The solutions in the two arms of this U-tube are separated by a membrane that is permeable to water and glucose but not to sucrose. A. Side A is half-filled with a solution of 2 M sucrose and 1 M glucose. B. Side B is half-filled with 1 M sucrose and 2 M glucose. C. Initially, the liquid levels on both sides are equal.

Sucrose is formed of two molecules of glucose but the membrane is impermeable to it.
The given membrane is said to be permeable to water and glucose.
Through a semi-permeable membrane, molecules tend to move from a region where its concentration is high to another region where its concentration is low by the process of diffusion until its concentration in the two regions becomes equal. This phenomenon is known as Osmosis.
Concentration gradient of a molecule can be defined as the difference in the concentration of the molecule in two different regions separated by a semi-permeable membrane.
Considering glucose, the concentration of glucose is low in side A (1M) and high in side B (2M), so it will tend to move from side B to side A down its concentration gradient.
Considering sucrose, although its concentration is high in side A (2M) but low in side B (1M), it is unable to move as the membrane is impermeable to it.
Water tend to move from a region where the concentration of solute is low (or water concentration is high) to a region where the concentration of solute is high (or water concentration is low).
Due to the movement of glucose from side B to side A, the concentration of total solute concentration becomes high in side A as compared to side B. Therefore, water would move from side B to side A.
Hence the level of liquid in Side A will rise after sometime.