Find the semi-vertical angle of the cone of maximum curved surface area that can be inscribed in a given sphere of radius R.

Find the point on the curve y = x² which is closest to the point A(0, a).  

Find the shortest distance between the line y – x = 1 and the curve x = y².

Find the vertical angle of right circular some of minimum curved surface that circumscribes in a given sphere.

 A, B > 0, then minimum value of sec A + sec B is equal to   

f (x) = x² – 4 | x | and

Then f (x) has    

If xy = 10, then minimum value of 12x² + 13y² is equal to

The function f (x) = x (x² – 4)ⁿ (x² – x + 1), n Ïµ N assumes a local minima at x = 2, then   

Total number of critical points of f (x) = maximum (sin x, cos x) ∀ x Ïµ (–2π, 2π) equal to