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Coefficient or constant term in a trinomial power (multinomial theorem)

This type of question, asked 4 times: 2021 Paper 23, 29 Jun 2022, 25 Jan 2023, 10 Apr 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 23

    81
    If the coefficient of a7b8a^{7}b^{8} in the expansion of (a+2b+4ab)10(a+ 2b+ 4ab)^{10} is K.216K.2^{16}, then KK is equal to

  2. Question 2

    29 Jun 2022

    76
    If the constant term in the expansion of (3x3−2x2+5x5)10\left( 3x^{3}- 2x^{2}+\frac{5}{x^{5}} \right)^{10} is 2k.l2^{k}.l, where ll is an odd integer, then the value of kk is equal to:

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  3. Question 3

    25 Jan 2023

    81
    The constant term in the expansion of (2x+1x7+3x2)5\left( 2x +\frac{1}{x^{7}}+ 3x^{2} \right)^{5} is

  4. Question 4

    10 Apr 2023

    81
    The coefficient of x7x^{7} in (1−x+2x3)10\left( 1 - x + 2x^{3} \right)^{10} is