Concept:
In the Survey of India indexing system, Inch Sheet topographical maps are designated using a sheet number followed by a quadrant such as NE, NW, SE, or SW.
Step 1: Identify the inch-sheet notation.
\[
\boxed{72\ \mathrm{F/NE}}
\]
Step 2: Eliminate the incorrect options.
\[
\begin{aligned}
A. &\ 72 \rightarrow \text{Only a sheet number.}
B. &\ 72\ \mathrm{F} \rightarrow \text{One-degree sheet.}
C. &\ 72\ \mathrm{F/NE} \rightarrow \text{Correct inch-sheet designation.}\checkmark
D. &\ 72\ \mathrm{F/10} \rightarrow \text{Metric-sheet notation.}
\end{aligned}
\]
Hence,
\[
\boxed{\text{(C)}}
\]