Step 1: Concept
Analyzing the diverse compositional outputs of prominent post-Trinity Vaggeyakaras (composers) of the late 19th and 20th centuries.
Step 2: Evaluating Statement I
Mysore Vasudevachar ($1865$–$1961$ AD), a disciple of Patnam Subramanya Iyer, was a highly prolific composer. While he is celebrated mostly for his classical Sanskrit and Telugu Kritis (like Brochevarevarura in Khamas), he also composed multiple varnams, tillanas, and light, romantic Javalis (e.g., Premato nato in raga Kanada). Hence, Statement I is true.
Step 3: Evaluating Statement II
Ramnad Srinivasa Iyengar ($1860$–$1919$ AD), popularly known as Poochi Srinivasa Iyengar, was also a legendary disciple of Patnam Subramanya Iyer. He composed over a hundred highly celebrated pieces, which included highly technical and popular concert Tillanas (such as the famous tillanas in ragas Paras, Kapi, and Hindolam). Hence, Statement II is true.
Step 4: Conclusion
Both Statement I and Statement II are correct and historically accurate, matching option (A).
Final Answer: (A)