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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
    In the expansion of \[{{\left( x+\frac{2}{{{x}^{2}}} \right)}^{15}}\], the term independent of \[x\] is                                           [MP PET 1993; Pb. CET 2002]

    A) \[^{15}{{C}_{6}}{{2}^{6}}\]

    B) \[^{15}{{C}_{5}}{{2}^{5}}\]

    C) \[^{15}{{C}_{4}}{{2}^{4}}\]

    D) \[^{15}{{C}_{8}}{{2}^{8}}\]

    Correct Answer: B

    Solution :

    \[(15-r)(1)+r(-2)=0\,\,\Rightarrow 15-3r=0\Rightarrow r=5\] Thus term independent of x is  \[={{\,}^{15}}{{C}_{5}}{{(1)}^{10}}{{(2)}^{5}}={{\,}^{15}}{{C}_{5}}{{2}^{5}}\].


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