Compound P reacts with 3 equivalents of NH2OH, indicating the presence of 3 carbonyl groups, forming oxime Q.
Excess CH3I with KOH reacts with Q to methylate all hydroxyl groups, resulting in compound R.
Compound R reacts with iso-butylmagnesium bromide (Grignard reagent) to add alkyl groups. Hydrolysis with \( \text{H}_3\text{O}^+ \) yields compound S.
\[ P \xrightarrow{\text{3 NH}_2\text{OH}} Q \xrightarrow{\text{CH}_3\text{I}, \text{KOH}} R \xrightarrow{\text{iso-BuMgBr}, \text{H}_3\text{O}^+} S \]
The structure of compound S contains a total of 12 methyl groups:
Total \( -\text{CH}_3 \) groups in compound S: 12
To solve this problem, we need to identify the structure of the organic compound P and follow its transformations to determine the number of methyl groups in compound S. Here's a breakdown of the analysis and reactions involved:
Conclusion: Each branch from original methoxy and appended iso-butyl raises the methyl group count beyond initial methoxy. Therefore, final computation on such rigorous assumptions stalwartly certifies the applicable number of methyl groups in S as 12.
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is