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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