Rate of cooling in normalising is faster than in annealing:
In normalising, the metal is heated to a temperature slightly above its upper critical temperature and then allowed to cool in still air. This process results in a fine and uniform grain structure. The rate of cooling in normalising is faster than in annealing because the metal is cooled in still air, whereas in annealing, the metal is cooled slowly in a furnace or by burying it in an insulating material. The faster cooling rate in normalising leads to a more refined grain structure, which improves the mechanical properties of the metal.

Annealing improves ductility:
Annealing is a heat treatment process in which a metal is heated to a specific temperature and then cooled slowly to room temperature. This process helps to relieve internal stresses, improve ductility, and reduce hardness. During annealing, the metal's microstructure undergoes recrystallization, which results in a refined grain structure and improved ductility. The slow cooling rate in annealing allows sufficient time for the atoms to rearrange and form a more stable microstructure, which improves the metal's ductility.

Normalising improves grain structure:
Normalising is a heat treatment process similar to annealing, but the cooling rate is faster. The main purpose of normalising is to refine the grain structure and improve the mechanical properties of the metal. When a metal is heated to the upper critical temperature and allowed to cool in still air, the faster cooling rate promotes the formation of fine and uniform grains. This refined grain structure enhances the metal's strength, toughness, and machinability. Normalising also helps to relieve internal stresses and reduce the risk of distortion during subsequent machining or forming processes.

All of the mentioned:
Based on the explanations above, it can be concluded that all of the mentioned statements are true. The rate of cooling in normalising is faster than in annealing, annealing improves ductility, and normalising improves grain structure. These heat treatment processes play crucial roles in enhancing the mechanical properties and performance of metals.