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

Prove that 4n^(2)-1 is an odd number for all n in N

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

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

Let A be a set of n(geq3) distance elements. The number of triplets (x ,y ,z) of the A elements in which at least two coordinates is equal to a. ^n P_3 b. n^3-^n P_3 c. 3n^2-2n d. 3n^2-(n-1)

The total number of five-digit numbers of different digits in which the digit in the middle is the largest is a. sum_(n=4)^9^n P_4 b. 33(3!) c. 30(3!) 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

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 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 triangles that can be formed with 10 points as vertices n of them being collinear, is 110. Then n is a. 3 b. 4 c. 5 d. 6

If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is a. 1/4m n(m-1)(n-1) b. 1/4m n(m-1)(n-1) c. 1/4m^2n^2 d. none of these