12k rank for SVU I think they may not encourage to take. In my point of view you may have scored a better rank than this so that there may be a probability of getting a seat in SVU. Since it is a university the chances of getting the seat in mechanical is probably less. 

Just speak to your seniors or the people who are pursuing there B.Tech in SVU so that you will get an idea whether you will get do you need to choose another college

But you still don't make your hopes go down try till the last movement mean while try to see another best colleges with the same capabilities which may differ a less.

All the Best..!