Math Chapter Wise question with answer

Q01 Let N be normal subgroup of a group G and f: G → G N is a mapping defined by f(x) = xN ∀ x∈G, then f is English · RPSC PGT 2022 Q02 If p is a prime number, then any group of order 2p has a normal subgroup of order English · UPPSC GDC 2021 UPPSC Polytechnic Lecturer 2021(II) Q03 Let 'H' be a subgroup of 'G' and 'N' be a normal subgroup of G, then H∩ ∩ ∩N is - English · UPPSC Polytechnic Lecturer 2021(II) JDD-75-PGT TIER II-X-15 28.06.2015 Q04 If 'G' is a cyclic group of order 30, then total number of subgroups of G is – English · UPPSC Polytechnic Lecturer 2021(II) UP PGT 2016 Q05 If H is a p - sylow subgroup of G and x∈G, then x–1 Hx is also a - English · UPPSC Polytechnic Lecturer 2021(II) Q06 If H and K are subgroups of a group G such that O(H) = 3 and O(K) = 5, then what will be O(H∩ ∩ ∩K)? English · UP PGT 2021, 2016