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JEE Main & Advanced Sample Paper JEE Main Sample Paper-39

  • question_answer
    Coefficient of \[{{x}^{6}}\]in the expansion\[{{\left( x+\frac{1}{{{x}^{2}}} \right)}^{6}}\]is

    A)  10                              

    B)  15

    C)  16                              

    D)  None

    Correct Answer: D

    Solution :

     \[{{T}_{r+1}}={{6}_{{{C}_{r}}}}{{x}^{{{6}^{-r}}}}{{\left( \frac{1}{{{x}^{2}}} \right)}^{r}}{{=}^{6}}{{C}_{r}}{{(x)}^{6-r-2r}}\] For coefficient of x 6,6-r -2r == 6, or r = 0 This means the term is the first term. \[\Rightarrow \] \[{{T}_{1}}{{=}^{6}}{{C}_{0}}{{x}^{6}}=1.{{x}^{6}}\]\[\Rightarrow \]coefficient of \[{{x}^{6}}=1\]


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