The total number of ways of selecting two numbers from the set `{1,,23,4,3n}` 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`

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 n in N , then 3^(2n)+7 is divisible by

If the number of ways of selecting 3 numbers out of 1, 2, 3, ……., 2n+1 such that they are in arithmetic progression is 441, then the sum of the divisors of n is equal to

n is selected from the set {1, 2, 3,.............,100} and the number 2^n+3^n+5^n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to (A) 50 (B) 49 (C) 48 (D) None of these.

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^1,3^2,3^3, ,3^(10)} so that they form a G.P. then the value of N//5 is ______.

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)

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n) !)/(2(n !)^2)

If 1+(1+2)/2+(1+2+3)/3+ddotto\ n terms is Sdot Then, S is equal to a. (n(n+3))/4 b. (n(n+2))/4 c. (n(n+1)(n+2))/6 d. n^2

The total number of ways in which n^2 number of identical balls can be put in n numbered boxes (1,2,3,.......... n) such that ith box contains at least i number of balls is a. .^(n^2)C_(n-1) b. .^(n^2-1)C_(n-1) c. .^((n^2+n-2)/2)C_(n-1) d. none of these

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)