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Sum of coefficients of the positive (or positive even) powers of x

This type of question, asked 2 times: 25 Jun 2022, 27 Jun 2022. All 2 questions below, oldest first.

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  1. Question 1

    25 Jun 2022

    174
    If the sum of the coefficients of all the positive even powers of xx in the binomial expansion of (2x3+3x)10\left( 2x^{3}+\frac{3}{x} \right)^{10} is 510−β⋅395^{10}-\beta\cdot3^{9}, then β\beta is equal to

  2. Question 2

    27 Jun 2022

    174
    If the sum of the coefficients of all the positive powers of xx, in the binomial expansion of (xn+2x5)7\left( x^{n}+\frac{2}{x^{5}} \right)^{7} is 939, then the sum of all the possible integral values of nn is: