A compound [A] with molecular formula `C_(5)H_(10)O` gave a positive `2,4`-D.N.P. Test but a negtive Tollen's test. It was oxidised to carboxylic acid [B] with molecular formula `C_(3)H_(6)O_(2)` when treated with alkaline `KMnO_(4)` under vigorous conditions. Sodium salt of [B] gave a hydrocarbon [C] on Kolbe's electrolyte reaction. Identify [A],[B] and [C] and write the chemical equations for the reactions.

Explanation

To solve the problem step by step, we will identify the compounds [A], [B], and [C] based on the information given in the question.

### Step 1: Identify Compound [A]
- The molecular formula of compound [A] is \( C_5H_{10}O \).
- It gives a positive 2,4-DNP test, which indicates that it contains a carbonyl group (either an aldehyde or a ketone).
- It gives a negative Tollen's test, which indicates that it is not an aldehyde (as aldehydes give a positive Tollen's test).
- Therefore, compound [A] must be a ketone.

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