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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 16

  • question_answer
    In the expansion of \[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}}\], the coefficient of \[{{x}^{4}}\] is

    A) \[^{40}{{C}_{4}}\]                 

    B) \[^{10}{{C}_{4}}\]

    C) 210                  

    D) 310

    Correct Answer: D

    Solution :

    [d]: \[{{(1+x+{{x}^{3}}+{{x}^{4}})}^{10}}={{(1+x)}^{10}}{{(1+{{x}^{3}})}^{10}}\] \[=(1{{+}^{10}}{{C}_{1}}.x{{+}^{10}}{{C}_{2}}.{{x}^{2}}+...)(1{{+}^{10}}{{C}_{1}}.{{x}^{3}}{{+}^{10}}{{C}_{2}}.{{x}^{6}}+...)\] \[\therefore \]Coefficient of \[{{x}^{4}}{{=}^{10}}{{C}_{1}}{{.}^{10}}{{C}_{1}}{{+}^{10}}{{C}_{4}}=310\]


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