Tollens test is a chemical test used to detect the presence of reducing sugars in a given sample. Reducing sugars are carbohydrates that have the ability to reduce certain metal ions, such as silver ions, in an alkaline solution. When a reducing sugar is present, it reacts with Tollens' reagent to form a silver mirror on the inside of the reaction vessel.

Tollens test involves the reaction between Tollens' reagent, which is a solution of silver nitrate in ammonia, and the reducing sugar in the sample. The reducing sugar is oxidized by the silver ions in the Tollens' reagent, leading to the reduction of the silver ions to metallic silver. This results in the formation of a silver mirror on the inside of the reaction vessel.

When it comes to the options provided:
a) Glucose is a reducing sugar, so it will give a positive Tollens test.
b) Mannose is also a reducing sugar, so it will give a positive Tollens test.
c) Sucrose, on the other hand, is a non-reducing sugar and will not give a positive Tollens test. This is because sucrose is a disaccharide composed of glucose and fructose, which are linked together by a glycosidic bond. The glycosidic bond prevents sucrose from reacting with Tollens' reagent and undergoing oxidation.
d) Galactose is another reducing sugar and will give a positive Tollens test.

Therefore, the correct answer is option 'C' - Sucrose. Sucrose is a non-reducing sugar and will not give a positive Tollens test.