Identify the correct statements from the following :
$I$. Tendency to form halide hydrates gradually increases from $Be$ to $Ba$ down the group.
$II$. Tendency to form stable superoxides increases from $Li$ to $Cs$ down the group.
$III$. Low solubility of $LiF$ is due to its high lattice energy.
$IV$. Solubility of carbonates of group-$2$ elements increases down the group.

• A
  $I, II$
• B
  $III, IV$
• C
  $II, III$
• D
  $I, III$