Concept: Coordination chemistry (geometry, magnetism, oxidation state)
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Step 1: Oxidation state of Co
• In both complexes:
\[
x + (-6) = -3 \Rightarrow x = +3
\]
• So Co is +3 in both
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Step 2: Geometry
• Both are octahedral complexes
✔ Statement (I) is TRUE
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Step 3: Magnetic behavior
• [CoF$_6$]$^{3-}$ → weak field ligand → high spin → paramagnetic
• [Co(C$_2$O$_4$)$_3$]$^{3-}$ → stronger field → low spin → diamagnetic
✔ Statement (II) is TRUE
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Step 4: Orbital type
• F$^-$ → outer orbital complex
• Oxalate → inner orbital complex
❌ Statement (III) is FALSE
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Step 5: Oxidation state comparison
✔ Same in both → TRUE
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Final Answer:
\[
\boxed{(III)\text{ is false}}
\Rightarrow \boxed{(A)}
\]