The total number of ways in which `2n` persons can be divided into `n` couples is a. `(2n !)/(n ! n !)` b. `(2n !)/((2!)^3)` c. `(2n !)/(n !(2!)^n)` d. none of these

Let N denotes the number of ways in which 3n letters can be selected from 2n A's, 2nB's and 2nC's. then,

Number of ways in which three numbers in A.P.can be selected from 1,2,3,...,n is a.((n-1)/(2))^(2) if n is even b.n(n-2)/(4) if n is even c.((n-1)^(2))/(4) if n is odd 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)

If x^(m) occurs in the expansion (x+1/x^(2))^(n) , then the coefficient of x^(m) is ((2n)!)/((m)!(2n-m)!) b.((2n)!3!3!)/((2n-m)!) c.((2n-m)/(3))!((4n+m)/(3))! none of these

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

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

The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these

The total number of terms which are dependent on the value of x in the expansion of (x^(2)-2+(1)/(x^(2)))^(n) is equal to 2n+1 b.2n c.n d.n+1

There are n seats round a table numbered 1,2,3,dots,n. The number of ways in which m(<=n) persons can take seats is