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Pune University - FY BSc MATHEMATICS - I, April 2010

4 pages, 32 questions, 2 questions with responses, 2 total responses,    0    0
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Total No. of Questions : 5] [Total No. of Pages : 4 [3717] - 1 P179 F.Y. B.Sc. MATHEMATICS Algebra and Geometry (Paper - I) (New Course) Time : 3 Hours] Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. [Max. Marks : 80 Q1) Attempt all the subquestions : a) Define power set of a set and equivalence relation on a set. b) [16] Let f be the function defined by f(x) = 3x 4. 1 Find f and f(a + h). 3 c) Show that (3) (10) (4) is a perfect square, where is Euler s function. d) Using synthetic division find the quotient and remainder when 7x4 + 3x3 + 8x + 1 is divided by x + 2. e) Discuss the nature of the conic x4 4xy 2y2 + 10x + 4y = 0. f) Obtain the equation of a line joining the points ( 2, 1, 3) and (3, 1, 2). g) Show that the line x 4 y+7 z+3 l ies wholly in the plane = = 3 6 4 2x y + 3z 6 = 0. h) Find x so that rank of the following matrix A is not equal to 3 2 3 4 A = 3 1 2 . x 2 2 P.T.O.

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