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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 \[{{x}^{32}}\]in the expansion of \[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\] is [MP PET 1994]

    A) \[^{15}{{C}_{5}}\]

    B) \[^{15}{{C}_{6}}\]

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

    D) \[^{15}{{C}_{7}}\]

    Correct Answer: C

    Solution :

    Let \[{{T}_{r+1}}\] term containing x32. Therefore \[^{15}{{C}_{r}}{{x}^{4r}}{{\left( \frac{-1}{{{x}^{3}}} \right)}^{15-r}}\] Þ \[{{x}^{4r}}{{x}^{-45+3r}}={{x}^{32}}\Rightarrow 7r=77\Rightarrow r=11\]. Hence coefficient of x32 is \[^{15}{{C}_{11}}\] or \[^{15}{{C}_{4}}\]


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