IIT

Yes, it is possible to get admission to IIT Indore for MSc in Mathematics with a rank of 250 in IIT JAM for candidates belonging to the General AI category. Round 4 of the cutoff list has been released and the cutoff rank for admission to MSc in Mathematics was closed at 436 for candidates belonging to the General AI category. For candidates belonging to the OBC AI category, the cutoff rank was closed at 562. For candidates belonging to the SC AI category, the cutoff was closed at 1593. For more categories such as ST AI and EWS AI category, getting admission to the college with this rank is possible. 

Yes, it is possible to get admission to IIT Dhanbad for MSc in Mathematics and Computing with a rank of 250 in IIT JAM for candidates belonging to the General AI category. Round 4 of the cutoff list has been released and the cutoff rank for admission to MSc in Mathematics and Computing was closed at 411 for candidates belonging to the General AI category. For candidates belonging to the OBC AI category, the cutoff rank was closed at 506. For candidates belonging to the SC AI category, the cutoff was closed at 1627. For more categories such as ST AI and EWS AI category, getting admission to the college with this rank is possible.

You can study a 5-month online Professional Certificate Course in Data Engineering offered by IIT Kanpur after completing your graduation in a related field. For the NITs, none of them offer a dedicated Data Engineering course as yet, but you can have a look at related courses like BTech in AI and Data Science or BTech CSE with some elective modules on Data Engineering basics.

Yes, definitely you can pursue Masters in Technology M.Tech in Data Science from Indian Institute of Technology IITs and National Institute of Technology NITs through Graduate Aptitude Test in Engineering GATE because both the institutions accepts GATE entrance exam scores primarily for admission to MTech. There are some other colleges in Delhi who offers M.Tech course through Gate scores like Delhi Technological University DTU, Amity University Noida, Netaji Subhas University of Technology NSUT, Indraprastha Institution of Information Technology IIIT Delhi.

Several NITs offer M.Sc. Mathematics programs through the IIT JAM exam. These include NIT Trichy, NIT Warangal, NIT Calicut, NIT Jalandhar, NIT Rourkela, NIT Allahabad (MNNIT), and NIT Durgapur. Additionally, NITs like NIT Agartala, NIT Hamirpur, NIT Jamshedpur, NIT Manipur, NIT Srinagar, and NIT Silchar also participate in the CCMN (Centralized Counseling for M.Sc./M.Sc. (Tech.) Admissions) for M.Sc. programs, including mathematics

With a rank of 2426 in IIT JAM (Mathematics), you are likely eligible for several NITs and some of the newer IITs for MSc programs. You should be able to get into NITs like NIT Silchar, NIT Srinagar, and possibly some others with your rank

You might also be eligible for newer IITs like IIT Jodhpur, IIT Mandi, or IIT Ropar, but it depends on the specific programme and cutoff for each institute. 

An AIR of 1410 in IIT JAM Mathematics does not get you through premier IITs such as Bomb, Kanpur, Madras, and Delhi because they have a very low closing rank. However, it gives a good opportunity for newer IITs like IIT Indore, IIT Hyderabad, IIT Gandhinagar, and maybe even IIT Bhilai or IIT Palakkad, which tend to have higher cutoffs but increased opportunities in research in Pure Mathematics. If you want to pursue a research-oriented career in the strong research area, then explore IISERs, CMI, or TIFR as an option along with considering the above ones for further studies or a Ph.D. in mathematics.

If an applicant wants to write the GATE Statistics (ST) paper and subsequently apply for Data Science courses in IITs, he/she must be either pursuing his/her final year studies or holding a bachelor's degree in Statistics, Mathematics, Engineering, Technology, or any appropriate Science stream. Many of these IITs accept GATE ST scores for the M.Tech or M.Sc. degrees in Data Science, but eligibility varies according to institutes, making it wise to consult the specific IIT's admission brochure to determine which GATE papers are accepted for their Data Science programs.

The closing rank for general category in M.Sc Chemistry was around 787.

You rank is actually very close to the cutoff.

You may receive a seat in 2nd round or 3rd round as it might change across the rounds when seats freed.

Congratulations on your excellent rank and all the best.