Mathematics - Binomial Theorem Question with Solution | TestHub

Given ${\left[\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\right]}^{10}$

$\Rightarrow {\left(\left(x^{1/3}+1\right)-\left(\frac{\sqrt{x}+1}{\sqrt{x}}\right)\right)}^{10}$

$\Rightarrow {\left(x^{1/3}-x^{-1/2}\right)}^{10}$

General term is $T_{r+1}=10C_r{\left(x^{1/3}\right)}^{10-r}{\left(-x^{-1/2}\right)}^r$

$\therefore \frac{10-r}{3}-\frac{r}{2}=0\Rightarrow 20-2r-3r=0$

$\Rightarrow r=4$

Then, $T_5={}^{10}C_4=\frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}=210$