The functional group $>\!\mathrm{C}\!=\!\mathrm{O}$ that is common to aldehydes, ketones, carboxylic acids and their derivatives is called:

$>\!\mathrm{C}\!=\!\mathrm{O}$ is the **carbonyl** group — a $C$ doubly bonded to $O$. The **carboxyl** group is $-\mathrm{COOH}$ (carbonyl + hydroxyl together — that's option B). The hydroxyl is $-\mathrm{OH}$ alone (alcohols, phenols). Alkoxy is $-\mathrm{OR}$ (ethers).