Nalanda Open University 2009 B.Sc Mathematics Bachelor of Science Hons., Part-II Final , (Subsidiary), -II (Integral Calculus, Differential Equations, Co-ordinate Geometry, Linear Programming) - Que

Bachelor of Science Hons., Part-II Final Examination, 2009 Mathematics (Subsidiary), Paper-II (Integral Calculus, Differential Equations, Co-ordinate Geometry, Linear Programming)

Nalnndvi Open University

Bachelor of Science Hons., Part-H Einal Examination, 2009 Mathematics (Subsidiary), Paper-EC (Integral Calculus, Differential Equations, Co-ordinate Geometry, Linear Rogrnmming) iTime: 3,00 Hrs.    Full Marks: 75

Answer any Eight Questions _f.selecjjftg$least.one qjesji.from eactigrojug...

Group-A

tc.' Evaluate any two of the following; h

^{(a) w (c)}

|L (a) Evaluate osx dx by expressing it as.the.'limit of a suin

(b) Shw-that _

dx

3.    (a) Evaluate / -*

' ' '    *5 + 4Smx

(b) Evaluate the integral Sinx dx using reduction formula.

4.    (a) Find the entire length of the cardioid r=a(l+Cos ?).

(b) Find the volume of the solid obtained by revolving the cardioid r=a(l+Cos$) about the

initial line.

? Solve any two of the following:.

.....'.-Si.-xi

(a) y=(l+p)x+ap^J    (b) y=2px+yV (c) y=px +

"p /

5. (a) Show that the system of confocal conics    + --1 is self-orthogonal.

a + A b + A

r

(b) Solve p²+2xp-3x²=Q..

7. (a) Solve Ct^{2 +}|y = Sin2x where ?'=rp-...

W"

(b) Solve Cl^{2 _}2D + l|y = x*e³*'...

Group-B

B-. (a) Filid ^!tfie equation of.the sphere which passes through the point 13, fiyC and the circle x²+y²+z²=a², z=0.

(b) Find the equation of the sphere whose ends of a diameter are Atxyj-, zj) arici B'.yj)--

9. (a) Find the g'eh'eral equation of the right circular cone whose vertex is a Art and axis

x-a _y- ft _z-y

; ^_-^_- and semi-vertical angle Q.

I m n

(b) Find the equation of a right circular cylinder whose axis is the z axis and radius is a.

Attachment: nalanda-open-university-2009-b-sc-mathematics-40556-1.tif

Earning:   Approval pending.