A

Step 1: Understand the U-tube behavior.
A U-tube demonstrates how hydrostatic pressure is applied. When the tube is vertical, the levels of liquid in both sides will remain equal due to the principle of communicating vessels.

Step 2: Analyze the tilted position.
When the tube is tilted, the liquid seeks to reach an equilibrium state, where the pressure at similar heights in both limbs remains equal. For this to happen, the density of the liquid must remain constant and the atmospheric pressure acting on both open ends must also be equal.

Step 3: Determine necessary conditions.
The primary condition for the liquid levels to stay equal when the U-tube is tilted is that the liquid must be a non-compressible fluid, such as water, which maintains its density regardless of orientation. Additionally, the U-tube must contain no external forces acting differently on either side (e.g., gravity acting uniformly).

Conclusion: The levels can remain the same as long as the fluid is incompressible and the system experiences uniform gravitational force without additional pressures influencing one side more than the other. Therefore, the correct condition can be expressed as a requirement for constant density and equal atmospheric pressure. Hence the answer is option A.