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Sum or mean of all coefficients (put x = 1)

This type of question, asked 3 times: 2021 Paper 24, 27 Jan 2024, 4 Apr 2025. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 24

    87
    If the sum of the coefficients in the expansion of (x+y)n(x+y)^{n} is 4096, then the greatest coefficient in the expansion is

  2. Question 2

    27 Jan 2024

    65
    If A denotes the sum of all the coefficients in the expansion of (1−3x+10x2)n\left( 1 - 3x + 10x^{2} \right)^{n} and BB denotes the sum of all the coefficients in the expansion of (1+x2)n\left( 1 +x^{2} \right)^{n}, then :

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  3. Question 3

    4 Apr 2025

    54
    For an integer n≥2n \geq 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)2n−3(x+y)^{2n- 3} is 16 , then the distance of the point P(2n−1,n2−4n)P\left( 2n - 1,n^{2}- 4n \right) from the line x+y=8x+y= 8 is:

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