I didn't register for B.Sc admission this year and have passed Gujarat board with 75%. Am I eligible for admission in a govt. college?

Hi, Since you have not filled the form this year you cannot appear this time. But, you can appear in the entrance exam next year. You have to score good rank to get admission.

Yes, you would be eligible for the admissions in 2020. Almost, all college seats have been filled, especially government for this year.