\(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) on heating liberates a gas. The same gas will be obtained by (a) Heating \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) (b) Heating \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) (c) Reating \(\mathrm{H}_{2} \mathrm{O}_{2}\) with \(\mathrm{NaNO}_{2}\) (d) Treating \(\mathrm{Mg}_{3} \mathrm{~N}_{2}\) with \(\mathrm{H}_{2} \mathrm{O}\)

Decomposition reactions play a pivotal role in inorganic chemistry. In these reactions, a single compound breaks down into two or more simpler substances when energy is supplied, commonly in the form of heat, light, or electricity. It's a type of chemical reaction represented by the general formula:
\[ AB \xrightarrow{\Delta} A + B \]
Ammonium dichromate \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) serves as a classic example. Upon heating, it decomposes into chromium(III) oxide \(\mathrm{Cr}_{2}\mathrm{O}_{3}\), water \(\mathrm{H}_{2}\mathrm{O}\), and nitrogen gas \(\mathrm{N}_{2}\), demonstrating a typical decomposition reaction in inorganic chemistry. In NEET exams and general studies, understanding these types of reactions assists in predicting the behavior of compounds under various conditions.

Gas evolution reactions are a subset of chemical reactions where a gas is released as a product. These reactions are easy to identify as they often involve bubbling or a change in pressure. An example from our exercise is the reaction of \(\mathrm{H}_{2}\mathrm{O}_{2}\) with \(\mathrm{NaNO}_{2}\), resulting in the liberation of nitrogen gas \(\mathrm{N}_{2}\). Recognizing gas evolution reactions is important because the formation of gases can be used to identify substances or predict reaction outcomes. To excel in NEET chemistry, students should familiarize themselves with common gases that evolve in chemical reactions and the conditions under which these reactions occur.

The skill of balancing chemical equations is fundamental in chemistry. It entails modifying the stoichiometric coefficients of the reactants and products to ensure that the number of atoms for each element is preserved across the reaction. In the given exercise, balancing the reactions was crucial to understanding which gases were formed and in what quantities. For example, the decomposition of \(\mathrm{NH}_{4}\mathrm{NO}_{3}\) forms nitrous oxide and water after balancing:
\[\mathrm{NH}_{4}\mathrm{NO}_{3}\xrightarrow{\Delta} \mathrm{N}_{2}O + 2\mathrm{H}_{2}O\]
While balancing might seem daunting at first, with practice, it becomes second nature. Accurate balancing is critical for NEET exams and will ensure a sound understanding of reaction stoichiometry.

Understanding the chemical properties of compounds is integral for mastering inorganic chemistry. Chemical properties describe the behavior of a substance when it undergoes a chemical change. For instance, ammonium dichromate is known for its ability to decompose and release nitrogen gas upon heating, a chemical property utilized in various chemical reactions and preparations. Similarly, recognizing that magnesium nitride reacts with water to produce magnesium hydroxide and nitrogen gas helps chemists foresee reaction outcomes and design routes for chemical synthesis. Learning about these properties not only boosts preparation for competitive exams like the NEET but also lays the groundwork for practical laboratory skills in chemistry.