X is the number of geometrical isomers exhibited by [ Pt ( NH ₃ ) ( H ₂ O ) BrCl ] . Y is the number of optically inactive isomer(s) exhibited by [ CrCl ₂( ox )₂ ]³⁻ Z is the number of geometrical isomers exhibited by [ Co ( NH ₃ )₃ ( NO ₂ )₃ ] . The value of X + Y + Z is _ _ _ _ .

Step-by-step solution

For [Pt(NH₃)(H₂O)BrCl] with square planar geometry and four different ligands, geometrical isomerism arises from different positional arrangements: X = 3. For [CrCl₂(ox)₂]³⁻ , the trans isomer is optically inactive (meso compound) while cis is optically active, giving Y = 1. For [Co(NH₃)₃(NO₂)₃] in octahedral geometry, facial (fac) and meridional (mer) isomers are possible: Z = 2. Therefore, X + Y + Z = 3 + 1 + 2 = 6