If the greatest value of the term independent of $^{\prime}x^{\prime}$ in the expansion of $\left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10}$ is $\frac{10 !}{(5 !)^{2}}$, then the value of $' a^{\prime}$ is equal to:

  • [JEE MAIN 2021]
  • A

    $2$

  • B

    $-1$

  • C

    $1$

  • D

    $-2$

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