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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mock Test - Binomial Theorem

  • question_answer
    The number of distinct terms in the expansion of \[{{\left( x+\frac{1}{x}+{{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{15}}\]is/are (with respect to different power of x)

    A) 255                  

    B) 61

    C) 127                 

    D) none of these

    Correct Answer: B

    Solution :

    [b] \[{{\left( x+\frac{1}{x}+{{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{15}}={{\left( \frac{{{x}^{3}}+x+{{x}^{4}}+1}{{{x}^{2}}} \right)}^{15}}\] \[=\frac{{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{60}}{{x}^{60}}}{{{x}^{30}}}\] Hence, the total number of terms is 61.


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