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

A spherical snowball is melting such that its volume is decreasing at the rate of $1 \mathrm{~cm}^3 / \mathrm{min}$. The rate at which the diameter is decreasing when the diameter is 10 cm is