JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    In expansion of \[{{({{4}^{1/}}^{3}+{{6}^{-1/4}})}^{20}}\], consider following statement:
    (i) The number of irrational terms =18
    (ii) The number of rational terms = 2
    (iii) the middle term is irrational
    Then correct statements are-

    A) (i), (iii)           

    B)        (ii), (iii)

    C) (i), (ii)           

    D)        All three

    Correct Answer: B

    Solution :

    [b] \[{{T}_{r+1}}{{=}^{20}}{{C}_{r}}{{.4}^{\frac{20-r}{3}}}{{6}^{\frac{-r}{4}}};r=0\] \[\frac{20-r}{3};\frac{r}{4}\] both must be integers. \[\therefore \text{ }r=8,\,20\] \[\therefore \] 2 Rational Terms & 19 Irrational Terms Also middle term is Irrational.


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