The total number of ways of distributing n identical balls among k diferent boxes if each box can hold ny number of balls is (A) `k^n` (B) `n^k` (C) `|__(k+n-1)/(|__(k-1)|__n)` (D) `|__(k+n-1)\(|__k|__(n-1))`

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

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-1C_(n+1) c. ^2n-1C_n d. none of these

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural number then k= 1/n b. (n-1)/n c. (n+1)/(2n) d. (n+1)/n

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural number then k= a. 1/n b. (n-1)/n c. (n+1)/(2n) d. (n+1)/n

If k in R_o then det{adj(k I_n)} is equal to (A) K^(n-1) (B) K^((n-1)n) (C) K^n (D) k

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

Let A_(1) , A_(2) ,…..,A_(n) ( n lt 2) be the vertices of regular polygon of n sides with its centre at he origin. Let veca_(k) be the position vector of the point A_(k) ,k = 1,2,….,n if |sum_(k=1)^(n-1) (veca_(k) xx veca_(k) +1)|=|sum_(k=1)^(n-1) (vecak.vecak+1)| then the minimum value of n is

The value of lim _( n to oo) sum _(k =1) ^(n) ((k)/(n ^(2) +n +2k))=

A box contains tickets numbered 1 to N. n tickets are drawn from the box with replacement. The probability that the largest number on the tickets is k, is

If total number of runs secored is n matches is (n+1)/(4) (2^(n+1) -n-2) where n ge 1 , and the runs scored in the k^(th) match is given by k.2^(n+1 - k) , where 1 le k le n, n is