The maximum value of $\left(\dfrac{1}{x}\right)^x$, $x > 0$ is

The point on the curve $9y^2 = x^3$ where the normal to the curve makes equal intercepts with the co-ordinate axes is

If the function $f(x) = ax^3 - bx^2 - 8x - 4$ satisfies Roll's theorem in $[1,3]$, if $f'(2) = 0$ then $a - b$ is equal to...

The co-ordinates of the point on the curve $y = x\log x$ at which the normal is parallel to the line $2x - 2y = 3$ are...