Concept:
In the Natyashastra, Vrittis refer to dramatic styles or modes of expression used in theatrical presentation. Bharata Muni classified four principal Vrittis that govern different forms of dramatic expression, movement, speech, and emotional presentation.
Step 1: Understand the four Vrittis.
The four important Vrittis mentioned in the Natyashastra are:
• Bharati
• Sattvati
• Kaishiki
• Arabhatti
Each Vritti represents a distinct style of dramatic and dance presentation.
Step 2: Know the traditional order of Vrittis.
According to the sequence described in the Natyashastra, the order is:
\[
\text{Bharati} \rightarrow \text{Sattvati} \rightarrow \text{Kaishiki} \rightarrow \text{Arabhatti}
\]
Using the given letters:
\[
D \rightarrow B \rightarrow C \rightarrow A
\]
Step 3: Compare with the given options.
Among the given choices:
\[
(A)\ D,B,C,A
\]
\[
(B)\ A,B,C,D
\]
\[
(C)\ B,D,A,C
\]
\[
(D)\ C,B,A,D
\]
the correct sequence is:
\[
\boxed{D,B,C,A}
\]
Hence:
\[
\boxed{\mathrm{(A)}}
\]