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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
    If \[{{x}^{4}}\] occurs in the \[{{r}^{th}}\] term in the expansion of  \[{{\left( {{x}^{4}}+\frac{1}{{{x}^{3}}} \right)}^{15}}\], then \[r=\]         [MP PET 1995; Pb. CET 2002]

    A) 7

    B) 8

    C) 9

    D) 10

    Correct Answer: C

    Solution :

     \[{{T}_{r}}={{\,}^{15}}{{C}_{r-1}}{{({{x}^{4}})}^{16-r}}{{\left( \frac{1}{{{x}^{3}}} \right)}^{r-1}}={{\,}^{15}}{{C}_{r-1}}{{x}^{67-7r}}\] Þ \[67-7r=4\Rightarrow r=9\].


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