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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Properties of binomial coefficients

  • question_answer
    The sum of the last eight coefficients in the expansion of \[{{(1+x)}^{15}}\] is

    A) \[{{2}^{16}}\]

    B) \[{{2}^{15}}\]

    C) \[{{2}^{14}}\]

    D) None of these

    Correct Answer: C

    Solution :

    We have \[^{15}{{C}_{0}}+{{\,}^{15}}{{C}_{1}}+...+{{\,}^{15}}{{C}_{15}}={{2}^{15}}\] \[\Rightarrow \,\,\,2{{(}^{15}}{{C}_{8}}+{{\,}^{15}}{{C}_{9}}+...+{{\,}^{15}}{{C}_{15}})={{2}^{15}}\]   \[(\because \,{{\,}^{n}}{{C}_{r}}={{\,}^{n}}{{C}_{n-r}})\] Þ \[^{15}{{C}_{8}}+{{\,}^{15}}{{C}_{9}}+...+{{\,}^{15}}{{C}_{15}}={{2}^{14}}\]


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