If $\alpha ,\,\beta ,\,\gamma ,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$ , then the value of $4\sin \frac{\alpha }{2} + 3\sin \frac{\beta }{2} + 2\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to 

  • A

    $2\sqrt {\left( {1 - k} \right)} $

  • B

    $\frac{1}{2}\sqrt {\left( {1 + k} \right)} $

  • C

    $2\sqrt {\left( {1 + k} \right)} $

  • D

    None of these

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