If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^{9}}+\ldots . .+\frac{10240}{3}=2^{ n } \cdot m$, where $m$ is odd, then $m . n$ is equal to

  • [JEE MAIN 2022]
  • A

    $15$

  • B

    $14$

  • C

    $13$

  • D

    $12$

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  • [JEE MAIN 2020]