A A1900 Pages: 3

21 Evaluate ‏مل‎ हैं .d? where F = )21 xy ‏ز‎ धात क) = + 2ಟಿ, 1st <3. (5)
22 Evaluate f ydx+zdy+xdz along the path x =cosnt,y=sinnt,z=t
from (1,0,0) to (—1,0,1) ப
5 23 IfF=xit+yj+zk ೩೧6 = |9| , prove that एत) 2௫ + ‏م “عر‎ . (5)
Module VI

Answer any three questions, each carries 5 marks.

24 Using Stoke’s theorem evaluate [ठ 7۰47 ; where F = xyi+yzj + xzk; ©
triangular path in the plane x + + 2 = 1 with vertices at (1,0,0),(0,1,0)and (5)
(0,0,1) in the first octant

25 Using Green’s theorem evaluate ‏ہل‎ (y? — 7998 + (2xy + 2x) dy where C is the (5)

circle x? +y2=1
26 Find the mass of the lamina that is the portion of the cone z = fx? + y?
between z = 1 and 2 = 3 if the density is (x,y,z) = ௩22,

(5)

27 Use divergence theorem to find the outward flux of the vector field
Px, y,z) = ‏3ع‎ + 23% across the surface ச bounded by (5)
८2 +- ‏شيو‎ = 4, 2 = 0 8110 2 = 4.

28 If S is the surface of the sphere x? + )2 + 22 = 1 ,Evaluate

| | (xi + 27 + 320.65 5 + (5)

C=)
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