CUET

Senior Sec. School Certificate or an equivalent examination with not less than 50% marks in aggregate of best 5-papers or in the subject concerned. B.A. Eligibility: Passed 10+2 with 50% marks from a recognised Board/University.

If I say the simple answer to your question is No! You don't have to apply separately to all colleges one by one however you have to fill the preference list on COMMON SEAT ALLOCATION SYSTEM (CSAS) after the entrance test known as CUET and you can fill the preference of the college which you want to also consider your score in mind.

No, you don't have to appear for CUET for taking admission in St. Xavier's College, Mumbai for pursuing BA History(Hons). You need to give Xavier's BMS Entrance Test for taking admission in St. Xavier's Mumbai. CUET is applicable for Central Universities till now.

CUET Official Eligibility and Remark in English for B.A. (Hons. ). Chinese from JNU (JAWAHARLAL NEHRU UNIVERSITY)
Eligibility
Senior School Certificate (10+2) or equivalent examination from a recognised Board/University with minimum of 45% marks. The candidates who are due to appear in Senior School Certificate (10+2) or equivalent examination are eligible to apply.

You need 45% Mark for doing LLB.