Two distinct numbers a and b are chosen randomly from the set `{2, 2^2, 2^3, 2^4,.....,2^25}.` Find the probability that `log_a b` is an integer.

Two distinct numbers a and b are chosen randomly from the set {2,2^(2),2^(3),….2^(25)} . Then the probability that log_(a)b is an integer is

If two distinct numbers a and be are selected from the set {5^(1), 5^(2), 5^(3)……….5^(9)} , then the probability that log_(a)b is an integer 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

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

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.

If two numbers p and q are choosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p^(2)ge4q is equal to

If two numbers p and q are choosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p^(2)ge4q is equal to

If two numbers p and q are choosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p^(2)ge4q is equal to

Suppose two numbers a and b are chosen randomly from the set {1, 2, 3, 4, 5, 6}. The probability that function f(x) = x^3+ ax^2 + bx is strictly increasing function on R is: