If $2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0$ and $y=5 x^2 \mathrm{f}(x)$, then $y$ is strictly increasing in

If the curve $y=a x^2-6 x+b$ passes through $(0,4)$ and has its tangent parallel to the X-axis at $x=\frac{3}{2}$, then the values of $a$ and $b$ respectively are

20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then these two parts are

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is