The number of pairs (a, b) of positive real numbers satisfying `a^(4)+b^(4)lt1" and "a^(2)+b^(2)gt1` is

If 2^(a)=7^(b) then number of ordered pairs (a,b) of real numbers is

The number of ordered pairs (a,b) of positive integers such that (2a-1)/b and (2b-1)/a are both integers is

Let a and b be positive real numbers with a^(3) +b^(3) = a -b and k = a^(2) + 4b^(2) , then (1) k lt 1 (2) k gt 1 (3) k = 1 (4) k gt 2

Let a and b be positive real numbers with a^(3) +b^(3) = a -b and k = a^(2) + 4b^(2) , then (1) k lt 1 (2) k gt 1 (3) k = 1 (4) k gt 2

Let a>0, a!=0 . Then the set S of all positive real numbers b satisfying (1+a^2)(1+b^2)=4ab is

a ne 0, b ne 0 . The number of real number pair (a, b) which satisfy the equation a^(4) + b^(4) = (a+b)^(4) is:

The number of positive integral pairs satisfying the equation tan^(-1)a+tan^(-1)b=tan^(-1)3

If a and b are positive real numbers such that a^(2)b^(3)=(4)/(9), then least value of a+b is