Step 1: Understanding the Concept:
Sugarcane agronomy defines specific botanical terminology and crop duration cycles across different agro-climatic zones of India.
Step 2: Detailed Explanation:
1. Statement I: The terminal open-branched panicle inflorescence of sugarcane is called an 'arrow', and its emergence is termed 'arrowing'. The tiny, true botanical seeds embedded in silken hairs are commercially termed 'fluff'. Thus, Statement I is correct.
2. Statement II: In peninsular India (e.g., Maharashtra), an Adsali sugarcane crop is planted during July--August and takes 15 to 18 months to mature. A one-year (12-month) crop planted in January--February is called Eksali. Thus, Statement II is false.
Step 3: Final Answer:
Therefore, Statement I is correct but Statement II is false, corresponding to option (C).