The correct statements among I to lII regarding group 13 element oxides are, 

(I) Boron trioxide is acidic oxide. 

(II) Oxides of aluminum and gallium are amphoteric. 

(III) Oxides of indium and thallium are basic.

Solution:

Acidic oxide is the one that forms acid or make solution acidic on addition of water. Boron trioxide is acidic oxide as it forms boric acid when reacts with water.

${\mathrm{B}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{B}{\left(\mathrm{OH}\right)}_3$

Al₂O₃ is amphoteric oxide because it reacts with both base and acid.

$\begin{array}{ccc}{\mathrm{Al}}_2{\mathrm{O}}_3+6\mathrm{HCl}& \to & 2{\mathrm{AlCl}}_3+3{\mathrm{H}}_2\mathrm{O}\\ {\mathrm{Al}}_2{\mathrm{O}}_3+2\mathrm{NaOH}+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{NaAl}{\left(\mathrm{OH}\right)}_4\end{array}$

Gallium oxide is amphoteric because it reacts with both acid and base.

$\begin{array}{ccc}{\mathrm{Ga}}_2{\mathrm{O}}_3+2\mathrm{NaOH}+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{Na}\left[\mathrm{Ga}{\left(\mathrm{OH}\right)}_4\right]\\ {\mathrm{Ga}}_2{\mathrm{O}}_3+6\mathrm{HCl}& \to & 2{\mathrm{GaCl}}_3+3{\mathrm{H}}_2\mathrm{O}\end{array}$

Basic oxide are those that form base when reacts with water. Indium and thallium are basic oxide as they form base when reacts with water.

$\begin{array}{ccc}{\mathrm{In}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{In}{\left(\mathrm{OH}\right)}_3\\ {\mathrm{Tl}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{TlOH}\end{array}$