Math Chapter Wise question with answer

Q01 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 Q02 Consider the congruence xn ≡ ≡ 2(mod13). This congruence has a solution for x if English · Bihar (TRE 1.0) -2023 Q03 Let a, b be positive integers with a > b and a + b = 24. Suppose that the following congruence's have a common inte... English · Bihar (TRE 1.0) -2023 Q04 The number of group homo-morphisms from Z10 to Z20 is English · Bihar (TRE 1.0) -2023 Q05 Let S7 denotes the group of permutations of the set {1,2,3, 4,5,6,7}. Which of the following is true? English · Bihar (TRE 1.0) -2023 Q06 Let p be a prime number. How many distinct sub-rings (with unity) of cardinality p does the field Fp2 have? English · Bihar (TRE 1.0) -2023