Here is a detailed explanation of the matching of List I with List II:

I. Potassium bromide - (B) Photography: Potassium bromide is commonly used in photography as a photographic developer. It helps in reducing the sensitivity of photographic emulsion to light.

II. Potassium nitrate - (D) Gunpowder: Potassium nitrate, also known as saltpeter, is an important ingredient in gunpowder. It provides oxygen for the combustion process, allowing gunpowder to burn rapidly and produce the explosive force.

III. Potassium sulphate - (A) Fertilizer: Potassium sulphate is a commonly used fertilizer in agriculture. It provides essential potassium to plants, which is important for their growth and development.

IV. Mono-potassium tartarate - (C) Bakery: Mono-potassium tartarate, also known as cream of tartar, is a key ingredient in baking. It is used as a leavening agent in baking powder and helps in stabilizing and adding volume to whipped egg whites.

Therefore, the correct matching of List I with List II is:

I. Potassium bromide - (B) Photography

II. Potassium nitrate - (D) Gunpowder

III. Potassium sulphate - (A) Fertilizer

IV. Mono-potassium tartarate - (C) Bakery

Hence, the correct answer is:

I-B, II-D, III-A, IV-C.