Formula of ferrocene is: (a) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\) (b) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3+}\) (c) \(\left[\mathrm{Fe}(\mathrm{CO})_{5}\right]\) (d) \(\left[\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2} \mathrm{Fe}\right]\)

Inorganic chemistry is a field of chemistry that deals with the synthesis, structure, and properties of all chemical compounds except the myriad organic compounds (carbon-based compounds, usually containing C-H bonds). One of the fascinating aspects of inorganic chemistry is the study of coordination compounds, which include complex molecules like ferrocene. Unlike organic compounds, which mostly involve carbon and hydrogen, inorganic compounds encompass the rest of the periodic table, creating a vast array of structures and applications.

When studying inorganic chemistry, students may encounter chemical formulas such as those presented in the exercise for ferrocene. Recognizing the structure of inorganic compounds, like ferrocene, is vital. This involves understanding that ferrocene is made of an iron atom bonded to two cyclopentadienyl rings, a classic example of organometallic chemistry, a subfield of inorganic chemistry where metals form direct bonds with carbon atoms in organic ligands.

Coordination compounds, such as ferrocene, are a class of compounds in which a central metal atom is surrounded by non-metal atoms or groups of atoms, known as ligands. The metal and its surrounding ligands are held together by coordinate covalent bonds.

In the case of ferrocene, the central metal atom is iron (Fe), and the ligands are cyclopentadienyl anions. Each ligand forms a 'sandwich' like structure, creating a unique stability attributed to the overlapping of p-orbitals in the cyclopentadienyl anions and the d-orbitals in the iron atom. This overlapping results in what is known as 'aromatic stabilization' which is a crucial concept when understanding why ferrocene is remarkably stable.

Therefore, when analyzing the given options in the exercise, the structure of coordination compounds must be properly understood to identify ferrocene correctly. Options (a) and (b) demonstrate typical coordination geometry called octahedral, found in the hexacyanoferrate ions, and are not descriptive of ferrocene's sandwich structure.

NEET Chemistry encompasses both inorganic and organic chemistry, and is crucial for students preparing for the National Eligibility cum Entrance Test (NEET), which is an entrance exam for students who wish to study graduate medical courses in India. It requires a deep understanding of various concepts, including coordination compounds like ferrocene.

As a key topic, understanding of the structure and composition of coordination compounds is essential for NEET aspirants. A typical exercise question, such as determining the chemical formula of ferrocene, ensures students are familiar with the characteristics of metal-organic frameworks and inorganic ligand systems. The right approach to solving these questions involves a combination of memorization and understanding of fundamental concepts, as seen in the step-by-step solution provided.

Preparing for NEET Chemistry demands attention to detail, and exercises like identifying ferrocene's formula serve as an excellent practice to hone students' skills in discerning complex structures and applying inorganic chemistry principles.