Let $f(x)= \begin{cases}\frac{x^4-5 x^2+4}{|(x-1)(x-2)|} & , x \neq 1,2 \\ 6 & , x=1 \\ 12 & , x=2\end{cases}$

Then $\mathrm{f}(x)$ is continuous on the set

If $x$ and $y$ are sides of two squares such that $y=x-x^2$, then the rate of change of area of the second square with respect to that of the first square is

The acute angle between the line $4 x-2 y+13=0$ and the line which makes equal intercepts with the co-ordinate axes is

$$ \int\limits_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x= $$