Let `S = {1,2,3,..., 40}` and let A be a subset of S such that notwo elements in A have their sum divisible by 5. What is themaximum number of elements possible in A?

Sets A and B have 3 and 6 elements respectively. What is the minimum number of elements in A cup B?

Let S={1,2,3, …, 100} . The number of non-empty subsets A to S such that the product of elements in A is even is

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

Let S = {1,2,3,.............. n} and A={(a ,b)"|"1lt=a ,blt=n}=SxxS . A subset B of A is such that (x ,x) in B for every x in Sdot Then find the number of subsets Bdot

Let S={1,2,...,20} A subset B of S is said to be "nice" , if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is: (a) 7/(2^20) (b) 5/(2^20) (c) 4/(2^20) (d) 6/(2^20)

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is