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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 \[{{\left( \frac{a}{x}+bx \right)}^{12}}\],the coefficient of x-10 will be

    A) \[12{{a}^{11}}\]

    B) \[12{{b}^{11}}a\]

    C) \[12{{a}^{11}}b\]

    D) \[12{{a}^{11}}{{b}^{11}}\]

    Correct Answer: C

    Solution :

    \[{{\left[ \exp \frac{a}{x} \right]}^{12-r}}+{{[\exp bx]}^{r}}=-10\] \[\Rightarrow -12+r+r=-10\Rightarrow r=1\] Then coefficient of \[{{x}^{-10}}\]is \[^{12}{{C}_{1}}{{(a)}^{11}}{{(b)}^{1}}=12{{a}^{11}}b\].


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