




The given sequence involves the following steps:
Step 1: Friedel-Crafts Acylation
Benzene (\(\text{C}_6\text{H}_6\)) reacts with acetyl chloride (\(\text{CH}_3\text{COCl}\)) in the presence of \(\text{AlCl}_3\), an electrophilic catalyst. This forms acetophenone (\(\text{C}_6\text{H}_5\text{COCH}_3\)) as compound \(A\):
\[\text{C}_6\text{H}_6 + \text{CH}_3\text{COCl} \xrightarrow[\text{AlCl}_3]{} \text{C}_6\text{H}_5\text{COCH}_3 \, (A).\]
Step 2: Clemmensen Reduction
Acetophenone (\(\text{C}_6\text{H}_5\text{COCH}_3\)) undergoes Clemmensen reduction using zinc amalgam (\(\text{Zn–Hg}\)) and hydrochloric acid (\(\text{HCl}\)). The carbonyl group (\(-\text{CO}\)) is reduced to a methylene group (\(-\text{CH}_2-\)), resulting in ethylbenzene (\(\text{C}_6\text{H}_5\text{CH}_2\text{CH}_3\)) as compound \(B\):
\[\text{C}_6\text{H}_5\text{COCH}_3 \xrightarrow[\text{Zn–Hg, HCl}]{} \text{C}_6\text{H}_5\text{CH}_2\text{CH}_3 \, (B).\]
Step 3: Acidic Oxidation
Ethylbenzene reacts with \(\text{H}^+\) under oxidation conditions to form acetophenone again. This completes the reaction cycle.
Final Products:
\(A = \text{C}_6\text{H}_5\text{COCH}_3\) (Acetophenone).
\(B = \text{C}_6\text{H}_5\text{CH}_2\text{CH}_3\) (Ethylbenzene).
Conclusion: The correct identification of \(A\) and \(B\) is given in option \((3)\).
Final Answer: (3).
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.