To be eligible for a BSc degree at Shri Pt. Yagya Narayan Dubey Smarak Mahavidyalaya, Allahabad, candidates must have completed their 10+2 education with a minimum of 50% aggregate marks in the science stream from a recognized board. Additionally, candidates may be required to pass an entrance exam or meet specific subject-wise eligibility criteria set by the college. It is important for students to check the official website or contact the college admissions office for detailed information on eligibility requirements and the admission process.