Fajan's rules state that covalent character in an ionic compound increases when: (i) the cation is small and highly charged (high charge density), and (ii) the anion is large and highly polarisable. Polarisation occurs when the cation distorts the electron cloud of the anion towards itself, creating partial covalent character. AgI maximises both factors: Ag^+ is a small cation with a pseudo-noble gas configuration (18-electron configuration) that polarises anions far more effectively than K^+ (noble gas configuration, 18 electrons in the penultimate shell), and I^- is the largest and most polarisable halide ion. Comparing all four options: KF has a large K^+ with a noble gas configuration and small, low-polarisability F^-; this is the most ionic. KI has large K^+ but large I^-; more covalent than KF but Ag^+ is a far better polariser than K^+. AgF has Ag^+ (good polariser) but F^- is too small and hard to polarise. AgI combines the most polarising cation (Ag^+) with the most polarisable anion (I^-), giving maximum covalent character. This is a core NCERT JEE concept under chemical bonding. Plausibility check: AgI is indeed known to be less soluble and show more covalent behaviour (e.g., it is soluble in thiosulfate but not water), while AgF is more ionic and soluble in water, confirming the predicted trend.