- Statement (A) is correct. Cellulose does not reduce Fehling's solution or Tollens' reagent because it does not have the free aldehyde group needed to carry out the reduction. This is in contrast to reducing sugars like glucose, which can reduce these reagents.
- Statement (B) is correct. When cellulose is heated with dilute H$_2$SO$_4$ under pressure, it undergoes hydrolysis to produce D-glucose.
- Statement (C) is correct. Cellulose is a straight-chain polysaccharide made up of $\beta$-D-glucose units linked together by $\beta$-glycosidic bonds.
- Statement (D) is incorrect. The $\beta$-glycosidic linkages in cellulose are between C$_1$ of one glucose unit and C$_4$ of the next glucose unit, not C$_5$. This is a key structural feature of cellulose.