CBSE 12th

See, it's not difficult to study PCB or PCM in 11th or 12th. The only things that bothers students the difference of level of course from 10th to 11th. Just bear the pressure smartly.
Good luck.

The cut-off goes really high. The cut-off in 6th round for B.A. (hon) history is 86.5%.

Hi,
If your school is affiliated to AICTE/state education council then no issue, you can easily apply to BA LLB Program at Dr. Ambedkar Government Law College.
Dr. Ambedkar Government Law College is a good college in Tamil Nadu for law.

After 12th you can go for the entrance exam of agriculture, i.e. PAT, conducted in every state or you can go for direct admission in a college for B.Sc or B.Tech in agriculture.

There are lots of ways after 12th. It depends on your interest, skills and stream of 12th. If you are from science stream with maths then you can go for BE/B.Tech and medical, in commerce you can choose B.Com management, business BBA and then MBA. Other options are mass media, arts, music, artists, etc. It depends on your interest and ability.

Definitely, you can apply for DU admissions on the basis of merit and your 12th grade.

Have you given any entrance exam for any government college like GPAT, UPSEE, JEE Mains paper 2, AU AIMEE, CPMT or PMET?

No, it's not necessary but in mathematical questions are asked in the BBA entrance exam.