Concept:
Vikrit swaras are those swaras which are altered from their natural or shuddha form.
They include:
\[
\text{Komal Re, Komal Ga, Komal Dha, Komal Ni}
\]
and
\[
\text{Tivra Ma}
\]
Step 1: Check Patdeep.
Raga Patdeep mainly uses komal Nishad as the vikrit swara.
So, it has fewer vikrit swaras.
\[
A = \text{Patdeep}
\]
Step 2: Check Bageshri.
Bageshri uses komal Ga and komal Ni.
So, it has more vikrit swaras than Patdeep.
\[
B = \text{Bageshri}
\]
Step 3: Check Puriya Dhanashri.
Puriya Dhanashri uses komal Re and tivra Ma.
It is placed after Bageshri in the given increasing order.
\[
C = \text{Puriya Dhanashri}
\]
Step 4: Check Bhairavi.
Bhairavi has many komal swaras:
\[
r,\ g,\ d,\ n
\]
So, it has the highest number of vikrit swaras among the given ragas.
\[
D = \text{Bhairavi}
\]
Step 5: Final arrangement.
Thus, the increasing order is:
\[
A \rightarrow B \rightarrow C \rightarrow D
\]
Hence:
\[
\boxed{\text{(A) A, B, C, D}}
\]