The minimum value of $\frac{\log x}{x}$ in the interval $[2, \infty)$ is

Let $f(x) = \int_0^{x^2} \frac{t^2-8t+15}{e^t} dt$,$x \in R$. Then the numbers of local maximum and local minimum points of $f$,respectively,are:

The equations of motion of two stones thrown vertically upwards simultaneously are $s_1 = 19.6t - 4.9t^2$ and $s_2 = 9.8t - 4.9t^2$ respectively. If the maximum height attained by the first stone is $h$,then when the first stone is at its maximum height,the height of the second stone will be:

Find two positive numbers whose sum is $15$ and the sum of whose squares is minimum.

The radius of the cylinder of maximum volume,which can be inscribed in a sphere of radius $R$ is

The function $f(x) = \int_1^x \{ 2(t - 1)(t - 2)^3 + 3(t - 1)^2(t - 2)^2 \} dt$ is maximum when $x$ is equal to