Hello ! According  to  my opinion yes there is definitely  other entrance  exams  also like UPSEE, VITEEE, COMEDK ,BITSAT etc . By which you can get admission in  B.tech.

Here i giving you some idea about colleges  and their entrance  exam names that is

VITEEE        - VIT, college

SRMJEEE     - SRM university

KEACET, COMEDK - R .V. college  of  engineering  .

MHT CET   - MIT , pune pune engineering college.  Etc..

These are some good college  and  admission  date ended in month of April  of course! But process  of  application forms depend  upon the university.

I hope this  information  will help you .

Thankyou!