hello athulya

yes there are NITs which provide integrated bsc msc courses like NIT rourkela ,NIT patna ,NIT surat etc .for getting admissions in such colleges you have to appear in jee mains and secure a good ranking . the admissions are taken through josaa counselling .the admission procedure is same as for other courses like btech.

you can also use jee main college predictor to know more

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer