Statement A is correct. The metal-carbon bond in metal carbonyls possesses both σ and π character due to synergic bonding.
Statement B is incorrect. The synergic bonding interaction between the metal and the CO ligand strengthens the metal-carbon bond.
Statement C is correct. The metal-carbon σ bond is formed by the donation of a lone pair of electrons from the carbonyl carbon into a vacant orbital of the metal.
Statement D is correct. The metal-carbon π bond is formed by the back-donation of electrons from a filled d-orbital of the metal into the vacant antibonding π∗ orbital of the CO ligand.
Therefore, statements A, C, and D are correct.
Answer: A, C and D Only