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

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

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

Number of sub parts into which ‘n’ straight lines in a plane can divide it is: (a) (n^(2)+n+2)/(2) (b) (n^(2)+n+4)/(2) (c) (n^(2)+n+6)/(2) (d) none

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

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)

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

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

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