NIT Kurukshetra - National Institute of Technology

The admission to government institutes for BTech varies from state to state and also depends on the availability of seats in each institute. Since you have not mentioned your state, it's difficult to provide a specific answer. However, with a category rank of 12000, you have a higher chance of getting admission to a government institute compared to your CRL rank.
I would suggest you check the cutoffs of various government institutes in your state for your category rank. You can also check the previous year's cutoffs to get an idea of the minimum score required for admission. Additionally, you can also consider participating in the counseling process of the state-level engineering entrance examination to explore various options available to you.

It's nice to see your query. Before I answer your query, here is some information that you should know. Even though percentile is of vital importance, it's the ranking released by NTA at the end of different sessions that matter most. NTA will announce ranking after the end of session of exam this year. In this, they will combine percentiles of both sessions with for those who appeared in both, best of two will be selected. Then ranking is released.
Last year students with ranking about 8000 got admission. I am attaching a link to help you understand.
https://www.shiksha.com/college/nit-kurukshetra-national-institute-of-technology-23159/cutoff
Best wishes to you.

First of all, I appreciate you for being dedicated to your career perspective and setting your goals right at the beginning. Those who begin at right time get placed in good positions as it's truly said Beginning is half done. During the First year course, you need to strengthen your basics of computer science and higher engineering mathematics that you will be applying in solving numerical problems. If you start preparing right now, you will definitely achieve your target.
At Lovely Professional University, you can opt for different career pathways such as preparing for GATE so that changes are done in your curriculum accordingly. To achieve the same on a regular basis special coaching lectures, seminars, and counselling sessions are organized by the experts. These inputs are largely divided into credited and non-credited inputs.
The syllabi of credited inputs are mapped with various competitive exams like GATE, SSC, UPSC, and CSIR NET. Non-Credited inputs include practice tests in collaboration with AMCAT, Co-Cubes, Bulls Eye, and MyPerfectice.
Wish you all the best.