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