Given below are two statements:
Statement I: Iron (III) catalyst, acidified $$K_2Cr_2O_7$$ and neutral $$KMnO_4$$ have the ability to oxidise $$I^-$$ to $$I_2$$ independently.
Statement II: Manganate ion is paramagnetic in nature and involves $$p\pi - p\pi$$ bonding.
In the light of the above statements, choose the correct answer from the options.

We need to evaluate both statements about d-block element chemistry.

The first statement asserts that "Iron (III) catalyst, acidified $$K_2Cr_2O_7$$ and neutral $$KMnO_4$$ have the ability to oxidise $$I^-$$ to $$I_2$$ independently." In this context, $$Fe^{3+}$$ can oxidise $$I^-$$ to $$I_2$$, as shown by the reaction:

$$ 2Fe^{3+} + 2I^- \rightarrow 2Fe^{2+} + I_2 $$

This is correct since $$E^\circ(Fe^{3+}/Fe^{2+}) = +0.77$$ V and $$E^\circ(I_2/I^-) = +0.54$$ V. Similarly, dichromate in acidic medium is a strong oxidising agent and can oxidise $$I^-$$ to $$I_2$$:

$$ Cr_2O_7^{2-} + 6I^- + 14H^+ \rightarrow 2Cr^{3+} + 3I_2 + 7H_2O $$

This reaction is also correct. In a neutral medium, $$KMnO_4$$ acts as a moderate oxidiser ($$MnO_4^- \rightarrow MnO_2$$) and oxidises $$I^-$$ to $$I_2$$:

$$ 2MnO_4^- + 6I^- + 4H_2O \rightarrow 2MnO_2 + 3I_2 + 8OH^- $$

Thus each oxidising agent can convert iodide to iodine. However, the term "Iron (III) catalyst" is misleading: $$Fe^{3+}$$ functions as an oxidising agent rather than a catalyst because it is reduced to $$Fe^{2+}$$ in the process. Therefore, the first statement is false.

The second statement claims that the manganate ion is paramagnetic and involves $$p\pi - p\pi$$ bonding. The manganate ion, $$MnO_4^{2-}$$, has manganese in the +6 oxidation state with the electronic configuration $$[Ar] 3d^1$$, which indeed gives one unpaired electron and makes it paramagnetic. However, the bonding in $$MnO_4^{2-}$$ involves $$d\pi - p\pi$$ overlap between Mn d-orbitals and O p-orbitals, not $$p\pi - p\pi$$ bonding. Since this description is incorrect, the second statement is also false.

Consequently, both statements are false, so the correct answer is Option B: Both Statement I and Statement II are false.