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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 in the expansion of \[{{(1+x)}^{21}}\], the coefficients of \[{{x}^{r}}\] and \[{{x}^{r+1}}\] be equal, then r is equal to [UPSEAT 2004]

    A) 9

    B) 10

    C) 11

    D) 12

    Correct Answer: B

    Solution :

    \[{{T}_{r+1}}={{\,}^{21}}{{C}_{r}}{{(1)}^{21-r}}{{(x)}^{r}}={{\,}^{21}}{{C}_{r}}\] \[\therefore \]Coefficient of \[{{x}^{r}}={{\,}^{21}}{{C}_{r}}\] and coefficient of \[{{x}^{r+1}}={{\,}^{21}}{{C}_{r+1}}\] So, we must have\[^{21}{{C}_{r}}={{\,}^{21}}{{C}_{r+1}}\Rightarrow r=10\].


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