Formula-derivation approach: Methane, ethane, propane and butane are the first four members of the alkane (paraffin) homologous series, which follows the general formula \( \mathrm{C_{n}H_{2n+2}} \).
For \( n = 1 \): \( \mathrm{CH_{4}} \) (methane). For \( n = 2 \): \( \mathrm{C_{2}H_{6}} \) (ethane). For \( n = 3 \): \( \mathrm{C_{3}H_{8}} \) (propane). For \( n = 4 \): \( \mathrm{C_{4}H_{10}} \) (butane).
Deriving each formula from the general series and matching it to the corresponding compound name, rather than recalling the formulas individually, gives the same correspondence as option (A)-(II), (B)-(IV), (C)-(I), (D)-(III).