1. Find the angle between the curves r = a sin 20, r = a cos 20. OR If y (x-1)", prove that (x - 1)yn +2 + 2xy +1-n(n + 1)yn = 0. 2. State and prove Lagrange's mean value theorem. 3. Evaluate: lim (cot x) lo logx 0+x 4. Find the surface of the right circular cylinder of greatest surface which can be inscribed in a sphere of radius r.