Concept:
Magnetic nature depends on the number of unpaired electrons.
Oxidation state determines electronic configuration and geometry of manganese oxoanions.
Statement-wise Analysis:
(A)
{\(\mathrm{KMnO_4}\) is diamagnetic while \(\mathrm{K_2MnO_4}\) is paramagnetic.}
In \(\mathrm{MnO_4^-}\), Mn is in \(+7\) oxidation state: \(d^0\) configuration.
No unpaired electrons \(\Rightarrow\) diamagnetic.
In \(\mathrm{MnO_4^{2-}}\), Mn is in \(+6\) oxidation state: \(d^1\).
One unpaired electron \(\Rightarrow\) paramagnetic.
\(\Rightarrow\) True
(B)
{Manganate ion contains \(\mathrm{Mn^{6+}}\) while permanganate ion contains \(\mathrm{Mn^{7+}}\).}
This is directly obtained from charge calculation.
\(\Rightarrow\) True
(C)
{\(\mathrm{Mn^{2+}}\) ion on reaction with \(\mathrm{S_2O_8^{2-}}\) gives manganate ion.}
\(\mathrm{S_2O_8^{2-}}\) is a strong oxidizing agent.
It oxidizes \(\mathrm{Mn^{2+}}\) directly to permanganate (\(\mathrm{MnO_4^-}\)), not manganate.
\(\Rightarrow\) False
(D)
{Both \(\mathrm{MnO_4^-}\) and \(\mathrm{MnO_4^{2-}}\) are tetrahedral.}
Both ions have four equivalent Mn–O bonds.
Hence both possess tetrahedral geometry.
\(\Rightarrow\) True
Final Conclusion:
Correct statements are \(\boxed{A,\,B\ \text{and}\ D}\).