The number of possible outcomes in a throw of `n` ordinary dice in which at least one of the die shows and odd number is a. `6^n-1` b. `3^n-1` c. `6^n-3^n` d. none of these

Three dice are rolled. Find the number of possible outcomes in which at least one dice shows 5.

In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a. 4n b. 4n-3 c. 4n+1 d. none of these

The number of throwing n dice simultaneously, is -

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

n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. sum_(k=1)^(n-1)k b. n(n-1) c. n^2 d. none of these

The number of diagonal matrix, A of order n which A^3=A is a. 1 b. 0 c. 2^n d. 3^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

If ""^n C_3+ ""^n C_4 > ""^(n+1)C_3 , then a. n >6 b. n >7 c. n 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 number of diagonal matrix, A or order n which A^3=A is a. is a a. 1 b. 0 c. 2^n d. 3^n