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JEE Main & Advanced JEE Main Online Paper (Held On 23 April 2013)

  • question_answer
                    The sum of the rational terms in the binomial expansion of \[{{\left( {{2}^{\frac{1}{2}}}+{{3}^{\frac{1}{5}}} \right)}^{10}}\]is     JEE Main Online Paper ( Held On 23  April 2013 )

    A)                   25                                        

    B)                                          32

    C)                                          9                                           

    D)                                          41

    Correct Answer: D

    Solution :

                     \[{{({{2}^{1/2}}+{{3}^{1/5}})}^{10=}}^{10}{{C}_{0}}{{({{2}^{1/2}})}^{10}}\] \[^{+10}{{C}_{1}}{{({{2}^{1/2}})}^{9}}({{3}^{1/5}})+.....{{+}^{10}}{{C}_{10}}{{({{3}^{1/5}})}^{10}}\] There are only two rational terms ? first term and last term. Now sum of two rational terms \[={{(2)}^{5}}+{{(3)}^{2}}=32+9=41\]


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