Solution

In aqueous solution the configuration of the ions are following:

$$Cr^{3+}(21)= 3d^34s^0 \Rightarrow {t_{2g}}^3 e_g^0$$

$$V^{3+}(20)= 3d^24s^0 \Rightarrow {t_{2g}}^2 e_g^0$$

$$Ti^{3+}(19)= 3d^14s^0\Rightarrow {t_{2g}}^1 e_g^0$$

$$Mn^{3+}(22)= 3d^44s^0\Rightarrow {t_{2g}}^4 e_g^0$$

We know that half-filled and fully filled orbitals are more stable than another half nor fully filled orbitals. Hence among the given ions the only ion which occupies half-filled $$t_{2g}$$ orbitals is Chromium (III) ion.

$$Note:$$ Although $$Mn^{3+}$$ ion has half-filledr $$t_{2g}$$ orbital but there is one more electron filled in $$e_{g}$$ orbital which reduces the stability.

Hence option A is the correct answer.