My brother goes to NIT Calicut so I can give you some insight into their M.Tech VLSI and EDT course. Here are the glimpses of the placement record for the year 2020.

• The placement percentage for the programs MTech Microelectronics and VLSI Design has been 100%. All the 12 registered students got placed.
• The placement percentage for the program MTech Electronics Design Technology has been 71.4%. 10 out of 14 registered candidates got placed.

The average CTC offered to both of these programs is almost similar. Also, the course has a good ROI. M.Tech Microelectronics and VLSI Design is in great demand and it is turning out to be one of the best courses at NIT Calicut.

It is not mentioned in your question whether the home state of Goa is applicable for you or not. Not only this, the category from which you belong is also not mentioned in the question (General/OBC/SC/ST).

However, I would try my best to provide you with a suitable answer based on official data for the past few years, the total number of seats vacant, and the various departments available at the institution.

• You can easily get enrolled in a better NIT like many of the older ones.
• You can surely try to opt for other courses at the older NITs as it would be extremely beneficial for your career.
• I would suggest that you do not lose hope after the seventh round of counselling.
• There would be a special round to fill up vacant seats at the NITs and IIITs.
• For this round, you are required to submit a fee of INR 1,000 along with the online application form on the CSAB portal.
• Fill in your desired branch and colleges once more; vacant slots can be seen at the portal.

I am quite confident you'll receive the branch you want after the special round. You can refer to the cutoff details available on various websites to estimate the chances of your getting admission to one of the courses offered by the institution.

I have a friend from NIT Goa and according to him, it will be really tough to get into NIT GOA with these statistics. The number of seats at NIT GOA is very few but also many of the students prefer it for its culture.

Here is the 2021 course-wise JEE cutoff for NIT Goa. 

This should give you an idea about the cutoff required at NIT Goa. 

According to the 2021 cutoff trend, the required cutoff of CSE for OBC category students is 14577 (HS). If you are an out-of-state student then the cutoff is 3779. So, getting admission to the institute will be tough if you are not a resident of Goa. 

The counseling process is done based on the AIR and not the category rank. The category rank is just a measure to rank you in your particular category. If your category is OBC NCL then your category rank would be the position among the other OBC students who had appeared for the examination. 

I have a few friends from the institute and according to them with a rank of 11900 in JEE Mains it will be difficult to get into CSE at NIT Goa. You should look for other colleges in order to get into your preferred branch. Here is the cutoff of NIT Goa for 2021.

Look for the previous year's cutoff on the previous JEE main website, which will give a pretty rough idea about what branch and college you can get into. However, I will not recommend NIT Goa for CSE. Since it is a new college and no big or well-known companies come there for placements. Infrastructure and resources are not as par according to NIT standards. You can also try some private universities such as BITS, Thapar, VIT, or MIT.

I have a friend who recently graduated from NIT Goa. According to him, for the home state, you should score around 160. Although it may vary since the mark required is increasing every year. 

According to the 2021 cutoff trends, the required cutoff (HS) for CSE is 14581. For more information on the cutoff, you can go through the JOSAA website. 

You should focus on your JEE Main preparation. Don’t worry about the required cutoff. Try to score 99 percentile, that way you can choose any branch that you like. If you are a student from Goa origin then 98 percentile is enough to get top branches. 

Here is the 2021 cutoff for various branches. 

This should give you some ideas about the required cutoff for NIT Goa. 

If you are a General category, Goa origin student then 70,000 should be enough to get you a seat. With your rank, you can get a seat for Mech or Civil. You have a good chance to get EEE or ECE too. 

Here is the recent cutoff for the branches. 

This should give you an idea about the cutoff required for NIT Goa.