To solve this problem, we need to analyze the boiling points of the hydrides of group 16 elements.$\\$Statement I claims that the boiling points increase in the order:$\\ H_2O < H_2S < H_2Se < H_2Te \\$Statement II suggests that the boiling points increase with an increase in molar mass.$\\$Let's evaluate these statements:$\\$• $$The boiling point of a substance is influenced by intermolecular forces. In the case of hydrides,$\\$hydrogen bonding, dipole-dipole interactions, and London dispersion forces play a role.$\\$• $$Water $(H_2O)$ has a significantly higher boiling point than $H_2S, H_2Se,$ and $H_2Te$ due to strong hydrogen bonding.$\\$• $$For $H_2S, H_2Se,$ and $H_2Te,$ the boiling points do increase with molar mass due to stronger London dispersion forces.$\\$• $$However, the order given in Statement I is incorrect because $H_2O$ has the highest boiling point among these hydrides.$\\$Therefore, the correct order of boiling points is:$\\ H_2S < H_2Se < H_2Te < H_2O \\$• $$Statement II is partially correct as it applies to $H_2S, H_2Se,$ and $H_2Te,$ but not to $H_2O. \\$Conclusion:$\\$Both Statement I and Statement II are incorrect.$\\$Thus, the correct option is:$\\$Option 2: Both Statement I and Statement II are incorrect.