A A1100 :
0 1
Module V ۱ ம
Answer any three questions, each carries 5 marks.

19 Find the work done byF (x,y) = (2 + y*)}i— xj along the curve (5)

‎counter clockwise from (1,0) to (0,1)‏ 1 = شير + ٹریم
‎conservative vector field. If (5)‏ و ‎it 12xyjis‏ شرہ = )9 ‎Determine whether F(x,‏ 20

‎so find the potential function for it.
21 Find the divergence and curl of the vector field (5)

‎F(x,y,z) = xyztit yzx? j+ 2xy? k
22 Prove that ( (x? - yz)it (y? - zx)j + (23 —xy)k. 6715 independent of the path 6)

‎and evaluate the integral along any curve from (0,0,0) to (1,2,3).
23 ۶۶ ‏د‎ + yy + ‏زع‎ andr = |7|, prove that V2f(r) = ತ ൪-൬. (5)

‎Module VI
Answer any three questions, each carries 5 marks.
निक मिमरे
[നണട

‎24 Using Green’s theorem evaluate f, (xy +y?)dx ഥ്‌ dy where C is the 00८० ८) ४७७७७ ‏درز وت‎

‎of the region bounded by क = x? and x = y?
25 Evaluate the surface integral 1 23 ds, where 6 is the portion of the curve (5)

‎z= fx? +y? between 2 ‏ع‎ 1 2110 2 = 3
26 Determine whether the vector field (८, 2, 2 ) is free of sources and sinks. If not, (5)

‎locate them.

‎DF (x,y,z) = (y + z)i— x2j+x*siny k
07 (x,y,z) = 524 y + 2278

‎27 Use divergence theorem to find the outward flux of the vector field (5)

‎F(x, y,z) = (2x + y”}itxyj+@y—2z)k across the surface © of the

‎tetrahedron bounded by x +y +z = 2 and the coordinate planes.
28 Using Stoke’s theorem evaluate ‏مل‎ F .d7 ; where F = xyi+ yz [ + xz k; (5)

‎C triangular path in the plane x + y+z = 1 with vertices at (1,0,0), (0,1,0) and

‎(0,0,1) in the first octant

‎೫೫೫%

‎Page 3 of 3