Step 1: Understanding the Concept:
Historical timeline of key institutions and national programmes in Indian agricultural, home science, and rural extension history.
Step 2: Detailed Explanation:
Tracing the historical establishment years:
1. B. Establishment of ICAR (Imperial/Indian Council of Agricultural Research): 16th July 1929 (Royal Commission on Agriculture).
2. C. Start of Lady Irwin College (New Delhi): 1932 (Pioneering institution for Home Science higher education in India).
3. E. Community Development Programme (CDP): 2nd October 1952.
4. D. First Agricultural University (GBPUAT Pantnagar): 17th November 1960.
5. A. The first KVK (Krishi Vigyan Kendra, Pondicherry): 1974 (Mohan Singh Mehta Committee).
Chronological sequence: B (1929) $\rightarrow$ C (1932) $\rightarrow$ E (1952) $\rightarrow$ D (1960) $\rightarrow$ A (1974).
Step 3: Final Answer:
Hence, the correct chronological order is B, C, E, D, A, corresponding to option (C).