Concept:
In Indian aesthetics and dramaturgy, Nayikas are classified according to their emotional nature, maturity, and temperament. These classifications are important in classical dance and dramatic representation.
Temperaments describe the behavioral and emotional qualities of heroines.
Step 1: Identify the temperament classifications of Nayikas.
\[
\text{Madhyadhira}
\]
is a recognized temperament type of Nayika.
\[
\text{Madhya adhira}
\]
also refers to a temperament category describing emotional disposition.
\[
\text{Pragalbhadhira}
\]
is another temperament type associated with bold and mature heroines.
\[
\text{Pragalbhādhira}
\]
is similarly a temperament classification.
Thus:
\[
A,\ B,\ C,\ E
\]
belong to Nayika temperament classifications.
Step 2: Identify the term that is not a temperament.
\[
\text{Parakiya}
\]
does not denote temperament.
It refers to:
\[
\text{A type of romantic relationship or heroine category}
\]
rather than emotional temperament.
Thus:
\[
D
\]
is excluded.
Step 3: Select the correct combination.
The correct set is:
\[
A,\ B,\ C,\ E
\]
Step 4: Compare with the given options.
Among the given choices:
\[
(A)\ A,B,C,D
\]
\[
(B)\ B,C,D,E
\]
\[
(C)\ A,C,E,D
\]
\[
(D)\ A,B,C,E
\]
the correct answer is:
\[
\boxed{A,B,C,E}
\]
Hence:
\[
\boxed{\mathrm{(D)}}
\]