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)
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+apJ (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 Ct2 +|y = Sin2x where ?'=rp-...
W"
(b) Solve Cl2 _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: |
Earning: Approval pending. |