Two natural numbers x and y are chosen at random from the set `{1,2,3,4,...3n}`. find the probability that `x^2-y^2` is divisible by 3.

Two numbers a and b are chosen at random from the set {1,2,3,..,3n}. The probability that a^(3)+b^(3) is divisible by 3, is

Two numbers a and b are chosen at random from the set {1,2,3,..,5n}. The probability that a^(4)-b^(4) is divisible by 5, is

If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that 2^(m) + 2^(n) + 1 is divisible by 3.

Two number a and b aer chosen at random from the set of first 30 natural numbers.Find the probability that a^(2)-b^(2) is divisible by 3 .

Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that a^(2)-b^(2) is divisible by 3 is:

Two integers x and y are chosen with replacement out of the set {0,1,2,3...,10}. Then find the probability that |x-y|>5