Math Chapter Wise question with answer

Q01 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 Q02 If f ∈ F[X] and degree of f is n, then f has a splitting field K over F with: English · OPSC PGT 2017 Q03 Let p be a prime number, then f (x) = xp – 1∈ Q [x] has splitting field Q (α), if English · UPPSC GDC 2021 Q04 Let Q be the field of rational numbers. Then over Q, 2 + 3 is algebraic of degree English · UPPSC GDC 2021 Q05 The splitting field of the polynomial x2 +4 over the field 'Q' of rational numbers is - English · UPPSC Polytechnic Lecturer 2021(II) Q06 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)