What is the formula of carboxylic acid and ketones???

Dear student,

Carboxylic acid and ketones both are functional groups. 
The formula of a carboxylic acid is -COOH. It has one free valency.
-C-O-H      O - Carboxylic acid

The formula of the ketone is -CO-. It has two free valencies.
-C-      O  - Ketone

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