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JEE Math Practice Question

If the set $$R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}$$ has $$m$$ elements and $$\sum\limits_{n=1}^m\left(1-i^{n !}\right)=x+i y$$, where $$i=\sqrt{-1}$$, then the value of $$m+x+y$$ is

  1. A.12
  2. B.4
  3. C.8
  4. D.5

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