Step 1: Understand ambidentate ligands.
Ambidentate ligands are ligands that can coordinate through two different donor atoms, but only one donor atom at a time.
Step 2: Identify ambidentate ligands.
\[
NO_2^-
\]
can coordinate through:
\[
N \quad \text{or} \quad O
\]
\[
CN^-
\]
can coordinate through:
\[
C \quad \text{or} \quad N
\]
\[
SCN^-
\]
can coordinate through:
\[
S \quad \text{or} \quad N
\]
Thus, all three are ambidentate ligands.
Step 3: Check remaining ligands.
\[
Br^-
\]
is monodentate only.
\[
C_2O_4^{2-}
\]
is bidentate, not ambidentate.
\[
NH_3
\]
and
\[
CO
\]
are monodentate ligands.
Hence, only option (2) contains exclusively ambidentate ligands.
Step 4: Final conclusion.
Therefore, the correct set is
\[
\boxed{NO_2^-,\ CN^-,\ SCN^-}
\]