Approach this by asking what activated carbon manufacture actually needs from its raw material, a hard, carbon dense, ligneous structure that can be charred and then have its pore network opened up by an activating agent.
Husks and shells fit this description. Rice husk is burned to charcoal and activated in commercial and small scale units alike. Groundnut shell, being a hard fibrous cover, behaves the same way once carbonized. Mango stone, the woody seed cover inside the fruit, is similarly hard and carbon rich, and it has been shown to convert into usable activated carbon.
Oil cake is a completely different kind of material. It is what remains after the oil has been extracted from seeds like groundnut, mustard or soybean, and it is full of protein and residual nutrients rather than tough ligneous carbon. That composition makes it valuable as cattle feed or manure, not as a carbon source for activation.
So the qualifying wastes are rice husk, groundnut shell and mango stone, leaving oil cake out.
\[\boxed{\text{Option 4: (A), (B) and (D) only}}\]