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JEE Math Practice Question

$$ \lim\limits_{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3 $$

  1. A.is equal to 9
  2. B.is equal to $\frac{27}{2}$
  3. C.does not exist
  4. D.is equal to 27

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