Let M be the product of integers from 1 to `50`, which has a factor `2^n`. The maximum value of n is

For any positive integer n, n! denotes the product of all integers from 1 through n, what is the value of 3! (7 - 2)! ?

If m,n are the positive integers (n gt 1) such that m^n = 121 , then value of (m-1)^(n +1) is :

Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a square of an integer and let n be the smallest even positive integer for which 1 + 2+ ……+ n is a square of an integer. What is the value of m + n ?

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

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

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

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