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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 \[{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{12}}\], the term independent of x  is  [MP PET 2001]

    A) 10th

    B) 9th

    C) 8th

    D) 7th

    Correct Answer: B

    Solution :

    \[{{T}_{r+1}}={}^{12}{{C}_{r}}{{(2{{x}^{2}})}^{12-r}}{{(-1)}^{r}}{{\left( \frac{1}{x} \right)}^{r}}\] For term independent of x, \[24-3r=0\Rightarrow r=8\]. So, 9th term independent of x.


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