Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is

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