Paragraph: While finding the sine of a contain angle x , an absent...

Paragraph: While finding the sine of a contain angle $x$, an absent minded professor failed to notice that his calculator was not in the correct angular mode. However he was lucky to get right answer. The two least positive value of $x$ for which the sine of $x$ degree is the same as the sine of $x$ radian found by him as $\frac{m \pi}{n-\pi}$ and $\frac{p \pi}{q+\pi}$, where $m, n, p$ and $q$ are positive integers. Suppose $\frac{m n}{p q}$ be denoted by quantity ' $L$ 'Question: If $x$ is measured in radians and $\lim _{x \rightarrow \infty}\left(\sqrt{A x^2+B x}-C x\right)=2$, the value of $\frac{B C}{A}$ equals $(A, B, C \in R)$