11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer The 4th term from the end in the expansion of\[{{\left( \mathbf{x}+\frac{2}{x} \right)}^{9}}\]

    A) \[\frac{5376}{{{x}^{4}}}\]                  

    B) \[\frac{{{x}^{3}}}{5376}\]

    C) \[\frac{5376}{{{x}^{3}}}\]                              

    D) \[\frac{{{x}^{4}}}{5376}\]

    Correct Answer: C

    Solution :

    [c] 4th term from the end of the expansion of \[{{\left( x+\frac{2}{x} \right)}^{9}}\] \[{{=}^{9}}{{C}_{3}}.{{\left( \frac{2}{x} \right)}^{6}}{{(x)}^{3}}{{=}^{9}}{{C}_{3}}\times \frac{{{\left( 2 \right)}^{6}}}{{{(x)}^{3}}}=\frac{\frac{9\times 8\times 7}{3\times 2}\times 64}{{{x}^{3}}}=\frac{168\times 32}{{{x}^{3}}}=\frac{5356}{{{x}^{3}}\,.}\]


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