Math Chapter Wise question with answer

Q01 Let G be a group with identity element e. Let a, b∈G be such that a5 =e and aba–1 =b2. Then o(b) is English · LT 2018/ PGT 2010, 2005 Q02 Let φ be a homomorphism of a group G into another group G' and e, e' be their identity elements. Which of the follo... English · PGT 2005 Q03 Let G be a commutative group of order 202. Then the number of element(s) of order 2 in G is English · Bihar (TRE 1.0) -2023 Q04 Let G be a cyclic group of order 6. Then, the number of elements g ∈ G, such that G = <g> is English · UP PGT 2021 Q05 Let G be a group with binary operation *defined by a*b=a+b+1, ∀ ∀ ∀ a, b ∈ G. Inverse of element C of G is English · UP PGT-2016 (02-02-2019) Q06 Let G be any group 'a' be an elements of order 12. Then what will be the degree of a8. English · PGT 2013