In case (a); 
The theorem of perpendicular axes applies only to laminar (plane) objects, and in the given case, it is applied along a 3D cube. Thus, this is false.
In case (b); 
\(z'\) is a parallel axis at a distance of \(\frac{a}{\sqrt 2}\) from \(z.\) By the parallel axis theorem,
\(\Rightarrow I_{z'}=I_z+m\left(\frac{a}{\sqrt{2}}\right)^2=I_z+\frac{m a^2}{2}\)
Thus, the given statement is true.
In case (c);
\(z"\) is not parallel to \(z.\) Thus, the theorem of the parallel axis cannot be applied. Thus, this is false.
In case (d);
As \(x\) and \(y\)-axes are symmetrical, the inertia about them will be equal, \(I_x=I_y.\) Thus, this statement is true.
Therefore, statements (b) and (d) are true for the given conditions.
Hence, option (3) is the correct answer.