The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively. The mean and variance of another set of $15$ numbers are $14$ and $\sigma^2$ respectively. If the variance of all the $30$ numbers in the two sets is $13$,then $\sigma^2$ is equal to $.........$.

  • [JEE MAIN 2023]
  • A

    $9$

  • B

    $12$

  • C

    $11$

  • D

    $10$

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  • [JEE MAIN 2021]