There are n identical red balls & m identical green balls. The number of different linear arrangements consisting of "n red balls but not necessarily all the green balls" is `"^xC_y` then (A) x=m+n , y=m (B) x=m+n+1, y=m (C) x=m+n+1, y=m+1 (D) x=m+n, y=n

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals.

If x^m . Y^n = (x + y)^(m + n) , then dx/dy is :

If x^m y^n = (x+y)^(m+n) then find (dy)/(dx) at x=1, y=2

7 lf If log (x y m 2n and log (x4 y n 2m, then log X is equal to (A) (B) m-n (c) men (D) m n

If m red balls and n white balls are placed in a row so that no two white balls are together, prove that if m gt n , the total number of ways in which this can be done is ""^(m+1)C_(n) .

If m red balls and n white balls are placed in a row so that no two white balls are together, prove that if m > n, the total number of ways in which this can be done is ""^(m+1)C_(n) .

The length of the subtangent to the curve x^m y^n = a^(m + n) at any point (x_1,y_1) on it is

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4