Step 1: Recall restriction sites in pBR322.
The \(\mathrm{amp}^R\) (ampicillin resistance) gene of pBR322 contains the restriction sites
\[
\boxed{\text{Pvu I and Pst I}.}
\]
BamHI and SalI are present elsewhere in the plasmid.
Step 2: Identify the correct combination.
Hence, the restriction sites present in the \(\mathrm{amp}^R\) gene are
\[
\boxed{\text{Pvu I and Pst I}.}
\]
Step 3: Choose the correct option.
Therefore, the correct option is
\[
\boxed{(C).}
\]