Choose the correct answer from the following Ix30=30 1. The analytic function f(z) whose real part is x2- y2 is a Z (O (C) 1Z1 2 The function f()=2* with z =x+iy is analytic (a in tne cep at y - 0 and y = 0 and y OLLy (d) on the line y = 1 only. 3 The value of the integral where C is a circle Iz - 11=1 is (C)Zt 4. The value of the integral Je tanz dz , where C is |z -1| =1 is (a) 2t (D (c)-4 (d 5. The residue of the function f2) = 2,4 at 2 =-2i is (b) e2 (C) e (d) e 6. The res idue of at z =i is (a)sinh 1 (b) 4 sinh 1 (C) sin (d) 0 7. The solution of the differential equation y" -Py =0 ; where y' = d is (a A evP +Be~vPx leP* +Be"P cl A eiPx + Be-p* (d) A e'vPx + Be-iypx 8. For the linear difierential equation y" + + y =0; where y'=a r-1) * = 018 a singular point. () xL 1B an iregular singular point. (1 x =i s a regular singular point. (iv) x = 0 is an ordinary point a ( and (i) (b) 9 and (ii) (C)() and (iv) (d) i)a and (r 9. The solution of differential equation y = e" is (a) y (b) y=-+c (c) y=e+C (d) y= e tC 3 10. Laplace's equation may be used in the study of (a) steady state temperature in a region containing heat source (b) variable state temperature in a region containing no heat source (c) steady state temperature in a region containing no heat source (a variable state temperature n a region containing heat source. 11. The solution of differential equation + =0 using the method of separation of variables is (a) ee b) (c) (xy) (d) e )/2 12. For the differential equation y"+y+ y 0, the solution of indicial equation is a 1,3 (b 1, c) 1, (d) 1, -3 13. The value of J. Po (x)dx is (a) 0 (d) 2 14. The value of o) is (ao (6) (c) C) (d) Jox) 15. For Legendre's polynomial, Pa(-1) is equal to (a)i (c) 0 (d) - 1)"