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 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

The sum of first n terms of a certain series is given as 2n^(2)-3n . Show that the series is an A.P.

If n in N >1 , then the sum of real part of roots of z^n=(z+1)^n is equal to n/2 b. ((n-1))/2 c. n/2 d. ((1-n))/2

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is (a). .^n C_3xx2^n (b). .^n C_2xx3^(n-2) (c). 3^(n-1) (d). none of these

Let s_(n) denote the sum of first n terms of an A.P. and S_(2n) = 3S_(n) . If S_(3n) = kS_(n) then the value of k is equal to

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

Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, then the least value of n is a. 3 b. 6 c. 9 d. 12

If the sum of n terms of a G.P. is 3-(3^(n+1))/(4^(2n)) , then find the common ratio.

The sum of the series a-(a+d)+(a+2d)-(a+3d)+ up to (2n+1) terms is- a. -n d . b. a+2n d . c. a+n d . d. 2n d