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

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Total No. of Questions : 5] P221 [Total No. of Pages : 4 [3717] - 53 F.Y. B.Sc. MATHEMATICS Analytical Geomery and Differential Equations (Paper - III) (Old Course) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. Q1) Attempt all the subquestions: a) [16] Find the centre of the conic x2 + 12xy 4y2 6x + 4y + 9 = 0. b) Find the equation of the plane making intercepts 4, 2, 3 on the coordinate axes. c) Find the equation of the sphere described on the join of the points A(2, 4, 3) and B(1, 0, 2) as a diameter. d) Find the angle through which the axes should be rotated so as to remove the xy term in the equation 4 x 2 3xy + y 2 = 5 . e) Find the order and degree of the differential equation d 3y dy 2 + 4 dx = 3 + x . dx dx f) Solve p = log (px y). g) Find orthogonal trajectories of the family ex + e y = c where c i s a parameter. h) Find integrating factor of the differential equation (2x2y 3y3 + 6x3) dx + (3xy2 2x3)dy = 0 P.T.O.

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Additional Info : F.Y.B.Sc. MATHEMATICS Analytical Geomery and Differential Equations (Paper - III) (Old Course), Pune University
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