let $A = \{m + n \sqrt{2}\}$ where $m,n$ are integers, then

$a.$ $A$ is dense in $R$.

$b$. $A$ has no limit point in $R$.

$c$. $A$ has only countably many limit points in $R$.

$d$. only irrational numbers can be limit point of $A$

Set $A$ is similar to the set $N \times N$, so all points are isolated in $A$.

therefore option $b$ should be correct.
In answer key, option $a$ is marked as correct.
Please suggest if I am doing something wrong.