Our university doesn't announce any rank and it is not present in our transcripts but I know that my rank is 7 out of 60 in my department. Can I mention this rank? Since I dont have any proof of my rank I am not sure if I can mention it or not.
If you can't prove it, I wouldn't put it in your C.V.
For one, anyone reviewing your application will have no way of knowing if you're lying or telling the truth. That's never a feeling you want a reviewer to have.
Even more importantly: what if you were actually wrong? What if you were 8 out of 60? Or 6 out of 60? I trust that when you say you're 7 out of 60, you have a pretty good idea of that, but you can't be sure if your school doesn't issue an official rank.
For what it's worth, if your GPA is high enough, I doubt rank will matter much. #7 is great, but #7 out of 60 students is different than #7 out of 600 students or 6000 students. For that reason, the rank itself is less valuable than your actual GPA.
You may want to say Top X% of the department or Top 10 or Top 20 rather than #8. I never really found this ranking to be all that useful because your previous work/experience and GPA are self-explanatory. These ranks are not gonna matter. If you go to a more competitive college, your rank could've been lower. Remember, you are competing with others from other universities, so how you rank against everyone else is far more important than how you rank against your peers.