Step 1: Understand the properties and uses of different allotropes of carbon.
Step 2: Match each allotrope with its primary application.
\begin{itemize}
\item A. Carbon black: A fine powder used extensively as a filler in automobile tyres (IV) to enhance strength and durability.
\item B. Graphite: A good conductor of electricity and has a layered structure making it suitable for electrodes in batteries (I).
\item C. Diamond: The hardest known natural material, making it ideal as an abrasive (III) for cutting and grinding.
\item D. Activated charcoal: Highly porous with a large surface area, used for adsorption in air conditioning systems (V) and filters to remove impurities and odors.
\end{itemize}
Step 3: Combine the matches to find the correct option.
The correct matching is A - IV, B - I, C - III, D - V.
Final Answer: The final answer is $\boxed{A - IV, B - I, C - III, D - V}$