Step 1: Understanding the Concept:
This question evaluates multiple concepts in coordination chemistry, including complex stability (chelate effect), hybridization (VBT/CFT), and types of isomerism/ligands.
Step 2: Detailed Explanation:
Statement A: Oxalate ($C_2O_4^{2-}$) is a chelating ligand, whereas $OH^-$ and $SCN^-$ are monodentate. Chelating complexes are significantly more stable than non-chelating ones due to the chelate effect. Thus, A is True.
Statement B: 'en' (ethylenediamine) is a bidentate chelating ligand, while $NH_3$ is monodentate. According to the chelate effect, $[Cu(en)_2]^{2+}$ is more stable than $[Cu(NH_3)_4]^{2+}$. Thus, B is False.
Statement C: In $K_4[Fe(CN)_6]$, iron is in the $+2$ oxidation state ($d^6$). $CN^-$ is a strong field ligand, causing electrons to pair up in the $t_{2g}$ orbitals. This leaves two empty $3d$ orbitals for hybridization. Thus, it undergoes $d^2sp^3$ hybridization. Thus, C is True.
Statement D: $NO_2^-$ is an ambidentate ligand (it can bind through N or O). Any complex containing an ambidentate ligand can exhibit linkage isomerism. Thus, D is True.
Statement E: $NO_2^-$ and $SCN^-$ are classic examples of ambidentate ligands because they have more than one potential donor atom. Thus, E is False.
Step 3: Final Answer:
Statements A, C, and D are correct.
Find the area of the region \[ R = \{(x, y) : xy \le 27,\; 1 \le y \le x^2 \}. \]
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______
