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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 the third term in the binomial expansion of \[{{(1+x)}^{m}}\] is \[-\frac{1}{8}{{x}^{2}}\],  then the rational value of m is

    A) 2

    B) \[1/2\]

    C) 3

    D) 4

    Correct Answer: B

    Solution :

     We have  \[{{(1+x)}^{m}}=1+mx+\frac{m(m-1)}{2!}{{x}^{2}}+...\] By hypothesis, \[\frac{m(m-1)}{2}{{x}^{2}}=-\frac{1}{8}{{x}^{2}}\] Þ \[4{{m}^{2}}-4m=-1\] Þ \[{{(2m-1)}^{2}}=0\Rightarrow m=\frac{1}{2}\].


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