Why does carbon undergo hybridization prior to bond formation ?

The compound in which carbon uses sp^(3) hybridization for bond formation

Chemical Bonding - Hybridization

Chemical Bonding - Hybridization 2

Bonding and Hybridization OF carbon

In metal carbonyls, there is synergic bonding interaction between metal and carbon monoxide. This leads to increase in strength of metal ligands bond and decrease in bond order of CO in carbonyl complex as compared to bond order in carbon monoxide. Simple carbonyls are invariably spin-paired complexes except for vanadium metal. Which one of the following metal carbonyl involves the d^(2)sp^(3) hybridization for the formation of metal-carbon sigma" "bonds and is paramagnetic ?

The compound in which underlined carbon uses only its sp^(3) -hybrid orbitals for bond formation is: