R.P.S. Teachers Training College, Patna

No, you cannot take admission to just any B.Ed. college in Patna you must qualify for the Bihar B.Ed. Common Entrance Test (CET) and then apply to specific college through the counseling process, meeting their eligibility criteria only then you can take admission 

But some tier 3 colleges allow you for B ed program 

R.P.S. Teachers Training College Patna also gives direct admission to its B.Ed. Programme on the merit of academics. The eligibility criteria require the candidates to have passed with at least 50 per cent marks in Bachelor's or Master's degree, Science, Social Science, Humanities, or Commerce. The College offers admission to various courses based on Merit in marks secured in the relevant Qualifying examination. For further information, interested persons should contact the college administration.