Electron-donating groups increase the reactivity of benzene rings towards electrophilic substitution
• Reactivity is influenced by the electron density on the benzene ring:
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• Dimethylamine (\(NMe_2\)) and methoxy \((OCH_3)\) are strong electron-donating groups, en hancing reactivity.
• Alkyl groups (CH3) show moderate activating effects, while electron-withdrawing groups like trifluoromethyl (CF3) reduce reactivity.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: