Explanation:

Introduction:
Alcohols are organic compounds that contain a hydroxyl (-OH) group attached to a carbon atom. They are known for their characteristic properties, including high boiling points. The high boiling points of alcohols can be attributed to the presence of intermolecular hydrogen bonding.

Intermolecular Hydrogen Bonding:
Intermolecular hydrogen bonding is a special type of intermolecular force that occurs between molecules containing hydrogen atoms bonded to highly electronegative atoms such as oxygen, nitrogen, or fluorine. In the case of alcohols, the hydrogen atom of the hydroxyl group forms a hydrogen bond with the electronegative oxygen atom of another alcohol molecule.

Effect of Intermolecular Hydrogen Bonding on Boiling Point:
The presence of intermolecular hydrogen bonding significantly affects the boiling points of alcohols. The boiling point of a substance is defined as the temperature at which its vapor pressure equals the atmospheric pressure. Higher boiling points indicate stronger intermolecular forces.

Explanation of Options:
a) Increase in van der Waals forces: Van der Waals forces are weak intermolecular forces that arise due to temporary fluctuations in electron distribution within molecules. While alcohols do experience van der Waals forces, these forces alone are not sufficient to explain their high boiling points. Therefore, option a is incorrect.

b) Presence of intermolecular hydrogen bonding in them: As explained earlier, alcohols can form intermolecular hydrogen bonds due to the presence of the hydroxyl group. These hydrogen bonds are stronger than van der Waals forces and contribute to the higher boiling points of alcohols. Therefore, option b is correct.

c) Increase in the number of carbon atoms: The number of carbon atoms in an alcohol molecule does not directly affect the presence or strength of intermolecular hydrogen bonding. Therefore, option c is incorrect.

Conclusion:
The correct answer is option b, i.e., the high boiling points of alcohols are primarily due to the presence of intermolecular hydrogen bonding. This unique type of bonding results in stronger intermolecular forces, leading to higher boiling points compared to similar compounds that do not exhibit hydrogen bonding.