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

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

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)

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 m and n are positive integers and f(x)=int_(1)^(x)(t-a)^(2n)(t-b)^(2m+1)dt,a!=b then

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

The number of all pairs (m, n), where m and n are positive integers, such that 1/(m)+1/(n)+1/(mn)=2/(5) is

x^(m)xx x^(n)=x^(m+n) , where x is a non zero rational number and m,n are positive integers.

x^(m)-:y^(m)=(x-:y)^(m) , where x and y are non zero rational numbers and m is a positive integer.

Statement-1: If x, y are positive real number satisfying x+y=1 , then x^(1//3)+y^(1//3)gt2^(2//3) Statement-2: (x^(n)+y^(n))/(2)lt((x+y)/(2))^(n) , if 0ltnlt1 and x,ygt0.