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Pune University - FY BSc MATHEMATICS - I (Old Course)

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Total No. of Questions : 5] P219 [Total No. of Pages : 3 [3717] - 51 F.Y. B.Sc. MATHEMATICS Algebra (Paper - I) (Old Course) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Candidates are advised to see the relevent question paper and solve the same. 2) All questions are compulsory. 3) Figures to the right indicate full marks. Q1) Attempt all the subquestions: a) [16] Consider the set N x N of all ordered pairs of natural numbers. For (a, b), (c, d) in N x N define an equivalence relation. (a, b) ~ (c, d) if ad = bc then find the equivalence class of (3, 5). b) Let A = {a, b, c}, B = {1, 2}. Find a possible function f from A to B which is onto but not one c) Let a, b, c, d be integers. If a | b and c | d then prove that ac | bd. d) Find (7 ) + (12) , where e) 2 +i . Find real and imaginary part of z, where z = 3 2i f) 2 2 If z = 3 cos + i sin 3 3 is Euler s s - function. , then by using De-Moivre s theorem 1 3 z4 = 3 4 + i prove that 2 2 g) If the equation x3 x2 8 x + 12 = 0 has one root 3 then find the other roots. h) If f(x) = 2x3 + 4x2 + 3x + 2 and g(x) and g(x) = 3x4 + 2x + 4 then find the deg [f(x) + g(x)] and deg [f(x) g(x)]. P.T.O.

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Additional Info : F.Y.B.Sc. MATHEMATICS Algebra (Paper - I) (Old Course), Pune University
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