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A compound [A] with molecular formula C(...

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.

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