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

The function $\mathrm{f}(x)=[x(x-2)]^2$ is increasing in the set

If $p, q, r, s$ are statements, where, $\mathrm{p}: \mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B}) ; \mathrm{A}, \mathrm{B}$ are matrices, $A B \neq B A$

q: $5 \leq 5$

r: ${ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2+{ }^8 \mathrm{C}_3+\ldots \ldots \ldots . .+{ }^8 \mathrm{C}_8=256$

s: Maximum value of ${ }^8 \mathrm{C}_{\mathrm{r}}$ is 70 then the statement from the following having truth value true is ….

The minimum value of $a x+b y$ where $x y=c^2$ is