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The maximum value of the term independent of ' \( t \) ' in the
\( \mathrm{P} \) expansion of \( \left(t x^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{10} \) where \( x \in(0,1) \) is:

W)
[JEE Main-2021 (February)]
(a) \( \frac{10 !}{\sqrt{3}(5 !)^{2}} \)
(b) \( \frac{2.10 \text { ! }}{3(5 !)^{2}} \)
(c) \( \frac{10 !}{3(5 !)^{2}} \)
(d) \( \frac{2 \cdot 10 !}{3 \sqrt{3}(5 !)^{2}} \)
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