Step 1: Understanding the Concept:
Chronological milestones of premier national agricultural research institutes and universities in India.
Step 2: Detailed Explanation:
Historical establishment years of the institutes:
1. B. Indian (Imperial) Agricultural Research Institute (IARI), Pusa, Bihar $\to$ Established in 1905.
2. A. Sugarcane Breeding Institute (SBI), Coimbatore $\to$ Established in 1912 (under Dr. C.A. Barber and T.S. Venkatraman).
3. E. Jute Agriculture Research Institute (now ICAR-CRIJAF), Barrackpore $\to$ Established in 1953 (originally as Jute Agricultural Research Laboratory in 1938/1953).
4. D. G.B. Pant University of Agriculture and Technology (GBPUA&T), Pantnagar $\to$ Inaugurated in 1960 (India's first State Agricultural University).
5. C. National Bureau of Plant Genetic Resources (NBPGR), New Delhi $\to$ Established in 1976.
Step 3: Final Answer:
Arranging in chronological order from oldest to newest: B (1905) $\to$ A (1912) $\to$ E (1953) $\to$ D (1960) $\to$ C (1976).