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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    The sum of rational terms in the binomial expansion of \[2\sqrt{2}+\sqrt[5]{3}{{)}^{10}}\] is

    A) 32                                          

    B) 25

    C) 41                                          

    D) 9

    Correct Answer: C

    Solution :

    \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{(2)}^{\frac{r}{2}}}.{{\left( {{3}^{\frac{1}{5}}} \right)}^{10-r}}{{=}^{10}}{{C}_{r}}{{.2}^{\frac{r}{2}}}{{.3}^{\frac{10-r}{5}}}\] \[r=0,\,\,1,\,\,2,\,......,\,\,9,\,10\]             \[\therefore \]For rational terms,\[r=0,\,\,r=10\] So, sum of rational terms\[=9+32=41\]


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