number of non Identity self inverse elements group theory iit jam 2007 mathematics

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Syllabus of Group Theory : Groups, Subgroups, Abelian Groups, Non-abelian groups, Cyclic Groups, Permutation Group, Normal subgroup, Lagrange's theorem for finite groups, Group Homomorphism and basic concepts of quotient groups (Only group Theory)
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number of non Identity self inverse elements group theory abstract algebra iit jam 2007 mathematics

Note : because every abelian group of order 10 is cylic...so number of elements of order 2 is phi(2)=1
(1) G is isomorphic to zn here
(2) Since S contain all the elements of G that is it's own inverse. But |G| is even. Thus S contain at least an element(excluding identity) which is it's own inverse. So option (d) is discarded. If S contain 2- element which is it's own inverse. Thus the remaining 7 elements must be divided into 2-equal parts which is strange. Again option (b) discarded. Thus possible option is (A) and (c). Now, confirm which one is(are) true

En Jam MA 2007, 6
Key (c)

[ashfakahmad]

Sir isme kaise Z10 le skte h D5 bi to le skte h

[akash.]

G is isomorphic to zn here...nice approach...easy to calculate the elements of order 2.🙏