$$\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}$$ is equal to :

Let f(x) = min {1, 1 + x sin x}, 0 $$\le$$ x $$\le$$ 2$$\pi $$. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :

The area of the region bounded by y² = 8x and y² = 16(3 $$-$$ x) is equal to: