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

  • question_answer
    If \[f(x)=1-x+{{x}^{2}}-{{x}^{3}}+...-{{x}^{15}}+{{x}^{16}}-{{x}^{17}}\]then the coefficient of \[{{x}^{2}}\]in f(x-1) is

    A) 826                  

    B) 816

    C) 822                 

    D) none of these

    Correct Answer: B

    Solution :

    [b] \[f(x)=1-x+{{x}^{2}}-{{x}^{3}}+...-{{x}^{15}}+{{x}^{16}}-{{x}^{17}}=\frac{1-{{x}^{18}}}{1+x}\] \[\Rightarrow f(x-1)=\frac{1-{{(x-1)}^{18}}}{x}\] Therefore, required coefficient of \[{{x}^{2}}\]is equal to coefficient of \[{{x}^{3}}\] in \[1-{{(x-1)}^{18,}}\]which is given by \[^{18}{{C}_{3}}=816\].


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