Given below are two statements:
Statement I: The number of pairs, from the following, in which both the ions are coloured in aqueous solution is 3.
$$[Sc^{3+},Ti^{3+}],[Mn^{2+},Cr^{2+}],[Cu^{2+},Zn^{2+}]\text{ and }[Ni^{2+},Ti^{4+}]$$
Statement II: $$Th^{4+}$$ is the strongest reducing agent among $$Th^{4+},Ce^{4+},Gd^{3+}\text{ and }Eu^{2+}$$.
In the light of the above statements, choose the correct answer from the options given below

We need to evaluate two statements about transition metal ions.

Statement I: The number of pairs in which both ions are coloured in aqueous solution is 3.

The pairs given are:

1. $$[Sc^{3+}, Ti^{3+}]$$: $$Sc^{3+}$$ has configuration $$[Ar]3d^0$$ — colourless (no d-electrons for d-d transition). $$Ti^{3+}$$ has $$[Ar]3d^1$$ — coloured (purple). Not both coloured.

2. $$[Mn^{2+}, Cr^{2+}]$$: $$Mn^{2+}$$ has $$[Ar]3d^5$$ — very faintly pink (spin-forbidden transitions, often considered coloured). $$Cr^{2+}$$ has $$[Ar]3d^4$$ — coloured (blue). Both coloured.

3. $$[Cu^{2+}, Zn^{2+}]$$: $$Cu^{2+}$$ has $$[Ar]3d^9$$ — coloured (blue). $$Zn^{2+}$$ has $$[Ar]3d^{10}$$ — colourless (fully filled d-orbital). Not both coloured.

4. $$[Ni^{2+}, Ti^{4+}]$$: $$Ni^{2+}$$ has $$[Ar]3d^8$$ — coloured (green). $$Ti^{4+}$$ has $$[Ar]3d^0$$ — colourless. Not both coloured.

Only 1 pair ($$Mn^{2+}, Cr^{2+}$$) has both ions coloured. The statement claims 3 pairs, which is false.

Statement II: $$Th^{4+}$$ is the strongest reducing agent among $$Th^{4+}, Ce^{4+}, Gd^{3+}, Eu^{2+}$$.

A reducing agent donates electrons (gets oxidized). Among the given species:

- $$Eu^{2+}$$ can be oxidized to $$Eu^{3+}$$ (gaining the stable $$4f^7$$ half-filled configuration), making it a strong reducing agent.

- $$Ce^{4+}$$ is actually a strong oxidizing agent (tends to gain electrons to become $$Ce^{3+}$$), not a reducing agent.

- $$Th^{4+}$$ has a noble gas core $$[Rn]$$ with no electrons in 5f. It is very stable and has no tendency to be further oxidized. It is a very poor reducing agent.

- $$Gd^{3+}$$ has the stable half-filled $$4f^7$$ configuration and is not easily oxidized.

The strongest reducing agent is $$Eu^{2+}$$, not $$Th^{4+}$$. Statement II is false.

Since both statements are false, the correct answer is Option (4): Both Statement I and Statement II are false.