Let $x _1, x _2 \ldots ., x _{100}$ be in an arithmetic progression, with $x _1=2$ and their mean equal to $200$ . If $y_i=i\left(x_i-i\right), 1 \leq i \leq 100$, then the mean of $y _1, y _2$, $y _{100}$ is

  • [JEE MAIN 2023]
  • A

    $10101.50$

  • B

    $10051.50$

  • C

    $10049.50$

  • D

    $10100$

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