IIT

Hello ! it totally depends on your interest whether you want to take a drop or go for some private institution.i must add that now days there are some private colleges who are doing equally good as top government universities so why to waste your precious one year when you are having good options with you rather you can invest your time in some effective manner.here are some of the colleges which are exceptionally good:
1.Symbiosis International
2.Lovely Professional University
3.SRM
These conducts their own entrance test and give scholarship based on its score Like Lovely Professional University conducts its LPU_NEST and give scholarship upto 1.5 lakh per annum.i have even heard that this university is having a good placement record.

Yes, to appear in JEE (Advanced) a diploma holder can apply in JEE Main but his rank and score for JEE (Main) will not be declared as diploma holders cannot apply for admission in NITs and CFTIs through JEE (Main) channel. * The criteria of marks for diploma holders will be : If a Board gives aggregate marks considering the results of all three years of a 3-year diploma or courses of equivalent duration, then only the marks scored in the final year will be considered. Similarly, for Boards which follow a semester system, the marks scored in the final two semesters will be considered. * One of the criteria for admission to IITs and ISM is that the candidate should satisfy at least one of these two criteria: 1-He/she is within the category-wise top 20 percentile of successful candidates in his/her respective Class XII (or Diploma) Board examination. 2-He/she has secured 75% (for GEN or OBC-NCL) or 70% (SC, ST or PwD) of aggregate marks in the Class XII (or equivalent) Board examination. *All the rules listed above were followed in 2015.So keep checking if there are any changes.* In order to get admission in aerospace engineering at IIT Bombay your AIR should be less than 1500 more or less.

Hi Prashant,
57 is not a pleasing score. Based on your JEE score your expected JEE rank will be more than 75000.
The above mentioned ranks are displayed only the basis of a candidate's score in JEE Main 2016. There can be variation in ranks when the same is calculated on the basis of normalization of scores, taking in account Class XII Board results along with reservation (SC / ST / OBC etc.) and JEE exam scores.
I would request you to attempt the remaining papers to the best of your capabilities. Always remember, you should pursue a stream/course based on two things :
-your career goal
-the type of job you want to do
I have already spoken about aeronautical and computer science engineering in your previous question.
Hope it helps. Please feel free to revert.
Wish you luck.