There is a chance your application might be rectified, but it depends on the specific university or institute you are applying to.Check the university or institute's website for any information on application corrections or error handling procedures. There might be a designated email address or a helpdesk system for addressing these issues.  Reach out to the admissions office of the university/institute you applied to. Explain your situation clearly  that you are a general category student from Bihar but mistakenly selected the "Distant Category" option.

I hope it helps !