Let $9 < x_1 < x_2 < \ldots < x_7$ be in an $A.P.$ with common difference $d$. If the standard deviation of $x_1, x_2 \ldots$, $x _7$ is $4$ and the mean is $\overline{ x }$, then $\overline{ x }+ x _6$ is equal to:

  • [JEE MAIN 2023]
  • A

    $18\left(1+\frac{1}{\sqrt{3}}\right)$

  • B

    $34$

  • C

    $2\left(9+\frac{8}{\sqrt{7}}\right)$

  • D

    $25$

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