The correct order of activating influence of the following groups when attached to benzene ring is (a) \(-\mathrm{O}^{-}>-\mathrm{OCOCH}_{3}>-\mathrm{OH}>-\mathrm{COCH}_{3}\) (b) \(-\mathrm{O}^{-}>-\mathrm{OH}>-\mathrm{OCOCH}_{3}>-\mathrm{COCH}_{3}\) (c) \(-\mathrm{OH}>-\mathrm{O}^{-}>-\mathrm{OCOCH}_{3}>-\mathrm{COCH}_{3}\) (d) \(-\mathrm{OH}>-\mathrm{OCOCH}_{3}>-\mathrm{O}^{-}>-\mathrm{COCH}_{3}\)

We need to determine the order of activating influence for the following groups when attached to a benzene ring: 1. \(-\mathrm{O}^{-}\) 2. \(-\mathrm{OCOCH}_{3}\) 3. \(-\mathrm{OH}\) 4. \(-\mathrm{COCH}_{3}\)

Consider each group and determine its electron-donating properties: 1. \(-\mathrm{O}^{-}\): This group has a negatively charged oxygen atom that can donate a pair of electrons through resonance, making this group a strong electron-donating group. 2. \(-\mathrm{OCOCH}_{3}\): This group has an oxygen atom which can donate a pair of electrons through resonance, however, its electron-donating ability is somewhat weakened due to the presence of the carbonyl group. 3. \(-\mathrm{OH}\): This group can donate a pair of electrons through resonance, making it an electron-donating group. However, since the oxygen atom is not negatively charged, it is a weaker electron-donor compared to \(-\mathrm{O}^{-}\). 4. \(-\mathrm{COCH}_{3}\): This group has a carbonyl group which is electron-withdrawing in nature due to the double bond with the oxygen atom. Thus, it is a weak electron-donating group.

Based on the electron-donating properties of each group, list them in descending order: 1. \(-\mathrm{O}^{-}\) (strongest electron-donating) 2. \(-\mathrm{OH}\) 3. \(-\mathrm{OCOCH}_{3}\) 4. \(-\mathrm{COCH}_{3}\) (weakest electron-donating) This order matches the order given in option: (b) \(-\mathrm{O}^{-}>-\mathrm{OH}>-\mathrm{OCOCH}_{3}>-\mathrm{COCH}_{3}\) Therefore, the correct order of activating influence is as given in option (b).