Banaras Hindu University Eligibility

You can check out the following link for more information - https://www.shiksha.com/university/bhu-banaras-hindu-university-varanasi-23336

The admission in M.A. Psychology in BHU are done through the following two streams.
1. Psychology Stream (Group -1) Intake 51 students : Candidates having B.A./B.Sc. (Hons.) in Psychology under 10+2+3 pattern or having studied Psychology as subject in all the three years at B.A./B.Sc. level.
2. Non-Psychology Stream (Group -2) Supernumerary intake for this group is of 7 students : Candidates having graduate degree in Science, Engineering & Technology and Medical Sciences without having studied Psychology at the graduate level.
So from above you are eligible for M.A./M.Sc. Psychology courses of BHU through the Group-2 stream.

The candidates having passed one year certificate course in Sanskrit of BHU after passing 10+2 examination with 50% marks in aggregate both in 10+2 examination and certificate examination are also eligible. MINIMUM ELIGIBILITY REQUIREMENTS: A candidate shall be eligible for admission to B.Sc.

B.Ed Course Eligibility: A minimum aggregate score of 50% in graduation is a requisite for admission. A minimum aggregate score of 55% at post-graduate level is mandatory for admission into colleges.

You may check the below link for courses and eligibility.
https://www.shiksha.com/university/bhu-banaras-hindu-university-varanasi-23336

Admission in M.Sc food science and technology is through entrance exam i.e. BHUT PET.
For more details, click in the link given below
https://www.shiksha.com/science/course/m-sc-in-food-science-and-technology-banaras-hindu-university-varanasi-272597

No, problem with that with your class 10th, they will consider your admission. All the very best.