The complex $[Pt(Py)(NH_3)BrCl]$ is a square planar complex of the type $[Mabcd]$, where the central metal ion (Pt) is coordinated to four different monodentate ligands (Py, $NH_3$, Br, Cl).

According to coordination chemistry principles found in NCERT:

1. Geometry: Platinum(II) forms square planar complexes.
2. Isomerism: For a square planar complex of the type $[Mabcd]$, there are 3 possible geometrical isomers. These are obtained by fixing the position of one ligand (say, Py) and placing the other three ligands ($NH_3$, Br, Cl) trans (opposite) to it sequentially. Isomer 1: Py is trans to $NH_3$. Isomer 2: Py is trans to Br.

• Isomer 3: Py is trans to Cl.

Therefore, the number of geometrical isomers is 3 .