The aqueous solution containing which one of the following ions will be colourless?

Sc³⁺

The correct answer is option 1. Sc³⁺

The aqueous solution containing $\text{Sc}^{3+}$ will be colorless because $\text{Sc}^{3+}$ has no unpaired electrons. The $d$-orbitals of $\text{Sc}^{3+}$ are completely filled, so there are no electrons that can absorb visible light and cause the solution to be colored.

The other ions in the question, $\text{Fe}^{3+}$, $\text{Fe}^{2+}$, and $\text{Mn}^{2+}$, all have unpaired electrons in their $d$-orbitals. These unpaired electrons can absorb visible light, which is why the aqueous solutions containing these ions are colored.

So the answer is (1), $\text{Sc}^{3+}$.