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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    The coefficient of \[{{x}^{20}}\]in the expansion of \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{20}}\]is

    A)  \[{{\,}^{60}}{{C}_{40}}\]                              

    B)         \[{{\,}^{30}}{{C}_{20}}\]                              

    C)         \[{{\,}^{15}}{{C}_{2}}\]                

    D)         None of these

    Correct Answer: A

    Solution :

    \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{20}}={{(1+x)}^{60}}\] \[\therefore \]Coefficient of \[{{x}^{20}}\]in \[{{(1+x)}^{60}}\]is \[{{\,}^{60}}{{C}_{20}}\]or \[{{\,}^{60}}{{C}_{40}}.\]


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