A polysaccharide 'X' on boiling with dil $$H_2SO_4$$ at $$393$$ K under $$2 - 3$$ atm pressure yields 'Y' 'Y' on treatment with bromine water gives gluconic acid. 'X' contains $$\beta$$-glycosidic linkages only. Compound 'X' is :

We need to identify polysaccharide X that has only $$\beta$$-glycosidic linkages and yields glucose on hydrolysis. On boiling with dilute $$H_2SO_4$$ at 393 K under 2-3 atm pressure, X gives Y, which on treatment with bromine water gives gluconic acid. Since bromine water oxidizes the aldehyde group ($$-CHO$$) of glucose to a carboxylic acid group ($$-COOH$$), Y must be glucose.

$$ \text{Glucose} + Br_2 + H_2O \rightarrow \text{Gluconic acid} + 2HBr $$

X must therefore be a polysaccharide that yields glucose on hydrolysis and contains only $$\beta$$-glycosidic linkages. Starch (including amylose and amylopectin) contains $$\alpha$$-glycosidic linkages and is eliminated, while cellulose consists solely of $$\beta$$-1,4-glycosidic linkages and yields glucose upon hydrolysis. The correct answer is Option B: Cellulose.