JEE Main & Advanced JEE Main Paper Phase-I (Held on 07-1-2020 Evening)

  • question_answer
    The coefficient of \[{{x}^{7}}\] in the expression \[{{(1+x)}^{10}}+x{{(1+x)}^{9}}+{{x}^{2}}{{(1+x)}^{8}}+\text{ }\ldots \text{ }+\text{ }{{x}^{10}}\] is [JEE MAIN Held on 07-01-2020 Evening]

    A) 120                 

    B) 330

    C) 420                 

    D) 210

    Correct Answer: B

    Solution :

    [b] \[{{(1+x)}^{10}}+x{{(1+x)}^{9}}+{{x}^{2}}{{(1+x)}^{8}}+\text{ }\ldots \text{ }+\text{ }{{x}^{10}}\]             \[=\frac{{{(1+x)}^{10}}\left( 1-{{\left( \frac{x}{1+x} \right)}^{11}} \right)}{1-\frac{x}{1+x}}\] \[={{(1+x)}^{11}}{{x}^{11}}\] \[\therefore \] Coeff. of  \[{{x}^{7}}={{\,}^{11}}{{C}_{7}}=\,{{\,}^{11}}{{C}_{4}}\] \[=\,\frac{11\times 10\times 9\times 8}{4\times 3\times 2\times 1}\] \[=330\]

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