statement 1:-- The order of a group is always divisible by the order of the subgroups. its is always coreect
stmt 2;- Intersection of two subgroups of a group G, may or may not be a subgroup of G. its incorrect it is always subgroup but union may or may not
stmt 3--- Proper subgroup of an infinite cyclic group is infinite. yes true
stmt 4;--Prime order group has both proper and improper subgroups. false as prime order group has no proper subgroup
https://proofwiki.org/wiki/Prime_Group_has_no_Proper_Subgroups so stament II and IV is wrong hence (B) is correct