Two pieces of information identify $X$.

(i) No reaction with bromine water. Bromine water oxidises the free aldehyde group present in reducing sugars. A disaccharide that is not oxidised must have no free anomeric hydroxyl, i.e. both anomeric carbons are engaged in the glycosidic linkage. Sucrose ($\alpha$-D-glucopyranosyl-$(1\to 2)$-$\beta$-D-fructofuranoside) satisfies this.

(ii) Acid hydrolysis gives a laevorotatory mixture. Sucrose ($[\alpha {]}_D\approx +66^{\circ }$) hydrolyses to an equimolar mixture of D-glucose ($+52.5^{\circ }$) and D-fructose ($-92^{\circ }$). The net rotation of the mixture (invert sugar) is negative.

Both clues uniquely identify the structure as sucrose, which is option (A). Options (B), (C), and (D) all contain a free anomeric -OH and are therefore reducing sugars that would be oxidised by bromine water.