Concept:
Hardness of water is mainly caused by the presence of calcium (\(\mathrm{Ca^{2+}}\)) and magnesium (\(\mathrm{Mg^{2+}}\)) ions.
Different softening methods remove hardness to different extents.
• Lime-soda process removes only temporary and part of permanent hardness.
• Excess lime treatment removes temporary hardness.
• Ion exchange process removes both temporary and permanent hardness almost completely.
Hence, zero hardness can be achieved only by the ion exchange process.
Step 1: Understand the ion exchange process.
In the ion exchange method,
\[
\mathrm{Ca^{2+}},\ \mathrm{Mg^{2+}}
\]
are replaced by
\[
\mathrm{H^+}\ \text{or}\ \mathrm{Na^+}
\]
using suitable ion exchange resins.
This removes practically all hardness-producing ions.
Step 2: Identify the correct method.
Therefore,
\[
\boxed{\text{Ion exchange method produces water with nearly zero hardness}.}
\]
Hence, the correct option is
\[
\boxed{(C)\;\text{Ion exchange method}.}
\]