A compound [A] has the formula `C_(4)H_(8)O_(2)`. When reacted with a Grignard reagent, `CH_(3)MgBr`, it takes up two molecules of it and upon acidification gives an alcohol [B]. The alcohol on reacting with Lucas reagent gives white coludiness on standing for sometime. When the alochol is oxidised, a compound [C] is produced with a pleasant smell. It neither reacts with Tollen's reagent, nor with Fehling's reagent.
The alcohol [B] is

Options

A. a primary alcohol
B. a secondary alcohol
C. a tertiary alcohol
D. cannot be predicted from availabe information.

Explanation

To solve the problem step by step, we will analyze the information given about compound [A] and its reactions.

### Step 1: Identify the structure of compound [A]
The molecular formula of compound [A] is C₄H₈O₂. This indicates that it could be a carboxylic acid or an ester, but since it reacts with a Grignard reagent, it is likely a carboxylic acid or a compound that can form a carboxylic acid upon reaction.

### Step 2: Reaction with Grignard reagent
When compound [A] reacts with the Grignard reagent CH₃MgBr, it takes up two molecules of it. This suggests that compound [A] is likely a carboxylic acid, which can react with Grignard reagents to form a tertiary alcohol. The reaction can be summarized as follows:
- The Grignard reagent attacks the carbonyl carbon of the carboxylic acid, forming a magnesium salt intermediate.
- A second molecule of Grignard reagent reacts with the carbonyl carbon of the resulting ketone, leading to the formation of a tertiary alcohol.

### Step 3: Identify the structure of alcohol [B]
The alcohol [B] formed from the reaction is likely a tertiary alcohol because it is formed from the reaction of a carboxylic acid with two equivalents of Grignard reagent. The structure of alcohol [B] can be represented as:
- A tertiary alcohol with the formula C₄H₉OH.

### Step 4: Reaction with Lucas reagent
The alcohol [B] reacts with Lucas reagent (a solution of zinc chloride in hydrochloric acid) and gives white cloudiness after some time. This indicates that alcohol [B] is a secondary or tertiary alcohol, as Lucas reagent distinguishes between primary, secondary, and tertiary alcohols. Since it gives cloudiness, it suggests that alcohol [B] is indeed a tertiary alcohol.

### Step 5: Oxidation of alcohol [B]
When alcohol [B] is oxidized, it produces compound [C] with a pleasant smell. The pleasant smell suggests that compound [C] is likely an ester or a ketone. Since it does not react with Tollen's reagent or Fehling's reagent, it indicates that compound [C] is not an aldehyde but could be a ketone or an ester.

### Conclusion
Based on the above analysis, the alcohol [B] is a tertiary alcohol formed from the reaction of a carboxylic acid with two equivalents of Grignard reagent.

The final answer is that the alcohol [B] is **2-methyl-2-propanol (tert-butanol)**.