Statement-I : Solubility of alkaline earth metal hydroxides in water increases from $\mathrm{Be}(\mathrm{OH}{)}_2$ to $\mathrm{Ba}(\mathrm{OH}{)}_2\text{. }$

Statement II : Solubility of alkaline earth metal carbonates and sulphates decreases down the group.
 

Solubility of alkaline earth metal hydroxides in water increases down the group because lattice energy of hydroxides decreases down the group.

Down the group, lattice energy of alkaline earth metals carbonates and sulphates increases, hence their solubility get decreased.