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Algebra mcqs tests 06

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1. In S_3,a=\begin{pmatrix} 1 & 2 & 3\\ 2& 3 & 1 \end{pmatrix} ,then \,\ a^{-1}=

 
 
 
 

2. The number of subgroups of a group is

 
 
 
 

3. A group G is abelian then

 
 
 
 

4. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

5. Let G be a group of order 36 and let a belongs to G . The order of a is

 
 
 
 

6. Let H,K be the two subgroups of a group G. Then set HK={hk|h∈H ^ k∈ K} is a subgroup of G if

 
 
 
 

7. The symmetries of square form a

 
 
 
 

8. Which of the following is the representation of C_4= \left \{1,-1,i,-i \right \}

 
 
 
 

9. which binary operation is not defined in the set of natural number

 
 
 
 

10. A mapping \Phi : G \rightarrow \rightarrow G' is called homorphism if a, b belongs to G

 
 
 
 

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