Concept:
Temple architecture in ancient and medieval India evolved gradually through different dynasties and regions.
Important temple styles include:
• Dravidian style,
• Nagara style,
• Vesara style.
Chronological order questions require identifying the ruling dynasty and approximate construction period.
Step 1: Identifying the earliest temple.
\[
\text{Shore Temple}
\]
The Shore Temple at Mahabalipuram was built during the Pallava period under Narasimhavarman II in the:
\[
8^{th}\text{ century CE}
\]
Thus:
\[
C = \text{First position}
\]
Step 2: Finding the next temple chronologically.
\[
\text{Vaikunthaperumala Temple}
\]
This Pallava temple at Kanchipuram was built slightly later during the Pallava age.
Thus:
\[
D = \text{Second position}
\]
Step 3: Identifying the next temple.
\[
\text{Mukteshwara Temple}
\]
This temple belongs to Odisha temple architecture and dates approximately to the:
\[
10^{th}\text{ century CE}
\]
Thus:
\[
B = \text{Third position}
\]
Step 4: Determining the latest temple.
\[
\text{Airavateshwara Temple}
\]
This Chola temple at Darasuram was constructed during the:
\[
12^{th}\text{ century CE}
\]
Thus:
\[
A = \text{Fourth position}
\]
Step 5: Writing the complete chronological order.
Hence:
\[
\boxed{C \rightarrow D \rightarrow B \rightarrow A}
\]
Therefore, the correct answer is:
\[
\boxed{(1)\ C, D, B \text{ and } A}
\]
Step 6: Architectural importance of these temples.
These temples demonstrate:
• advancement in stone architecture,
• sculptural excellence,
• religious patronage,
• and regional artistic traditions.
They remain masterpieces of Indian cultural heritage.