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Maximum value of the term independent of t in (t x^(1/5) + (1-x)^(1/10)/t)^n

The same question, asked 2 times: 2021 Paper 25*, 25 Jul 2022. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 25

    62
    The maximum value of the term independent of ' tt ' in the expansion of (tx15+(1−x)110t)10\left( tx^{\frac{1}{5}}+\frac{(1 -x)^{\frac{1}{10}}}{t} \right)^{10} where x∈(0,1)x\in (0,1) is:

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  2. Question 2

    25 Jul 2022

    83
    If the maximum value of the term independent of tt in the expansion of (t2x15+(1−x)110t)15,x≥0\left( t^{2}x^{\frac{1}{5}}+\frac{(1 - x)^{\frac{1}{10}}}{t} \right)^{15},x \geq 0, is KK, then 8 K8\text{ }K is equal to