The correct options are
B Solution becomes homogeneous
C Solution becomes milky in appearance
A detergent is a long molecule with two ends of different nature.
One end is water attracting and the other is oil attracting.
When it is added to the mixture of oil and water, oil particles stick to one end and the water to another end.
It spreads throughout evenly and makes the solution homogenous and milky.
In this manner, it also performs its cleansing action when used to clean stains.