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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 coefficient of \[{{x}^{-7}}\] in the expansion of \[{{\left( ax-\frac{1}{b{{x}^{2}}} \right)}^{11}}\] will be                       [IIT 1967; RPET 1996; Pb. CET 2003]

    A) \[\frac{462{{a}^{6}}}{{{b}^{5}}}\]

    B) \[\frac{462{{a}^{5}}}{{{b}^{6}}}\]

    C) \[\frac{-462{{a}^{5}}}{{{b}^{6}}}\]

    D) \[\frac{-462{{a}^{6}}}{{{b}^{5}}}\]

    Correct Answer: B

    Solution :

    For number of term, \[(11-r)(1)+r(-2)=-7\Rightarrow 11-r-2r=-7\]\[\Rightarrow r=6\] Thus coefficient of x-7 is  \[^{11}{{C}_{6}}{{(a)}^{5}}{{\left( -\frac{1}{b} \right)}^{6}}=\frac{462}{{{b}^{6}}}{{a}^{5}}\]


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