JEE Math Practice Question

Let $$x=2$$ be a root of the equation $$x^2+px+q=0$$ and $$f(x) = \left\{ {\begin{matrix} {{{1 - \cos ({x^2} - 4px + {q^2} + 8q + 16)} \over {{{(x - 2p)}^4}}},} & {x \ne 2p} \\ {0,} & {x = 2p} \\ \end{matrix} } \right.$$ Then $$\mathop {\lim }\limits_{x \to 2{p^ + }} [f(x)]$$, where $$\left[ . \right]$$ denotes greatest integer function, is

1. A.2
2. B.1
3. C.0
4. D.$$-1$$