The maximum value of the term independent of

$T_{r+1}={ }^{10} C_{r}\left(t x^{1 / 5}\right)^{10-r}\left[\frac{(1-x)^{1 / 10}}{t}\right]^{r}$

$={ }^{10} C_{r} t^{(10-2 r)} \times x^{\frac{10-r}{5}} \times(1-x)^{\frac{t}{10}}$

$\Rightarrow 10-2 r=0 \Rightarrow r=5$

$T_{6}={ }^{10} C_{5} x \sqrt{1-x}$

$\frac{d T_{6}}{d x}={ }^{10} C_{5}\left[\sqrt{1-x}-\frac{x}{2 \sqrt{1-x}}\right]=0$

$=1-x=x / 2 \Rightarrow 3 x=2$

$\Rightarrow x=2 / 3$

$\left.T_{6}\right|_{\max }=\frac{10 !}{5 ! 5 !} \times \frac{2}{3 \sqrt{3}}$