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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 middle term in the expansion of \[{{(1+x)}^{10}}\] is [UPSEAT 2001]

    A) \[\frac{10!}{5!\,6!}\]

    B) \[\frac{10\,!}{{{(5\,!)}^{2}}}\]

    C) \[\frac{10\,!}{5\,!\,7\,!}\]

    D) None of these

    Correct Answer: B

    Solution :

    Here, index = 10, an even number, therefore, middle term is \[{{\left( \frac{10+2}{2} \right)}^{th}}\] i.e. 6th term.  Also,\[{{T}_{6}}\,\,=\,\,{}^{10}{{C}_{5}}\,{{x}^{5}}\]ÞCoefficient of middle term \[={}^{10}{{C}_{5}}.\]


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