Step 1: Analyze statement (a).
\[
BeSO_4
\]
is soluble in water because beryllium sulfate has comparatively higher covalent character and appreciable hydration energy.
Therefore, statement (a) is correct.
Step 2: Analyze statement (b).
\[
BeO
\]
is amphoteric in nature.
It reacts with both acids and bases:
\[
BeO+2HCl\rightarrow BeCl_2+H_2O
\]
and
\[
BeO+2NaOH+H_2O\rightarrow Na_2[Be(OH)_4]
\]
Hence, statement (b) is correct.
Step 3: Analyze statement (c).
On heating,
\[
CaCO_3
\]
decomposes as
\[
CaCO_3 \rightarrow CaO+CO_2
\]
It produces
\[
CO_2
\]
and not
\[
CO
\]
Therefore, statement (c) is incorrect.
Step 4: Final conclusion.
Thus, the correct statements are:
\[
\boxed{\text{a, b only}}
\]