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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    If \[(\alpha ,\beta ,\gamma )\] is a point on the line \[\frac{x-1}{2}=\frac{y+1}{-3}=z\]at distance \[2\sqrt{7}\] from the point M(1, -1, 0), then the coefficient of \[{{x}^{\alpha +\beta +\gamma }}\] in the expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{9}}\]is equal to

    A)  -84                              

    B)  84

    C)  672                             

    D)  -672

    Correct Answer: C

    Solution :

    \[(\alpha ,\,\beta ,\,\gamma )\] lie on straight line \[\Rightarrow \,\alpha +\beta +\gamma =0\]\[\Rightarrow \] coefficient of term independent in the expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{9}}=672\] is the required answer.


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