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

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) 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)!)/((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)

In a n- sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is (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

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

If (1+x)^n=C_0+C_1x+C_2x^2++C_n x^n ,t h e nC_0C_2+C_1C_3+C_2C_4++C_(n-2)C_n= ((2n)!)/((n !)^2) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((n-2)!(n+2)!) d. none of these

A rectangle with sides of lengths (2n-1) and (2m-1) units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) m^2n^2 (b) mn(m+1)(n+1) (c) 4^(m+n-1) (d) non of these