`X overset(NH_(3)//Delta)toB underset(Delta)overset(KOBr)to overset(HNO_(2))to(CH_(3))_(3)C-OH,X` is :

Options

A. `(CH_(3))_(3)C-COOH`
B. `(CH_(3))_(3)C-CH_(2)O`
C. `(CH_(3))_(3)C-CONH_(2)`
D. none is true

Answer

To solve the question `X overset(NH_(3)//Delta)toB underset(Delta)overset(KOBr)to overset(HNO_(2))to(CH_(3))_(3)C-OH,X`, we will analyze the sequence of reactions step by step.

### Step 1: Identify the structure of compound B
The first step involves treating compound X with ammonia (NH₃) under heat (Δ). Given that X is a carboxylic acid, we can represent it as:
\[ \text{X} = \text{RCOOH} \]
where R is a hydrocarbon chain. The reaction of a carboxylic acid with ammonia under heat typically leads to the formation of an amide:
\[ \text{RCOOH} + \text{NH}_3 \xrightarrow{\Delta} \text{RCONH}_2 + \text{H}_2\text{O} \]
Thus, compound B will be:
\[ \text{B} = \text{RCONH}_2 \]
This is a primary amide.

### Step 2: Reaction of B with KOBr
Next, compound B (the primary amide) is treated with KOBr (potassium hypobromite). This is known as the Hofmann degradation reaction, which converts primary amides to primary amines:
\[ \text{RCONH}_2 + \text{KOBr} \xrightarrow{\Delta} \text{RNH}_2 + \text{CO}_2 + \text{HBr} \]
Thus, the product after this reaction will be:
\[ \text{C} = \text{RNH}_2 \]
This is a primary amine.

### Step 3: Reaction of C with HNO₂
The primary amine C is then treated with nitrous acid (HNO₂). The reaction of a primary amine with nitrous acid leads to the formation of an alcohol and nitrogen gas:
\[ \text{RNH}_2 + \text{HNO}_2 \rightarrow \text{R-OH} + \text{N}_2 + \text{H}_2\text{O} \]
Thus, the final product after this reaction will be:
\[ \text{(CH}_3)_3\text{C-OH} \]
This indicates that R is a tert-butyl group (C₄H₉).

### Conclusion
From the above steps, we can conclude that compound X is:
\[ \text{X} = \text{(CH}_3)_3\text{C-COOH} \]
This is the carboxylic acid corresponding to the tert-butyl alcohol formed at the end of the reaction sequence.

### Final Answer
X is **tert-butanoic acid** (or 2-methylpropanoic acid).