In amines, the nitrogen atom is A and B hybridized, making geometry of amines as C. Then A, B and C respectively are:

trivalent, \(sp^3\), pyramidal

The correct answer is option 3. trivalent, \(sp^3\), pyramidal.

Let us break down the conditions:

1. Trivalent Nitrogen: In amines, the central nitrogen atom is bonded to three other atoms or groups (usually carbon or hydrogen), which means it forms three bonds. Hence, it's trivalent.

2. \(sp^3\) Hybridized: Nitrogen in amines undergoes hybridization to form its bonding orbitals. In the case of \(sp^3\) hybridization, one \(s\) orbital and three \(p\) orbitals mix together to form four equivalent hybrid orbitals. These orbitals are then used for bonding with other atoms.

3. Pyramidal Geometry: Due to the lone pair of electrons on the nitrogen atom, there are four regions of electron density around the nitrogen atom (three bonding pairs and one lone pair). This results in a trigonal pyramidal geometry. The lone pair occupies more space than the bonding pairs, causing the bonded atoms to be pushed closer together, giving the molecule a pyramidal shape.

So, in summary, amines have trivalent nitrogen atoms that are \(sp^3\) hybridized, resulting in a pyramidal geometry.