If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$, then the ordered pair $(m, M)$ is equal to

If the height of a cone of greatest volume that can be inscribed in a sphere of radius $R$ is $kR$,then the ratio of the volume of the cone to the volume of the sphere is

The number of points of local maxima and local minima of the function $f(x) = |x^2 - 2|x||$ in $\mathbb{R}$ are $M$ and $m$ respectively. Then,the value of $2M + m$ is -

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

The minimum value of $2x^2+x-1$ is:

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always $12$,then the equation of that line which forms a triangle of maximum area with the coordinate axes is