A) 4
B) 120
C) 210
D) 310
Correct Answer: C
Solution :
\[{{\left[ \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x-1}{x-{{x}^{1/2}}} \right]}^{10}}\] \[\Rightarrow \]\[{{\left[ ({{x}^{1/3}}+1)-(1+{{x}^{-1/2}}) \right]}^{10}}\] \[\Rightarrow \]\[{{[{{x}^{1/3}}-{{x}^{-1/2}}]}^{10}}\] \[\Rightarrow \]\[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{({{x}^{1/3}})}^{10-r}}{{(-{{x}^{-1/2}})}^{r}}\] \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{x}^{\frac{10-r}{3}\frac{-r}{2}{{(-1)}^{r}}}}\] \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{x}^{\frac{20-5r}{6}{{(-1)}^{r}}}}\] \[\Rightarrow \]\[20-5r=0\] \[\Rightarrow \]\[r=4\] \[\Rightarrow \] \[{{T}_{5}}=10{{C}_{4}}=210\]
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