If $A=(0,4,-3), B=(5,0,12)$ and $C=(7,24,0)$, then $\sqrt{B A C}=$

A plane $\pi$ is passing through the points $A(1,-2,3)$ and $B(6,4,5)$. If the plane $\pi$ is perpendicular the plane $3 x-y+z=2$, then the perpendicular distance from $(0,0,0)$ to the plane $\pi$ is

$$ \mathop {\lim }\limits_{y \to 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}= $$

If $\mathop {\lim }\limits_{x \to 0} \frac{\cos 2 x-\cos 4 x}{1-\cos 2 x}=k$, then $\lim\limits_{x \rightarrow k} \frac{x^k-27}{x^{k+1}-81}=$