If $a^2 x^4 + b^2 y^4 = c^6$,then the maximum value of $xy$ is:

The difference between the greatest and the least values of the function $f(x) = \sin(2x) - x$ on the interval $\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$ is:

The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$-axis and vertices $C$ and $D$ lie on the parabola $y = x^{2}-1$ below the $x$-axis,is

The abscissae of the points,where the tangent to the curve $y = x^3 - 3x^2 - 9x + 5$ is parallel to the $x$-axis,are

If rectangles are inscribed in a circle of radius $r$ units,then the dimensions of the rectangle which has maximum area are:

If $m$ and $M$ are the absolute minimum and absolute maximum values of the function $f(x) = 2\sqrt{2} \sin x - \tan x$ in the interval $[0, \pi/3]$,then $m + M =$