To determine where hyperconjugation occurs, we need to analyze each compound.$\\$Hyperconjugation involves the delocalization of electrons from a $\sigma$-bond (usually C-H) to an adjacent empty or partially filled p-orbital or $\pi$-orbital.$\\$Let's examine each compound:$\\$• Compound (I):$\\$This is a tertiary carbocation with a benzene ring. The presence of C-H bonds adjacent to the carbocation allows hyperconjugation.$\\$• Compound (II):$\\$This is a triphenylmethyl radical. The radical is stabilized by resonance with the phenyl groups, not by hyperconjugation.$\\$• Compound (III):$\\$This is a cyclohexyl radical with a methyl group. The C-H bonds adjacent to the radical can participate in hyperconjugation.$\\$Therefore, hyperconjugation occurs in compounds (I) and (III).$\\$The correct answer is Option 3: I and III. However, the provided correct option is 2, indicating a possible error in the question or options.$\\$