Step 1: Rule to remember:
Diamond tools are made of carbon, and carbon dissolves readily into iron at machining temperatures.
So any material that contains iron will chemically attack a diamond tool and is normally kept away from diamond machining.
Step 2: Sorting the four materials by chemistry:
Ferrous group (contains iron): mild steel and stainless steel both belong here, since stainless steel is just steel with chromium and nickel added.
Non ferrous group (no iron): silicon and aluminium alloy belong here.
Step 3: Matching with real practice:
Silicon wafers in the electronics industry are diced and ground using diamond tools all the time, because silicon is hard, brittle, and has zero iron content.
Aluminium alloys are also commonly turned and milled with polycrystalline diamond (PCD) inserts, since aluminium gives excellent finish with diamond and does not react with carbon.
Mild steel and stainless steel, being iron rich, cause rapid graphitisation of the diamond edge, so shops switch to carbide or CBN tools for these instead.
Final Answer:
The materials not commonly machined with diamond tools are mild steel and stainless steel, options (A) and (B).
\[ \boxed{\text{(A) and (B)}} \]