Consider two G.Ps. $2,2^{2}, 2^{3}, \ldots$ and $4,4^{2}, 4^{3}, \ldots$ of $60$ and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is $(2)^{\frac{225}{8}}$, then $\sum_{ k =1}^{ n } k (n- k )$ is equal to.

  • [JEE MAIN 2022]
  • A

    $560$

  • B

    $1540$

  • C

    $1330$

  • D

    $2600$

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  • [JEE MAIN 2018]

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  • [IIT 1998]

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