




Step 1: The reaction involves the oxidation of toluene with \(\text{CrO}_2\text{Cl}_2\) and \(\text{CS}_2\). \(\text{CrO}_2\text{Cl}_2\) is a strong oxidizing agent, typically oxidizing the methyl group (\(\text{-CH}_3\)) in toluene to a carboxylic acid (\(\text{COOH}\)) group. This results in a formyl group (\(\text{CHO}\)) being left behind in residue (A), as toluene is partially oxidized.
Step 2: The treatment with water and NaHSO\(_3\) ensures further oxidation of the formyl group (\(\text{CHO}\)) into a carboxyl group (\(\text{COOH}\)). Diluting with HCl gives a sodium salt of the carboxyl group (\(\text{COONa}\)) in compound (B).
Thus, the structures of residue (A) and compound (B) are as follows: Residue (A) has a formyl group (\(\text{CHO}\)) and compound (B) has a carboxylate group (\(\text{COONa}\)).
Match the following:

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: