Q(1)-(i)Show that F=y+x is irrotational. x+y2 (ii) If (t) = 5t + t tk Find Q(2) -(i) Prove that div(grad)=m(m+1)rm2. (ii) Prove that x dr = rxdr 12 d dtadt. Q(3)-lf 7 = a cost + a sin t + at tanak. Find dr 27 and []. dt dt Q(4)-In what direction from (2,-1,-1) is directional derivative f=xyz maximum And what its magnitude? Q(5)-Evaluate ff (yz + zx + xyk).ds, Where F = y + (x 2xz) xyk,S is the surface of the sphere x + y+z = a above xy plane. Q(6)- Evaluate ff curlF.nds, Where S is the surface of the sphere x + y+z = 1 lies on first octant. - - Q(7)-Verify Green theorem (3x - 8y)dx + (4y - 6xy)dy Where C is Region bounded by parabola y = x and y = x.