Statement I: A sucrose solution in water is dextrorotatory but on hydrolysis in the presence of little HCl, it becomes laevorotatory

Statement II: Sucrose on hydrolysis gives unequal amounts of glucose and fructose as a result of which change in sign of rotation is observed

Statement I is correct but Statement II is false

The correct answer is option 3. Statement I is correct, but Statement II is false.

Statement I: A sucrose solution in water is dextrorotatory but on hydrolysis in the presence of little HCl, it becomes laevorotatory

Statement I is correct. A sucrose solution in water is indeed dextrorotatory, meaning it rotates plane-polarized light to the right. However, upon hydrolysis of sucrose in the presence of a small amount of hydrochloric acid (HCl), it does not become laevorotatory. The hydrolysis of sucrose results in the formation of equal amounts of glucose and fructose, which do not cause a change in the sign of rotation.

Statement II: Sucrose on hydrolysis gives unequal amounts of glucose and fructose as a result of which change in sign of rotation is observed

Statement II is false. Sucrose, upon hydrolysis, does not give unequal amounts of glucose and fructose. The hydrolysis of sucrose results in the formation of an equimolar mixture of glucose and fructose. The glycosidic bond linking glucose and fructose in sucrose is cleaved, resulting in the formation of one molecule of glucose and one molecule of fructose.

Therefore, the correct answer is that Statement I is correct, but Statement II is false.