With respect to resonance structures of $\text{CO}_3^{2-}$ ion, which of the following statements are correct?
(a) All $\text{C}-\text{O}$ bonds in $\text{CO}_3^{2-}$ are equivalent
(b) There are three resonance structures possible for $\text{CO}_3^{2-}$ ion
(c) The position of carbon and oxygen should change in every resonance structure
(d) The formal charge on carbon atom is $-2$

The carbonate ion, $\text{CO}_3^{2-}$, has three equivalent resonance structures where the double bond is shared among the three oxygen atoms.

Due to resonance, all three $\text{C}-\text{O}$ bonds have partial double bond character and are equivalent in length and strength. Thus, statement (a) is correct.

There are exactly three equivalent resonance structures for the $\text{CO}_3^{2-}$ ion. Thus, statement (b) is correct.

In resonance structures, the positions of the atoms must remain fixed; only the arrangement of electrons changes. Thus, statement (c) is incorrect.

The formal charge on the carbon atom in $\text{CO}_3^{2-}$ is calculated as: Formal charge = (Valence electrons) - (Non-bonding electrons) - (Bonding electrons)/2 = $4 - 0 - \dfrac{8}{2} = 0$. Thus, statement (d) is incorrect.

Therefore, only statements (a) and (b) are correct.

Answer: a and b only