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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 ratio of the coefficient of third and fourth term in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{n}}\] is 1 : 2, then the value of  n  will be

    A) 18

    B) 16

    C) 12

    D) - 10

    Correct Answer: D

    Solution :

     \[{{T}_{3}}={{\,}^{n}}{{C}_{2}}{{(x)}^{n-2}}{{\left( -\frac{1}{2x} \right)}^{2}}\] and \[{{T}_{4}}={{\,}^{n}}{{C}_{3}}{{(x)}^{n-3}}{{\left( -\frac{1}{2x} \right)}^{3}}\] But according to the condition, \[\frac{-\,n(n-1)\times 3\times 2\times 1\times 8}{n(n-1)(n-2)\times 2\times 1\times 4}=\frac{1}{2}\Rightarrow n=-10\]


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