Tamil Nadu Open University (TNOU) 2006 B.Sc Mathematics 1st Year " Trigonometry Analytical Geometry of the Three Dimensions and Vector Calulus " UG 744 - Question Paper
B.Sc. DEGREE EXAMINATION - JUNE, 2006.
First Year Mathematics TRIGONOMETRY, ANALYTICAL GEOMETRY OF THREE DIMENSIONS AND VECTOR CALCULUS
Time : 3 hours Maximum marks : 75
PART A (5 x 5 = 25 marks)
Answer any FIVE questions.
Each question carries 5 marks.
1. Show that
cos 6 0=1-18 sin2 0 + 48 sin4 0-32 sin6 0.
2. Prove that cosh2 x - sinh2 x = 1.
3. Find the real and imaginary parts of Log (a + i6).
(2,3,7) and (2,-5,8).
5. Find the centre and radius of the sphere x2 + y2 +z2-2x-4y +6z-ll = 0.
6. Find the equation of the cone of the second degree which passes through the axes.
7. Find the divergence of x2 /+y2y+z2 k .
8. If F = 3x2 y /+ [x3-3y2)y, compute along y2 =4x from (0,0) to (4,4).
PART B (5 x 10 = 50 marks) Answer any FIVE questions. Each question carries 10 marks.
9. Prove that cos5 0sin4 #=-4- [cos90 + cos70-
2
4 cos 50-4 cos 30 + 6 cos 6].
10. If cos(jr+/>,)= cos0 + /sin0, show that cos 2x + cosh 2y = 2.
11. Sum the series upto n terms:
-= --- are coplanar. Find also the point of
-4 7 1
intersection and the plane through them.
13. Find the shortest distance between the lines
x + 3 y-8 z-3 , x + 3 y +7 z-6 A1 ~ ,
-= --=- and -= --=-. Also find
3-11 -3 2 4
the equation of the line of shortest distance.
14. Find the equation of the sphere which passes through the point (l,-2,3) and the circle z = 0,
x2 +y2 +z2 -9 = 0.
15. Find V F and V x/ of the vector point function F=xz3 i -2x2y zy + 2j>z* k at the point (l,-l,l).
16. Evaluate jj.F hds where F = Axz i-y2 j+yz&
S
and S is the cube bounded by x = 0,x = l,y =0,y =l,z = 0,z=l.
3 UG-744
|
Attachment: |
| Earning: Approval pending. |
