If the maximum value of the term independent of t in the expansion of (t² x^(1/5)+((1-x)^(1/10))/t)¹⁵, x 0, is K, then 8 ~K is equal to _ _ _ _ _ _.

Binomial Theorem and Its Simple Applications: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q27

JEE Main 202225 Jul, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

If the maximum value of the term independent of

t

in the expansion of

\left(\mathrm{t}^{2} x^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{\mathrm{t}}\right)^{15}, x \geqslant 0

, is

\mathrm{K}

, then

8 \mathrm{~K}

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.