If 2x = 1 (mod 3), then positive integral values of x are

$2x\equiv 1(mod3)\Rightarrow (2x-1)$ is divisible by 3

$\begin{array}{r}\Rightarrow 2x-1=3\lambda , \lambda \in \mathrm{I}\\ \Rightarrow x=\frac{3\lambda +1}{2}, \lambda \in \mathrm{I}\end{array}$

Putting $\lambda =1, 2, 3, 4, 5,\dots$ we get

$x=2,\frac{7}{2}, 5, \frac{13}{2}, 8,\dots$

So, positive integral values of x are 2, 5, 8, ...

$\therefore$ Option (b) is the correct answer.