If n positive integers taken at random are multiplied together.

Out of 3n consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3.

Given positive integers a and b, there exists unique integers q and r satisfying a = bq + r. In this statement r should be smaller than which integer ?

Two non negative integers are chosen at random. The probability that the sum of the square is divisible by 10, is

Prove that the sum of any positive integer and its square is an even number.

The frequency distribution : Where A is a positive integer , has a variance of 160. Determine the value of A.

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m.+ 1 for some integer m.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

The ratio of sum of first n terms of two Aps is (8n+1)/(7n+3) for every positive integer n. Find the ratio of their 7th terms.

Show that the square of any positive integer is of the form 4m or 4m + 1 for some integer m.

Show that the cube of any positive integer j is of the form 4m or 4m + 1 or 4m + 3 for some integer m.