It is not impossible to get into NIT Trichy or any top institution for an average student. I was an average student during school time and got a 7.6 CGPA in my 10th board examination. During my 12th boards, I worked hard and scored an astonishing 94.6%.
During my first attempt in JEE Mains, I got a 93.1 percentile. My score depressed me and I decided to prepare well for my second attempt. On my next attempt, I scored 98.120 percentile. It was a huge improvement for me.
Even though I had an OBC quota through which I got a seat at NIT Kurukshetra in an Electrical Engineering course, the point of this answer is that if I could’ve picked myself up and improved to such a great extent, even you can do so. However, I must warn you that for NIT Trichy you will have to work extremely hard.