Note: All questions are compulsory and carry equal marks. [11. Test if the force field?"(x,y) = [2x + .91\")? + (43.: xe'hjr' is path independent and find the work done in moving a particle along the curve 3; = x4 + lnx + 1) from the origin to the point (1,1) in R2. [12. Find the polar moment of inertia using rectangular coordinates for a lamina formed by the intersection of two parabolas x = 3:2 + 2 and x = 6 3:2, where the density at any point P in the lamina is inversely proportional to the square of the distance from the origin. [13. Find the surface area of the end cap of the solid formed by the portion of the cylinder 31:2 + y2 = 231 that lies inside the sphere x2 + 3.12 + 22 = 4 above the x-y plane. {14. Use the Green's Theorem to evaluate the line integral r (ny 362de + (x + ydy, where C is the boundary of the region determined by the graphs of x = y2 and y = x2. Q5. Find the work done using polar coordinates in moving a particle in the force fieldl: = (x 3:3)? + AC3)? along the left half of the circle x2 + y2 =