Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution 

$X_i$ $0$ $1$ $2$ $3$ $4$ $5$
$f_i$ $k+2$ $2k$ $K^{2}-1$ $K^{2}-1$ $K^{2}-1$ $k-3$

where $\sum f_i=62$. if $[x]$ denotes the greatest integer $\leq x$, then $\left[\mu^2+\sigma^2\right]$ is equal $.........$.

  • [JEE MAIN 2023]
  • A

    $8$

  • B

    $7$

  • C

    $6$

  • D

    $9$

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  • [JEE MAIN 2023]

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