Math Chapter Wise question with answer

Q01 If G is a finite group and O(G) = pn, where p is prime number and n is positive integers, then English · UP Higher Asst. Prof. 2021 Q02 If in a group G, O(a) = m and O(b) = n where a, b ∈G, then which of the following statements is correct? English · PGT 2005 Q03 In a group (G, o) if n is the order of an element a, where a∈G, and p is prime to 'n' then the order of ap is. English · TGT 2004 Q04 For any positive integers a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy English · Bihar (TRE 1.0) -2023 Q05 In the field () R,, ⊕ ⊙, where R is the set of real numbers and a ⊕ ⊕ ⊕ b = a + b – 1; a b ⊙ = a+b-ab ∀ ∀ ∀ a, b ∈... English · UPPSC Polytechnic Lecturer 2021(II) Q06 Consider the group (z,*), where Z is the set of all integers and * is defined by a*b=a+b+1, a, b∈z The inverse of a... English · UP PCS (Pre) 2006