Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Find the number of ways of selecting 3 pairs from 8 distinct objects.

Find the number of all onto functins from the set {1,2,3..,n} to itself.

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.

A number is chosen at random from the set 1,2,3 …100 and another number is chosen at random from the set 1,2,3,…50 what is the expected value of the product ?

Find the number of distinct rational numbers x such that oltxlt1 and x=p//q , where p ,q in {1,2,3,4,5,6} .

Three distinct numbers are selected from first 100 natural numbers. The probability that all the three numbers are divisible by 2 and 3 is -