To solve the question regarding which statements are correct, we will analyze each statement one by one.
### Step-by-Step Solution:
**Statement I:** The ligand thiosulphate, \( S_2O_3^{2-} \), can give rise to linkage isomers.
- **Analysis:** Linkage isomers occur when a ligand can coordinate to a metal through different atoms. The thiosulphate ion can coordinate through either the sulfur or one of the oxygen atoms. Therefore, it can indeed form linkage isomers.
- **Conclusion:** This statement is **correct**.
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**Statement II:** In metallic carbonyls, the ligand CO molecule acts both as donor and acceptor.
- **Analysis:** In metal carbonyls, carbon monoxide (CO) acts as a Lewis base by donating a pair of electrons from the carbon atom to the metal center. Additionally, the metal can back-donate electrons into the empty π* orbitals of CO, making CO act as a Lewis acid as well.
- **Conclusion:** This statement is **correct**.
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**Statement III:** The complex \([Pt(Py)(NH_3)(NO_2)ClBr]\) exists in eight different geometrical isomeric forms.
- **Analysis:** The complex has four different ligands, which can lead to geometrical isomerism. However, for coordination complexes of the type \( MA_4B_2 \) (where M is the metal and A and B are different types of ligands), the maximum number of geometrical isomers is typically less than eight. In this case, it can form only three distinct geometrical isomers due to the arrangement of the ligands.
- **Conclusion:** This statement is **incorrect**.
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**Statement IV:** The complex ferricyanide ion does not follow the effective atomic number (EAN) rule.
- **Analysis:** The effective atomic number rule states that the total number of valence electrons around the metal should be 18 or a multiple of 18 for stability. For ferricyanide, \( [Fe(CN)_6]^{3-} \), iron in the +3 oxidation state contributes 23 electrons (3d^5 configuration). Each cyanide ion contributes 2 electrons, giving a total of 12 from 6 cyanides. Thus, \( 23 + 12 = 35 \), which does not equal 36 or a multiple of 18.
- **Conclusion:** This statement is **correct**.
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### Final Conclusion:
The correct statements are **I, II, and IV**.
### Summary of Correct Statements:
- **I:** Correct
- **II:** Correct
- **III:** Incorrect
- **IV:** Correct
Thus, the final answer is that statements I, II, and IV are correct.
