Statement - I : The set of concentric circles in a plane is infinite 

Statement - II: The set $\left\{x:x^2-3=0\right.$and x is rational} is finite. 

There are infinite concentric circles in a plane. So, the given set is infinite.  

Now, $x^2-3=0$

$\begin{array}{r}\Rightarrow x^2=3\\ \Rightarrow x=\pm \sqrt{3}\end{array}$

Thus, there is no rational number satisfied $x^2-3=0$ So, given set is null set.