The product of the given reaction ,
`CH_3 - underset( OH )underset( |) overset(| ) overset( CH_3 ) overset(|) C-underset(NH_2 ) underset(|) overset(CH_(3) ) overset( |) C -CH_(3) overset( HNO_2 ) to ` Product is :

Options

A. `CH_(3) - underset(OH) underset( |) overset( CH_3)overset(|)C-underset(OH)underset(|) overset(CH_3)overset(|)C-CH_3`
B. `CH_(3) - overset(O) overset(||) C- underset(CH_3) underset(|) overset( CH_3) overset( |) C- CH_3`
C. `CH_(3) - underset( OH) underset( |) overset(CH_3) overset(|)C- underset(CH_3 )underset(|) CH-CH_3`
D. `CH_3 - underset(CH_3) underset(|)C=underset(CH_3 ) underset(|)C-CH_3`

Answer

To solve the problem, we will analyze the reaction of the given compound with HNO2 step by step.

### Step 1: Identify the Reactants
The reactant is a compound with both an alcohol (OH) and an amino group (NH2). The structure can be represented as:
\[ CH_3 - C(OH)(NH_2) - C(CH_3)(CH_3) \]

### Step 2: Reaction with HNO2
When HNO2 (Nitrous acid) is introduced, it reacts with the amino group (NH2). This reaction is characteristic of primary amines, leading to the formation of a diazonium ion.

### Step 3: Mechanism of Reaction
1. **Formation of Diazonium Ion**:
- The NH2 group reacts with HNO2, which can be represented as HONO.
- The nitrogen in NH2 acts as a nucleophile and attacks the electrophilic nitrous acid, leading to the formation of a diazonium ion.

2. **Formation of Carbocation**:
- The diazonium ion is unstable due to the presence of alkyl groups, which leads to the loss of nitrogen gas (N2) and the formation of a carbocation.

### Step 4: Rearrangement of Carbocation
- The carbocation formed is subject to rearrangement to form a more stable carbocation. In this case, a methyl shift occurs, where a methyl group from one carbon moves to the adjacent carbon, stabilizing the positive charge.

### Step 5: Nucleophilic Attack by Water
- Water, acting as a nucleophile, attacks the carbocation, leading to the formation of a geminal diol (a compound with two hydroxyl groups on the same carbon).

### Step 6: Dehydration to Form Ketone
- The geminal diol is unstable and can lose a molecule of water, resulting in the formation of a ketone.

### Final Product
The final product after the reaction with HNO2 and subsequent rearrangements and dehydration is:
\[ CH_3 - C(=O) - C(CH_3)(CH_3) \]
This is a ketone.

### Conclusion
The correct answer for the product of the reaction is a ketone derived from the original compound.

---