The correct geometries for the metal carbonyl clusters, A‐C

A. [Ru6(CO)₁₇B]^-

B. [Os6(CO)₁₈P]^-

C. [Os4(CO)₁₆]

are

Concept - 

• The gemoteries of the organometaalics compound depends on the bonding molecular orbital and bonding molecular orbital can be calculated by calculating cluster electrons 
• Cluster electrons can be calculated as - Valence electron of metal * No. of metal present + Electron donated by ligand * No. of ligands + Electron onated by any atom present 

Explanation - 
For  [Ru6(CO)17B]- = 8*6+2*17+3+1 = 83 

Hence, bonding molecular orbital = 43

Geometery = Octahedral (According to the standard geometery chard given)

 [Os6(CO)18P]-    = 8*6+2*18+5+1 = 90

Hence, Bonding molecular orbital = 45

Geometery = Trigonal BiPrismatic

[Os4(CO)16] = 8*4+2*16 = 64

Bomding molecular orbital = 32

So, Geometry = Square Plannar

Conclusion:-

So, The correct geometries A: octahedral, B: trigonal prismatic, and C: square