CBSE

If your main goal is to get nits then you don't need for improvement but I think if you are looking for JEE advance then surely you should go for improvement as it is compulsory to get 75% marks and above with a good JEE advance rank.

Hello Shraddha,
Yes, there is a hope for you. But it all depend upon seats availability and cutoff, so it is difficult to say. But, hope for best.

CBSE is a better option after 10th board in comparison to state boards because it's syllabus is aligned with majority of medical and engineering entrance examinations.

Yes, you can apply and rest will be the cutoff that will decide if you get admission in the specific college or not.

If you have already done 11th with science you cannot move to 12th for humanities however you can opt humanities in BA. If you opt humanities in Bachelor in Delhi university, there will be additional 2.5 percent penalty like if cut off for a 12th humanities is 92 percent, you have to score 95.5 percent however in Mumbai University 30% students have quota to opt from.other than the same faculties.

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It's 60% marks in PCB and separately 60% in honors subject. Like for chemistry honors must have 60% in chemistry and aggregate 60% in PCB. For B.sc maths as a subject in 10+2 level is mandatory.