Using Hamilton's equation, find the acceleration for a sphere rolling down a rough inclined plane, if x be the distance of the point of contact of the sphere from a fixed point on the plane.

2Medium15 marks

Prove that, in general, three normals can be drawn from a given point to the paraboloid x^2 + y^2 = 2az, but if the point lies on the surface 27a(x^2 + y^2) + 8(a - z)^3 = 0, then two of the three normals coincide.

3Medium15 marks

Is f(x) = |cos x| + |sin x|, x = pi/2 differentiable at x = pi/2? If yes, then find its derivative at x = pi/2. If no, then give a proof of it.

84 more Mathematics 2019 questions await

Generate a full-length practice test on Mathematics — pick the exact year, topic or chapter you want, and solve as many questions as you like with instant scoring and explanations.

Generate a Mathematics Test

Mathematics — All Years|All Subjects