JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Multinomial theorem, Terms free from radical sign in the expansion(a1/p+b1/q), Problems regarding to three four consecutive terms or coefficients

  • question_answer
    The number of integral terms in the expansion of \[{{({{5}^{1/2}}+{{7}^{1/6}})}^{642}}\] is [Kurukshetra CEE 1996]

    A) 106

    B) 108

    C) 103

    D) 109

    Correct Answer: B

    Solution :

    \[{{T}_{r+1}}{{=}^{642}}{{C}_{r}}{{({{5}^{1/2}})}^{642-r}}.\,{{({{7}^{1/6}})}^{r}}\] Obviously, r should be a multiple of 6. Total numbers = \[\frac{642}{6}=107\]; But first term for \[r=0\] is also integral. Hence total terms are\[107+1=108\].


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