Hello ,12 class examination passed eligible for  applying to appear for common University entrance test for admission in undergraduate courses and PG courses, diploma or certificate courses in 45 Central University in India. You have combination of economic and environmental science in 10 + 2 class examination. Now you want to appear in cute examination for BA LLB 5 years integrated course. It is possible to appear for cute exam for admission in centre University of 5 years integrated Ballb course. There is no educational problem taking admission in Ballb course though you have combination of economic and environmental subject in 10 + 2 examination. Generally BAllb course admission is taken after any arts commerce science 10 + 2 class examination pass student

Hope this will help.