With a TS EAMCET rank of 35,680, you may have a chance of securing a BSc Agriculture seat at Professor Jayashankar Telangana State Agricultural University (PJTSAU), but it depends on the cutoff ranks for the current year.

A few key points:

- In 2021, the closing rank for BSc Agriculture at PJTSAU under the general category was around 35,000[3].

- However, the cutoff ranks can vary each year based on factors like total applicants, available seats, and performance of other candidates. The 2024 cutoff is likely to be higher than 2021.

- There are also reservation policies for different categories that impact the cutoffs. Your rank may be competitive for the general category, but you should check the specific cutoff for your category.

To improve your chances:

1. Monitor the official PJTSAU website and counseling updates for the latest information on cutoffs and seat availability for BSc Agriculture.

2. Apply for counseling and indicate your preference for PJTSAU along with other suitable options.

3. Explore other agricultural universities as well, as the cutoffs may vary.

With a rank of 35,680, you have a reasonable chance, but the final outcome depends on the 2024 cutoff.

I suggest checking the official sources for the most up-to-date information closer to the counseling dates.