Tollens test and its principle:
Tollens test is a chemical test used to detect the presence of aldehydes in a given sample. It is also known as the silver mirror test. The test is based on the principle that aldehydes are easily oxidized to carboxylic acids and can be reduced to form silver mirror-like precipitates in the presence of Tollens reagent.

Negative Tollens test for Sucrose:
Sucrose is a disaccharide composed of glucose and fructose monomers. It is a non-reducing sugar, meaning that it does not have an aldehyde or ketone functional group that could be oxidized to form a silver mirror-like precipitate. Therefore, Tollens test will not give a positive result for sucrose.

Positive Tollens test for Glucose, Mannose and Galactose:
Glucose, Mannose, and Galactose are monosaccharides that have an aldehyde functional group capable of being oxidized by Tollens reagent. When these sugars are treated with Tollens reagent, they will undergo oxidation and reduce the Tollens reagent to form a silver mirror-like precipitate. Hence, Tollens test will give a positive result for glucose, mannose, and galactose.

Conclusion:
In conclusion, Tollens test is a chemical test used to detect the presence of aldehydes in a given sample. Sucrose is a non-reducing sugar, and it does not have an aldehyde functional group, so Tollens test will not give a positive result for sucrose. On the other hand, glucose, mannose, and galactose are reducing sugars, and they have an aldehyde functional group, so Tollens test will give a positive result for these sugars.