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

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tails is ((2n !))/((n !)^2)(1/2)^(2n) b. 1-((2n !))/((n !)^2) c. 1-((2n !))/((n !)^2)1/(4^n)^ d. none of these

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

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+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)

2n boys are randomly divided into two subgroups containint n boys each. The probability that the two tallest boys are in different groups is a. n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 d. none of these

In a n- sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is: (a.) (2^n C_2)/(^(^(n C_(2-n)))C_2) (b.) ("^(n(n-1))C_2)/(^(^(n C_(2-n)))C_2) (c.) (^n C_4)/(^(^(n C_2-n))C_2) (d.) none of these

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 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

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

Let f(n ,k) denote the number of ways in which k identical balls can be colored with n colors so that there is at least one ball of each color. Then f(n ,2n) must be equal to a. ""^(2n) C_n b. ""^(2n-1)C_(n+1) c. ""^(2n-1)C_n d. none of these