The obtuse angle between the lines whose direction ratios are determined by the equations $a+b+c=0$, $2 a b+2 a c-b c=0$ is

A plane meets the coordinate axes at $A, B, C$ respectively such that the centroid of the $\triangle A B C$ is $(2,3,5)$. Then, the equation of that plane is

Let $[x]$ denote the greatest integer less than or equal to $x$ and $k \geq 2$ be an integer. Then

$$ \mathop {Lt}\limits_{x \to k} \frac{\sin \left(2 \pi\left([x]-\left[\frac{x}{k}\right]\right)-x\right)+\sin k}{x-k}= $$

Define $f(x)=\left\{\begin{array}{ll}1+x, & 0 \leq x \leq 2 \\ 3-x, & 2 < x \leq 3\end{array}\right.$.

If $f \circ f(x)$ is discontinuous at $a$ and $b$ in $[0,3]$ and $a