If `x,y` is positive real numbers then maximum value of `(x^my^m)/((1+x^(2m))(1+y^(2n)))` is (A) `1/4` (B) `1/2` (C) `(m+n)/(6mn)` (D) `1`

If x,y is positive real numbers then maximum value of (x^my^n)/((1+x^(2m))(1+y^(2n))) is (A) 1/4 (B) 1/2 (C) (m+n)/(6mn) (D) 1

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

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

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

If the expression [m x-1+(1//x)] is non-negative for all positive real x , then the minimum value of m must be -1//2 b. 0 c. 1//4 d. 1//2

For natural numbers m, n if (1-y)^(m)(1+y)^(n) = 1+a_(1)y+a_(2)y^(2) + "……." and a_(1) = a_(2) = 10 , then (m,n) is :

If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the angle between the lines x y=0 , then m is (a) 1 (b) 2 (c) -1/2 (d) -1

If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the angle between the lines x y=0 , then m is (a) 1 (b) 2 (c) -1/2 (d) -1

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