What does a semi-permeable membrane allow to pass through?

An unripe mango placed in a concentrated salt solution to prepare pickle,shrivels because . . . . . . .

The osmotic pressure of a urea solution at $10\,^oC$ is $500\, mm\, of\, Hg$. The solution is diluted such that the temperature increases to $25\,^oC$ and the osmotic pressure becomes $131.6\, mm\, of\, Hg$. By what factor has the solution been diluted?

$A$ solution of polystyrene in benzene contains $10 \, g/L$. The equilibrium height of the column of solution having density $0.9 \, g/mL$ in the osmometer is $11 \, cm$ at $27 \, ^\circ C$. What is the average molar mass of polystyrene? (Assume the solution is ideal)

Which one of the following is an isotonic pair of solutions?

How can you remove the hard calcium carbonate layer of the egg without damaging its semipermeable membrane? Can this egg be inserted into a bottle with a narrow neck without distorting its shape? Explain the process involved.