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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Binomial theorem for any index

  • question_answer
    If \[{{(r+1)}^{th}}\] term is the first negative term in the expansion of  \[{{(1+x)}^{7/2}}\], then the value of r is

    A) 5

    B) 6

    C) 4

    D) 7

    Correct Answer: A

    Solution :

    We have, \[{{T}_{r+1}}=\frac{\frac{7}{2}\left( \frac{7}{2}-1 \right)\,\,\left( \frac{7}{2}-2 \right)...\left( \frac{7}{2}-r+1 \right){{x}^{r}}}{r!}\] This will be the first negative term when \[\frac{7}{2}-r+1<0\]i.e. \[r>\frac{9}{2}\] Hence r = 5.


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