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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 term independent of x in the expansion of \[{{\left( \frac{1}{2}{{x}^{1/3}}+{{x}^{-1/5}} \right)}^{8}}\] will be [Roorkee 1985]

    A) 5

    B) 6

    C) 7

    D) 8

    Correct Answer: C

    Solution :

    \[\frac{1}{3}(8-r)+r\left( -\frac{1}{5} \right)=0\Rightarrow \frac{8}{3}-\frac{r}{3}-\frac{r}{5}=0\Rightarrow r=5\] Thus term independent of \[x={{\,}^{8}}{{C}_{5}}\times {{\left( \frac{1}{2} \right)}^{3}}{{(1)}^{5}}\]                    \[=\frac{8\times 7\times 6}{3\times 2\times 1}\times \frac{1}{8}=7\]


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