The following cooking processes does not rely on coagulation taking place

The correct option is frying chips.

Coagulation is a chemical process where liquid proteins are denatured (unfolded) by heat, mechanical action, or acids, and subsequently bind together to form a solid or semi-solid gel-like structure.

Let's analyze why each of the options relies or does not rely on coagulation:
1. Making yoghurt: This process relies on coagulation. When bacteria ferment milk, they produce lactic acid. The increase in acidity denatures milk proteins (specifically casein), causing them to coagulate and thicken the milk into yoghurt.
2. Boiling an egg: This relies on coagulation. Heating the egg causes the liquid proteins in the egg white (albumen) and yolk to denature and cross-link, setting into a firm solid.
3. Whipping cream: Whipping involves mechanical action that denatures proteins and structures fat globules around air bubbles to form a stable foam, which is a form of mechanical coagulation and physical trapping.
4. Frying chips: This process involves cooking potato starch in hot oil. The primary changes during frying are starch gelatinization (where starch absorbs water and swells), dehydration of the outer surface to form a crispy crust, and caramelization/Maillard reactions (browning), rather than the coagulation of proteins.

Therefore, frying chips is the cooking process that does not rely on coagulation taking place.