Let $r$ be a real number and $n \in N$ be such that the polynomial $2 x^2+2 x+1$ divides the polynomial $(x+1)^n-r$. Then, $(n, r)$ can be

  • [KVPY 2010]
  • A

    $\left(4000,4^{1000}\right)$

  • B

    $\left(4000, \frac{1}{4^{1000}}\right)$

  • C

    $\left(4^{1000}, \frac{1}{4^{1000}}\right)$

  • D

    $\left(4000, \frac{1}{4000}\right)$

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