Engineering

In Mumbai there are too many top college for Computer science and engineering from my personal knoweldege and from surroundings i have got the list of some Computer science and engineering (CSE) in mumbai
Veermata Jijabai Technological Institute.
Sardar Patel Institute of Technology.
K.J. Somaiya College of Engineering.
Amity University Panvel
Vidyalankar institute of technology
Thadomal Shahani College of Engineering.
Thakur College of Engneering.
Athrava College of Engineering.
Pillai college of Engineering.
MGM College of Engineering.
Terna Engineering College.
Rizvi College of Engineering.
A P Shah Institute of Technology.
Bhartiya Vidyapeet College of Engineering.
TSEC Mumbai.
These are the top 15 College For Computer science Engineering

At rank 40000, you will get some good colleges but you will have to compromise with the branches as you will get lower branches, but if you don't want to compromise and want to get upper branches or core branches then you will have to go for some lower colleges
The admission cutoffs are usually released by JoSAA on behalf of the colleges that are participating in the counseling process. According to the JoSAA given below are opening and closing ranks of some NITs ( open category only)
NIT Agartala
4,080- Opening rank
25,737- Closing rank
NIT Calicut
470- Opening rank
17,731- Closing rank
NIT Delhi
707- Opening rank
13,423- Closing rank
NIT Durgapur
7,376- Opening rank
21,206- Closing rank
NIT Goa
2,574- Opening rank
18,383 - Closing rank

After giving State Engineering Entrance exam and getting marks above cut off, you can go for counselling which generally starts after one month of result declaration there you will have options of locking seats in different colleges and in different branches and this Counselling generally goes up to 3 to 5 round including where you can free or float the option of locked college then after you will be called for document verification at the locked selected college or it may be any college nearby you. For getting into counseling you may have to pay registration fees which may or may not refundable, generally, it is not refundable. Finally after documents verification you will have to pay the semester fee or annual fees and then you are ready to start your engineering.

If your category rank (OBC Rank) is 3032, then the IITs available to you are:-
1] IIT Dhanbad - Geophysics (5 Y)
2] IIT BHU - Bio (5 Y)
3] IIT Kharagpur - Applied Geology (5 Y)
Unless you need the IIT Tag to flaunt in front of your relatives and unless you have some specific interest in these fields or unless you are planning to work hard to get a vertical branch transfer, go for NITs on the basis of your Mains rank or go for a drop. If your Open Rank is 3032, then you have a lot to choose from: - (The best options in no specific order, according to me are chosen as there are 50 and more branches open)
1] IIT Delhi Chemical (Dual Degree)
2] IIT Bombay Civil Engineering
3] IIT Madras Aerospace
4] IIT BHU Electrical Engineering
5] IIT Jodhpur Artificial Intelligence
6] IIT Guwahati Mechanical
7] IIT Bombay Metallurgical
8] IIT Bhubaneswar CS (5 Y) CS from all the newest IITs
9] IIT Indore Electrical Engineering
10] IIT Delhi Production Engineering
But if I were you, I had pick IITM Aerospace
PS - Data based on JEE 2020.

Automation and robotics engineering is interdisciplinary branch. One should have knowledge of mechanical engineering, electronics engineering and computer Science engineering. To automate any process one should have deep knowledge of that process and its variable parameters also control parameters. Mechanical engineering provides this knowledge. Now we need to measure this variable parameters to compute values of control parameters to achieve desired output from process. This is achieved with implementation of right sensors to measure variable parameters. And control system controls actuators to get desired outputs. (EnTC)
The values of output or control parameters is based on inputs or variable parameters. The relation between input and optput is given by programme. (CSE). .

As I myself got 185 marks in JEE Main and cracked JEE Advanced with a rank of 20k and went through JoSAA in 2017, I think I am the right person to answer this. First of all, I would like to say you that you cannot predict about the marks very accurately so rank should be the parameter. Coming to NITs, there are 3 tiers of them. Not all NITs are the same. If you want to get CSE in any of the tier 1 NIT, then your rank should be less than 2000 in JEE Main. If you want CSE in any of the tier 2 NITs, then your rank should not exceed 5000 in JEE Main. And if you just want an NIT tag (which you shouldn't as NIT tag is not any big tag), then for CSE your rank should be less than 10,000.

Well, the best colleges through JEE Mains are:
NIT Trichy: average CSE package (17 to 20) LPA.
IIIT Hyderabad: average CSE package 26 LPA
NIT Rourkela: average CSE package (15 to 18) LPA
NIT Suratkal: average CSE package 17 LPA
NIT Warangal: average CSE package 18.55 LPA
NIT Calicut: average CSE package 15 LPA
NSUT, Delhi: average CSE package 17 LPA
DTU: average CSE package 15 LPA
MNNIT Allahabad: average CSE package 15 LPA
IIIT Delhi: average CSE package 18 LPA
IIIT Allahabad: average CSE package 16 LPA
BIT Mesra: average CSE package 14 LPA
IIIT Bangalore: average CSE package (17 to 20)LPA. This college offers Dual degree programme M.Tech not B.Tech. NIT Kurukshetra: average package 7 LPA
IITH, IIITD, IIITB are private institution & rests are Government institutions.