Shell moulding coats sand with a resin, drops it onto a metal pattern heated to roughly \( 230\text{-}260^\circ\text{C} \), and needs that resin to cure into a rigid shell within seconds.
So the resin used in shell moulding is phenol formaldehyde.
Shell moulding (the Croning process) was specifically developed around a resin that could be pre-coated onto sand and then rapidly hardened by contact heat alone, and comparing the options against that specific requirement is informative.
The historical and practical basis of the Croning shell process confirms phenol formaldehyde as the resin used.
Therefore, the correct answer is Phenol formaldehyde.