Step 1 (Formula / Governing Law & Given Data): [½ Mark]

In $3d$ transition elements, variable oxidation states arise because the energy difference between $(n-1)d$ and $ns$ orbitals is very small, allowing electrons from both subshells to participate in chemical bonding.

The maximum number of oxidation states is exhibited by the element having the maximum number of unpaired electrons in its $(n-1)d$ subshell along with $ns$ electrons.

Step 2 (Step-by-Step Mathematical & Chemical Analysis): [½ Mark]

Analyzing the outer electronic configurations and possible oxidation states for the given $3d$-series elements:

• Scandium ($Sc$, $Z = 21$): Configuration = $[Ar] 3d^1 4s^2 \implies$ Exhibits only $+3$ state ($1$ state).
• Zinc ($Zn$, $Z =