The problem asks to identify the correct statements from a list of five related to coordination chemistry and metallurgy and then select the option that contains all the correct statements.
The solution requires knowledge from different areas of chemistry:
We will evaluate each statement individually.
(A) Ethane-1,2-diamine is a chelating ligand.
Ethane-1,2-diamine, commonly known as ethylenediamine (en), has the structure \(H_2N-CH_2-CH_2-NH_2\). It possesses two nitrogen atoms, each with a lone pair of electrons, making it a bidentate ligand. When it coordinates to a single central metal ion, it forms a stable five-membered ring structure. A ligand that can bind to a central metal ion through two or more donor atoms to form a ring is called a chelating ligand. Therefore, this statement is correct.
(B) Metallic aluminium is produced by electrolysis of aluminium oxide in presence of cryolite.
This statement describes the Hall-Héroult process for the industrial extraction of aluminium. Aluminium oxide (\(Al_2O_3\)) has a very high melting point (over 2000°C). To make its electrolysis economically feasible, it is dissolved in molten cryolite (\(Na_3AlF_6\)). Cryolite acts as a solvent, lowering the melting point of the mixture to around 950-1000°C and also increasing its electrical conductivity. The subsequent electrolysis of this molten mixture yields metallic aluminium at the cathode. Therefore, this statement is correct.
(C) Cyanide ion is used as ligand for leaching of silver.
This refers to the cyanide process (or MacArthur-Forrest process) for extracting silver and gold. In this hydrometallurgical process, the crushed ore is treated with a dilute solution of sodium cyanide (\(NaCN\)). The silver present in the ore reacts with the cyanide ions (\(CN^-\)) in the presence of oxygen from the air to form a soluble complex, \( [Ag(CN)_2]^- \). The cyanide ion acts as a ligand, complexing with the silver ion and bringing it into the solution, which is known as leaching. Therefore, this statement is correct.
(D) Phosphine act as a ligand in Wilkinson catalyst.
Wilkinson's catalyst is a coordination complex of rhodium with the chemical formula \( [RhCl(P(C_6H_5)_3)_3] \), which is chloridotris(triphenylphosphine)rhodium(I). The ligand in this catalyst is triphenylphosphine (\(PPh_3\)), not phosphine (\(PH_3\)). Although phosphine can act as a ligand, it is not the ligand present in Wilkinson's catalyst. Therefore, this statement is incorrect.
(E) The stability constants of \(Ca^{2+}\) and \(Mg^{2+}\) are similar with EDTA complexes.
EDTA (ethylenediaminetetraacetic acid) is a hexadentate ligand that forms very stable complexes with most metal ions, including \(Ca^{2+}\) and \(Mg^{2+}\). However, the stability of these complexes is not similar. The stability constant depends on factors like the size and charge density of the metal ion. The complex formed with \(Ca^{2+}\) is significantly more stable than the one formed with \(Mg^{2+}\). The log of the stability constant (\(\log K_f\)) for \([Ca(EDTA)]^{2-}\) is about 10.7, while for \([Mg(EDTA)]^{2-}\) it is about 8.7. A difference of 2 in the log values means the stability constants differ by a factor of 100. This difference is the basis for the selective titration of \(Ca^{2+}\) and \(Mg^{2+}\) in water hardness analysis. Therefore, this statement is incorrect.
The correct statements are (A), (B), and (C).
We now choose the option from the list that includes exactly these statements.
The correct answer is (3) (A), (B), (C) only.

Let \( C_{t-1} = 28, C_t = 56 \) and \( C_{t+1} = 70 \). Let \( A(4 \cos t, 4 \sin t), B(2 \sin t, -2 \cos t) \text{ and } C(3r - n_1, r^2 - n - 1) \) be the vertices of a triangle ABC, where \( t \) is a parameter. If \( (3x - 1)^2 + (3y)^2 = \alpha \) is the locus of the centroid of triangle ABC, then \( \alpha \) equals: