A) 2
B) 3
C) 4
D) 5
Correct Answer: B
Solution :
In the expansion of\[{{\left( \frac{x}{3}-\frac{2}{{{x}^{2}}} \right)}^{10}},\]the rth term is \[{{T}_{r}}={{(-1)}^{r-1}}\,{{\,}^{10}}{{C}_{r-1}}{{\left( \frac{x}{3} \right)}^{10-(r-1)}}.{{\left( \frac{2}{{{x}^{2}}} \right)}^{r-1}}\] \[={{(-1)}^{r-1}}\,{{\,}^{10}}{{C}_{r-1}}\frac{{{2}^{r-1}}}{{{3}^{11-r}}}.{{x}^{10-r+1-2(r-1)}}\] \[={{(-1)}^{r-1}}\,{{\,}^{10}}{{C}_{r-1}}\frac{{{2}^{r-1}}}{{{3}^{11-r}}}.{{x}^{13-3r}}\] For coefficient of \[{{x}^{4}},13-3r=4\] \[\Rightarrow \] \[-3r=4-13\] \[\Rightarrow \] \[3r=9\] \[\Rightarrow \] \[r=3\]
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