JEE MAINS 2019 Question

Let x, y be positive real numbers and m, n  positive integers. The maximum value of the expression \frac{x^m y^n}{(1+x^{2m})(1+y^{2n})} is:

(A)   \frac{1}{2}                                  

(B)  \frac{1}{4}  

(C)  \frac{m+n}{6mn}                            

(D)   1

Answer: B

Solution:

Using A.M \ge G.M inequality, we get

Therefore, maximum value is \frac{1}{4}  .