I am from Nepal and have B.Tech degree only. I have not given CAT exam or any other exam, so am I eligible for MBA or not?

The present faculty-to-student ratio of GIBS Business School, Bangalore, is about 1:15, with one faculty member for every fifteen students. This balanced ratio enables personalized attention, close mentorship, and interactive classroom learning to ensure that each student gets proper academic guidance and support. It helps the faculty understand individual learning needs; provide constructive feedback; and encourage active participation in discussions, projects, and research, ultimately enhancing the overall learning experience, confidence, and career readiness of the students. This makes education at GIBS all the more engaging and outcome-driven.

Getting into the MBA programme of NIT Trichy with a 300 SC CAT rank is somewhat uncertain. As the recent data sets suggest, NIT Trichy's CAT cutoff for SC category admission stands around 65th percentile. A 300 SC rank could be borderline depending on how many SC candidates apply and the quality of the overall candidate pool.
In CAT marks terms, to reach around the 300 SC rank, you'd likely need a CAT percentile of 65–70, which roughly translates to a CAT score of about 60–65 out of 198, assuming the normalization and difficulty remain similar. 
However, final admission also depends on other factors like your academic profile, work experience, and performance in interview, not just CAT. So while you're in a reasonable range, make sure to strengthen your overall profile.

That's a wonderful goal to push your son toward right at the start. To obtain previous CAT model papers, you can check many available popular exam preparation books in any bookstore or online store. Coaching interest such as TIME, IMS, Career Launcher, etc., usually have mock tests and sample papers for students. Educational YouTube channels  offer thought forums regarding past patterns. Almost all the sites discussed before offer free PDFs with question paper solutions to look over the previous years' papers. You could also consult seniors and teachers who had taken the standardized test as well. All these resources will help with becoming familiar with the types of questions that are being asked, specifically way too many questions regarding Quant, Verbal, and Logical Reasoning, which are also key for the CAT model.