The least area of a circle circumscribing any right-angle triangle of area $\frac{9}{\pi}$ sq units is

Let $A$ and $G$ denote the arithmetic mean and geometric mean of positive real numbers $5^x$ and $5^{1-x}$. Then the minimum value of the expression $5^x+5^{1-x}$ where $x \in R$ is

In the interval $(0,1)$ the function $f(x)=x^2-x+1$ is

The least value of ' $a$ ' such that the function $x^2+a x+1$ is increasing on $[1,2]$ is