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 middle term in the expression of \[{{\left( x-\frac{1}{x} \right)}^{18}}\] is   [Karnataka CET 2005]

    A) \[^{18}{{C}_{9}}\]

    B) \[{{-}^{18}}{{C}_{9}}\]

    C) \[^{18}{{C}_{0}}\]

    D) \[{{-}^{18}}{{C}_{10}}\]

    Correct Answer: B

    Solution :

    If n is even. \[\therefore \]Middle term is 10th term. Þ \[{{T}_{10}}={}^{18}{{C}_{9}}{{(x)}^{9}}.\,{{\left( -\frac{1}{x} \right)}^{9}}=\text{ }-{}^{18}{{C}_{9}}\].


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