Annamalai University 2008-1st Year B.Sc Mathematics " 550 - I " ( PART - III - B - ANCILLARY ) ( ) 5243 - Question Paper
4
a 4
7. (a) Expand sin 0, cos 0 in terms of sines of
multiples of 0.
a
(b) Express sin 0 in terms of sines of multiples of x.
8. Find the equation of the sphere through the circle
x2 + y2 + z2 + 2x + 3y + 5z = 0 ;
2x + 6y + 5z - 6 = 0 and passing through the center of the sphere x2 + y2 + z2 - 2x - 4y + 6z + 1 = 0
9. Find the shortest distance between the lines
2x - 2y + 3z - 12 = 0 = 2x + 2y + z and 2x - z = 0 = 5x - 2y + 9.
10. Verify the lines
x - 2 y - 4 z-5
1 ~ 2 ~ 2
and x ~ 5 = y ~ 8 = z ~ 7
2 3 2
are coplanar. Find the equation of the plane containing them.
Name of the Candidate :
5 2 4 3 B.Sc. DEGREE EXAMINATION, 2008
(APPLIED CHEMISTRY/ELECTRONIC SCIENCE/ PHYSICS)
(FIRST YEAR)
(PART - III - B - ANCILLARY)
December ] [ Time : 3 Hours
Maximum : 75 Marks
Answer any FIVE questions.
All questions carry equal marks.
(5 x 15 = 75)
1. (a) Find the sum to infinity of the series 7 7-28 7-28-49
- + - + - + .....oo
72 72-96 72-96-120
2 3/4 \ 4 5/42
+ I + ) T + ..... = z log V"~L2.
2. (a) State and prove Lagranges theorem on finite groups.
(b) If / is a homomorphism of a group G into a group G' with Kernal K, prove that
 |
|
K |
(b) Find the maxima and minima of the
a 9
function x y (6-x-y).
4. Show that the systems of equations
x + y + z = 6 x + 2y + 3z = 14 x + 4y + 7z = 30 is consist and hence, solve it.
5. Find the eigen value and eigen vectors of the matrix
A
6. (a) Separate into real and imaginary part of sin (x - iy).
(b) If
tan l-y = tanh U-
prove that
sinh y = tan x
Turn over
(a) If
y = sinh-1 x prove that
+x2>>'n + 2 + <2n + 3>X>'n+l
+ (n+ l)2 yn = 0.
|
Attachment: |
| Earning: Approval pending. |
