As per the question, the correct answer is to be chosen from the given options that is identical to the logic given in the statement of the question that is, "like dissolves like".
Polar molecules can get dissolved in water because they are hydrophilic or water-loving in nature. They have such functional groups in their structure which have the capability of forming hydrogen bonds with water molecules, hence get dissolved in water.
Non-polar molecules can get dissolved in non-polar solvents like fats and oils because either of them are hydrophobic or water-hating in nature. They have such functional groups which can form hydrophobic and Van-der-Waal's forces of interaction with each other , hence they get dissolved in non-polar solvents.
Polar and non-polar substances are unable to get dissolved in each other because the polar molecules are incapable forming hydrophobic or Van-der-Waals forces of interaction with the non-polar molecules and the non-polar molecules are incapable of forming hydrogen bonding with the polar molecules.
Trans-membrane proteins are those which remain integrated in the lipid bilayer of the plasma membrane and spans across the membrane forming a connection between the cell interior and the cell exterior.
They are required for transporting small polar molecules and ions across the plasma membrane.
The lipid bilayer of the plasma membrane is otherwise impermeable to the movement of polar molecules and ions due to the hydrophobicity of the lipid molecules.
The trans-membrane proteins are amphipathic molecules, that is, they are made up of both polar and non-polar amino acid residues.
These amino acid residues are such arranged in the structure of the proteins that the non-polar amino acids face towards the lipid molecules in the bilayer thereby forming hydrophobic and Van-der-Waals forces of interaction with the lipid molecules.
The polar amino acids face towards the channel or lumen formed by the protein across the lipid bilayer so that they can form hydrogen bonds with the polar molecules and ions which are transported across the plasma membrane.
