The correct answer is option 4: Saprophytic. Saprophytic nutrition refers to the mode of obtaining nutrients by decomposing dead organic matter. Mushrooms are a type of fungus that obtain their nutrients by breaking down and absorbing nutrients from decaying organic material, such as dead plants, trees, or animal remains.

Option 1, Photosynthetic, is incorrect as mushrooms do not have chlorophyll or any other pigments to carry out photosynthesis. They cannot convert sunlight into energy like plants do.

Option 2, Chemosynthetic, is also incorrect. Chemosynthetic organisms obtain energy by breaking down inorganic compounds such as hydrogen sulfide or ammonia. Mushrooms do not derive their energy in this way.

Option 3, Parasitic, is incorrect as well. Parasitic organisms obtain nutrients by living off a host organism and causing harm to it. While there are parasitic fungi, mushrooms obtain their nutrients independently by decomposing dead organic matter.

Therefore, the correct mode of nutrition for mushrooms is saprophytic.