JEE Main & Advanced Sample Paper JEE Main - Mock Test - 42

  • question_answer
    The ratio of 11th term from the beginning and 11th term from the end in the expansion of \[{{\left( 2x-\frac{1}{{{x}^{2}}} \right)}^{25}}\] is

    A) \[{{x}^{15}}\]                        

    B)        \[-{{2}^{5}}{{x}^{15}}\]

    C) \[{{2}^{15}}{{x}^{5}}\]           

    D)        \[{{2}^{5}}{{x}^{-15}}\]

    Correct Answer: B

    Solution :

    [b] \[{{T}_{11}}_{(staiting)}{{=}^{25}}{{C}_{10}}{{2}^{15}}\left( \frac{1}{{{x}^{5}}} \right)\] \[{{T}_{11}}_{\left( enfing \right)}={{T}_{16\left( starting \right)}}\] \[={{-}^{25}}{{C}_{15}}{{2}^{10}}\left( \frac{1}{{{x}^{20}}} \right)\] Then \[\frac{{{T}_{11(starting)}}}{{{T}_{11(ending)}}}=-{{2}^{5}}{{x}^{15}}\]


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