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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    The term independent of x in the expansion of \[{{\left( {{x}^{2}}-\frac{1}{x} \right)}^{9}}\] is   [EAMCET 1982; MP PET 2003]

    A) 1

    B) -1

    C) - 48

    D) None of these

    Correct Answer: D

    Solution :

    (9 - r) (2) + r (-1) = 0 Þ 18 - 2r - r = 0 Þ \[r=6\] Thus term independent of x is \[^{9}{{C}_{6}}{{(1)}^{3}}{{(-1)}^{6}}=84.\]


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