Let `A` be a set of `n(geq3)` distance elements. The number of triplets `(x ,y ,z)` of the `A` elements in which at least two coordinates is equal to a. `^n P_3` b. `n^3-^n P_3` c. `3n^2-2n` d. `3n^2-(n-1)`

Let A be a set of n (>=3) distinct elements. The number of triplets (x, y, z) of the A elements in which at least two coordinates is equal to

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

If A={n:(n^(3)+5n^(2)+2)/(n)"is an integer"}, then the number of elements in the set A, is

Let S_n denotes the sum of the first of n terms of A.P. and S_(2n)=3S_n . then the ratio S_(3n):S_n is equal to

Let 1 le m lt n le p . The number of subsets o the set A={1,2,3, . . .P} having m, n as the least and the greatest elements respectively, is

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is a. .^n C_3xx2^n b. .^n C_2xx3^(n-2) c. 3^(n-1) d. none of these

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is a. .^n C_3xx2^n b. .^n C_2xx3^(n-2) c. 3^(n-1) d. none of these

The number of diagonal matrix, A or order n which A^3=A is a. is a a. 1 b. 0 c. 2^n d. 3^n

If there is a term independent of x in ( x+1/x^2)^n , show that it is equal to (n!)/((n/3)! ((2n)/3)! )

If A and B are two sets such that n(A)=2 and n(B)=4 , then the total number of subsets of AxxB each having at least 3 elements are