The correct order of increasing intermolecular hydrogen bond strength is

The strength of a hydrogen bond depends on the electronegativity of the atoms involved (typically $$N$$, $$O$$, or $$F)$$.

• $$CH_{4}$$ (Methane): Carbon is not electronegative enough to form hydrogen bonds. It only exhibits weak London dispersion forces. Therefore, it has the lowest strength (zero).
• $$HCN$$ (Hydrogen Cyanide): While it contains Nitrogen, the hydrogen is bonded to Carbon. $$HCN$$ can form very weak hydrogen bonds, but it primarily interacts through dipole-dipole forces.
• $$NH_{3}$$ (Ammonia): Hydrogen is directly bonded to a highly electronegative Nitrogen atom with a lone pair. This allows for significant intermolecular hydrogen bonding, making it the strongest in this list.

Hence, Option C is correct