Step 1: Check Statement I
Micelles consist of:
Hydrophilic (water-loving) head
and
Hydrophobic (water-repelling) tail
Thus, they have both lyophilic and lyophobic parts.
\[
\boxed{\text{Statement I is correct}}
\]
Step 2: Check Statement II
Starch in water is an example of:
Macromolecular colloid
not multimolecular colloid.
\[
\boxed{\text{Statement II is incorrect}}
\]
Step 3: Check Statement III
Micelles form only when concentration is:
greater than CMC
Given CMC:
\[
10^{-3}\,\text{mol L}^{-1}
\]
The statement says less than CMC, which is wrong.
\[
\boxed{\text{Statement III is incorrect}}
\]
Step 4: Check Statement IV
Gold sol is prepared by:
Bredig's Arc Method
which is a dispersion method.
\[
\boxed{\text{Statement IV is correct}}
\]
Correct statements are:
\[
I,\ IV
\]
\[
\boxed{\text{I, IV only}}
\]
Therefore, the correct answer is:
\[
\boxed{(C)}
\]