The correct statement(s) about the following reaction sequence is (are)
Cumene `(C_(9)H_(12))underset((ii)H_(3)O^(+))overset((i)O_(2))rarrPoverset(CHCl_(3)//NaOH)rarr`
Q(major)+R(minor), `Q underset(PhCH_(2)Br)overset(NaOH)rarrS`

Options

A. R is steam volatile
B. Q gives dark violet coloration with `1%` aqueous `FeCl_(3)` solution
C. S gives yellow precipitate with 2,4-dinitrophenyhydrazine
D. S gives dark violet coloration with `1%` aqueous `FeCl_(3)` solution

Answer

To analyze the reaction sequence involving cumene and identify the correct statements, we will break down the steps involved in the reactions and the products formed.

### Step-by-Step Solution:

1. **Identify Cumene Structure**:
- Cumene is isopropyl benzene, with the molecular formula \(C_9H_{12}\). Its structure can be represented as:
\[ \text{C}_6\text{H}_5\text{C}(\text{CH}_3)_2 \]

2. **Reaction with Oxygen**:
- When cumene is treated with oxygen (\(O_2\)), it undergoes oxidation. This reaction typically leads to the formation of hydroperoxide intermediates.

3. **Hydrolysis of the Hydroperoxide**:
- The hydroperoxide formed from the oxidation of cumene is then treated with \(H_3O^+\) (acidic hydrolysis). This step cleaves the hydroperoxide, resulting in the formation of phenol and acetone:
\[ \text{Cumene} + O_2 \xrightarrow{H_3O^+} \text{Phenol (P)} + \text{Acetone} \]

4. **Riemann-Tiemann Reaction**:
- The phenol (P) is then treated with chloroform (\(CHCl_3\)) and sodium hydroxide (\(NaOH\)). This is a Riemann-Tiemann reaction, which generates a carbene intermediate. The reaction leads to the formation of two products: one is the major product (Q) and the other is the minor product (R).
- The major product (Q) is typically the ortho-substituted product due to the activating nature of the phenolic group, while the minor product (R) is the para-substituted product.

5. **Formation of Products Q and R**:
- The major product (Q) is salicylaldehyde (ortho-hydroxybenzaldehyde), and the minor product (R) is the para-hydroxybenzaldehyde.

6. **Further Reaction of Q**:
- The major product Q (salicylaldehyde) is then treated with benzyl bromide (\(PhCH_2Br\)) and sodium hydroxide (\(NaOH\)). This reaction is a Williamson ether synthesis, leading to the formation of compound S:
\[ Q + PhCH_2Br \xrightarrow{NaOH} S \]

### Summary of Products:
- **P**: Phenol + Acetone
- **Q**: Salicylaldehyde (major product)
- **R**: Para-hydroxybenzaldehyde (minor product)
- **S**: Benzyl salicylate or similar ether product.

### Correct Statements:
1. **R is steam volatile**: This statement is incorrect because R, being a phenolic compound, exhibits strong intermolecular hydrogen bonding, which increases its boiling point and decreases its volatility.
2. **Q gives dark violet coloration with FeCl3**: This statement is correct because salicylaldehyde contains a phenolic group that forms a complex with FeCl3, resulting in a violet color.
3. **S gives yellow precipitation with 2,4-dinitrophenylhydrazine**: This statement is correct because S contains a carbonyl group, which reacts with 2,4-DNP to form a yellow precipitate.
4. **S gives violet coloration with 1% ferric chloride**: This statement is incorrect because S does not contain a phenolic group and thus cannot react with FeCl3 to give a violet color.

### Final Answer:
The correct statements are **B and C**.