Answer:
A thin, flexible, semipermeable barrier around the cell which regulates what enters and leaves the cell is cell membrane. The plasma membrane is another name of the cell membrane.
The plasma membrane is semipermeable because it allow only some molecules to enter and exit the cell. Small polar molecules can easily cross the plasma membrane along the concentration gradient diffusion.
For the passage of large, non-polar and charge molecules plasma membrane have carrier proteins which can be used to transport the molecules along the concentration gradient by facilitated diffusion or against the concentration gradient by active transport. Therefore, the correct answer is the cell membrane.