Concept:
In the Bharata Natyam repertoire, different dance items are arranged in a traditional sequence known as the Margam. Among all these items, the Varnam is considered the most elaborate and important composition because it combines both technical dance and expressive storytelling.
Step 1: Understand the meaning of Varnam.
Varnam is the central and longest item in a Bharata Natyam performance. It combines:
• Nritta (pure dance)
• Nritya (expressional dance)
• Complex rhythmic patterns
• Emotional interpretation
It tests the dancer's stamina, technique, rhythm, and expressive ability.
Step 2: Understand the other compositions.
The remaining options represent other dance or musical items:
• Keertanam -- Devotional musical composition.
• Karatal Cholom -- A dance form involving cymbals.
• Tillana -- A rhythmic concluding dance item in Bharata Natyam.
Step 3: Identify the most elaborate composition.
Since Varnam combines both technical and expressive aspects extensively, it is regarded as the most elaborate composition in Bharata Natyam.
Therefore, the correct answer is:
\[
\boxed{\text{Varnam}}
\]
Hence:
\[
\boxed{\mathrm{(C)}}
\]