The element which show only one oxidation state other than its elemental form is :

The correct answer is Scandium.

Step-by-Step Explanation:

1. Variable Oxidation States in Transition Metals:
Transition metals (d-block elements) typically exhibit variable oxidation states. This is because the energy difference between the $(n-1)d$ orbitals and the $ns$ orbital is very small, allowing electrons from both subshells to participate in bond formation.

2. Electronic Configuration and Stability of Scandium ($\mathrm{Sc}$):
Scandium has an atomic number of 21. Its ground-state electronic configuration is:
$\mathrm{Sc}=\left[\mathrm{Ar}\right]{\mathrm{3d}}^1{\mathrm{4s}}^2$
To achieve chemical stability, Scandium easily loses its two $4s$ electrons and one $3d$ electron. Losing these three electrons results in a stable, closed-shell noble gas configuration corresponding to Argon ($\left[\mathrm{Ar}\right]$):
${\mathrm{Sc}}^{3+}=\left[\mathrm{Ar}\right]$
Because the noble gas core is extremely stable, it is highly unfavorable to remove further electrons, and because losing fewer than three electrons does not yield a stable configuration, Scandium does not exhibit intermediate oxidation states like +1 or +2. Therefore, the only oxidation state Scandium shows (other than 0 in its elemental form) is +3.

3. Comparison with Other Options:
- Titanium ($\mathrm{Ti}$): Has the electronic configuration $\left[\mathrm{Ar}\right]{\mathrm{3d}}^2{\mathrm{4s}}^2$ and exhibits multiple oxidation states such as +2, +3, and +4.
- Nickel ($\mathrm{Ni}$): Has the electronic configuration $\left[\mathrm{Ar}\right]{\mathrm{3d}}^8{\mathrm{4s}}^2$ and exhibits multiple oxidation states including +2, +3, and +4.
- Cobalt ($\mathrm{Co}$): Has the electronic configuration $\left[\mathrm{Ar}\right]{\mathrm{3d}}^7{\mathrm{4s}}^2$ and shows variable oxidation states such as +2, +3, and +4.

Consequently, Scandium is the only element among the choices that exhibits only a single oxidation state (+3) other than its elemental state.