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JEE Main & Advanced JEE Main Paper (Held On 12-Jan-2019 Evening)

  • question_answer
    The total number of irrational terms in the binomial expansion \[{{({{7}^{1/5}}-{{3}^{1/10}})}^{60}}\]is [JEE Main Online Paper Held On 12-Jan-2019 Evening]

    A) 55   

    B)                           54   

    C) 48                                

    D)   49

    Correct Answer: B

    Solution :

    Given expression is \[{{({{7}^{1/5}}-{{3}^{1/10}})}^{60}}\] General term of this expansion is \[{{T}_{r+1}}={{(-1)}^{r}}{{\,}^{60}}{{C}_{r}}{{7}^{\frac{60-r}{5}}}{{3}^{\frac{r}{10}}}\] For rational terms, r = 0, 10, 20, 30, 40, 50, 60 So, number of rational terms = 7. \[\therefore \]Number of irrational terms =\[61-7=54\].


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