\(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO} \underset{(\mathrm{HCl})}{\stackrel{\mathrm{NaCN}}{\longrightarrow} \mathrm{A}} \stackrel{\mathrm{H}_{3} \mathrm{O}+}{\longrightarrow} \mathrm{B}\) in the above sequence of reactions \(\mathrm{A}\) and \(\mathrm{B}\) are (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH}) \mathrm{CN},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCOOH}\) (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH}) \mathrm{CN},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH})_{2}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH}) \mathrm{CN},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH}) \mathrm{COOH}\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}(\mathrm{OH}) \mathrm{CN},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O}\)

Organic chemistry is a profound and essential branch of chemistry focusing on the study of the structure, properties, and reactions of organic compounds. These are compounds that contain carbon atoms bonded to hydrogen atoms and often include other elements like oxygen, nitrogen, and chlorine. The behavior and transformations of these compounds are often determined by the functional groups they contain.

For example, in the exercise provided, acetone ((CH_{3})_{2}CO) is an organic compound with a carbonyl group — a functional group characterized by a carbon atom double-bonded to an oxygen atom. This functional group plays a pivotal role in the nucleophilic addition reaction, which is a type of reaction where a nucleophile, such as cyanide (CN-), donates an electron pair to an electrophilic carbon atom in the carbonyl group, forming a new covalent bond.

Understanding the nuances of different functional groups and their reactivities is fundamental for students of organic chemistry as it allows them to predict and explain the behavior of organic molecules under various conditions, and is crucial for solving problems efficiently.

A reaction mechanism describes the step-by-step sequence by which reactants transform into products at the molecular level. These detailed descriptions include bond-making and bond-breaking processes, the movement of electrons, the intermediate stages, and the energy changes throughout the reaction.

In the context of the given exercise, the mechanism of the nucleophilic addition reaction involves several key steps. First, cyanide ion (CN-), the nucleophile, attacks the electrophilic carbon of the carbonyl group in acetone. The carbon's partial positive charge attracts the nucleophile's lone pair of electrons, forming a single bond — this is the addition phase of the reaction. As a result, the oxygen from the carbonyl group takes up the electrons from the double bond, becoming an alkoxide ion. Subsequent protonation by an acid, in this case, hydrogen ion (H3O+), leads to a molecule of hydroxycyanohydrin ((CH_{3})_{2}C(OH)CN), which is compound A in the exercise.

Additionally, an acid-catalyzed hydration occurs when compound A is treated with an acid, leading to the hydrolysis of the cyanide group and formation of the carboxylic acid group, resulting in compound B ((CH_{3})_{2}C(OH)COOH). The ability to follow and understand these reaction mechanisms equips students with crucial problem-solving skills in organic chemistry.

The National Eligibility cum Entrance Test (NEET) is a significant pre-medical examination in India for students who wish to pursue undergraduate medical courses. Chemistry, being one of the primary subjects in the NEET syllabus, requires a deep understanding of both organic and inorganic chemistry.

For NEET Chemistry preparation, mastering reaction mechanisms like nucleophilic addition reactions is essential. A solid grasp of such reactions aids in solving complex reaction sequence problems, which are a common occurrence in the NEET chemistry section. High-yield topics like isomerism, nomenclature, biomolecules, and reaction mechanisms should be at the forefront of students' preparation strategies.

Students should focus on conceptual clarity and problem-solving skills by practicing through similar exercises, understanding step-by-step solutions, and enhancing their knowledge with supportive articles and materials. Regular revisions, taking mock tests, and solving previous years' NEET papers are encouraged to familiarize oneself with the exam pattern and the type of questions asked. Efficient preparation will invariably consist of integrating theoretical knowledge with practical applications to answer the questions skillfully within the given time frame.