The number of ways of choosing triplet `(x , y ,z)` such that `zgtmax{x, y}` and `x ,y ,z in {1,2,.......... n, n+1}` is `(A)` `.^n+1C_3+^(n+2)C_3` `(B)``n(n+1)(2n+1)//6` `(C)``1^2+2^2+..............+n^2` `(D)` `2(.^(n+2)C_3)-(.^(n+1)C_2)`

Show that (.^(4n)C_(2n))/(.^(2n)C_(n))=(1.3.5......(4n-1))/({1.3.5......(2n-1)}^(2)) .

Show that : (^(4n)C_(2n))/(^(2n)C_n) = (1.3.5...(4n-1))/{1.3.5...(2n-1)}^2

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

Evaluate .^(n)C_(0).^(n)C_(2)+.^(n)C_(1).^(n)C_(3)+.^(n)C_(2).^(n)C_(4)+"...."+.^(n)C_(n-2).^(n)C_(n) .

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)+2.C_(2)+3.C_(3)+....+n.C_(n)=n.2^(n-1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)-2C_(2)+3C_(3)-....+(-1)^(n-1)n.C_(n)=0

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(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

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(1)-2^(n)C_(2)+3^(n)C_(3)-…+(-1)^(n-1).n^(n)C_(n)=0 .