Statement (I): This statement is incorrect. Dimethyl glyoxime forms a square planar complex with nickel, not a six-membered covalent chelate, when treated with NiCl$_2$ solution in the presence of NH$_4$OH. The resulting complex, known as a nickel-dimethylglyoxime complex, is characterized by a square planar structure where the nickel is coordinated by the nitrogen and oxygen atoms of two glyoxime molecules.
Statement (II): This statement is true. Prussian blue (Fe$_4$[Fe(CN)$_6$]$_3$) is a coordination compound containing iron in both +2 and +3 oxidation states. The compound forms due to the combination of Fe$^{3+}$ ions and [Fe(CN)$_6$]$^{4-}$ complex ions, leading to a structure with mixed oxidation states of iron.
Conclusion: Statement I is false, and Statement II is true.
Given below are two statements:
Statement I: A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism
Statement II: cis- and trans-platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer from the options given below
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: