Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $\left(a x^2+\frac{70}{27 b x}\right)^4$ is equal to the coefficient of $x^{-5}$ is equal to the coefficient of $\left(a x-\frac{1}{b x^2}\right)^7$, then the value of $2 b$ is

  • [IIT 2023]
  • A

    $5$

  • B

    $3$

  • C

    $4$

  • D

    $10$

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