) G be a finite group of order n,thrn for every a belongs to G we have

2 points

a^n=e

a^n=a^-1

a^n=a

Not

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5) The numbf elements of order 5 in a non abelian group of order 10 is

2 points

Clear selection

6) The number of conjugate classes of a non abelian group of order 125 are

2 points

125

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7) The number of all subgroups of the group (Z^6,+) is

2 points

Clear selection

8) Suppose o(a)=24,then the generator for<a^21> &<a^10> are

2 points

a^6,a^8

a^5,a^7

a^3,a^2

a^9,a^15

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9) Which of the following statement are not true?

2 points

Every group of prime order is cyclic

Every cyclic group is of prime order

Every cyclic group is abelian

Every abelian group is cyclic

Clear selection

10) pick out the abelian groups from the following list

2 points

Any group of order 49

Any group of order 36

Any group of order 47

Any group of order 77

Clear selection

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