The positive value of $a$ so that the co-efficient of $x^5$ is equal to that of $x^{15}$ in the expansion of ${\left( {{x^2}\,\, + \,\,\frac{a}{{{x^3}}}} \right)^{10}}$ is

  • A

    $\frac{1}{{2\,\sqrt 3 }}$

  • B

    $\frac{1}{{\sqrt 3 }}$

  • C

    $1$

  • D

    $2 \sqrt 3$

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