Step 1: Analyze statement (A).
Fructose, a monosaccharide, can exist in two forms – a five-membered ring (furanose) and a six-membered ring (pyranose). The furanose form is the more common one when fructose is in solution. Hence, statement (A) is correct.
Step 2: Analyze statement (B).
Glucose does not give saccharic acid (also called gluconic acid) on reaction with bromine water. In fact, bromine water is used to oxidize the aldehyde group in glucose to a carboxyl group, forming gluconic acid, not saccharic acid. Therefore, statement (B) is incorrect.
Step 3: Analyze statement (C).
Amylose is a form of starch and is a linear polymer of \( \alpha \)-D-glucose, not branched. The statement about amylose being a branched-chain polymer is incorrect, as amylose does not have branches. Thus, statement (C) is incorrect.
Step 4: Analyze statement (D).
Cellulose is a polysaccharide made up of \( \beta \)-D-glucose units, not \( \alpha \)-D-glucose units. The structure of cellulose involves β-1,4 glycosidic linkages between glucose molecules, unlike starch or glycogen which involve α-1,4 linkages. Therefore, statement (D) is incorrect.
Step 5: Conclusion.
Only statement (A) is correct, and the correct answer is option (A).