Hello
Your ST certificate will work in all over India in all states. You can apply for admission in NIT Goa with a ST certificate from Rajasthan. The certificate must be genuine and must be verified.
Yes you can get into NIT Goa. NIT Goa was established in 2010. It is one of the well recognised NITs. It's infrastructure is very well setup and has facilities like laboratories, classrooms, and many more. All its faculties are eager to teach students.
Companies like WIPRO, TCS ,SAP, INFOSYS, ACCENTURE ,IGATE ,CTS, IBM and much more does campus placement.

For more details please visit this link https://www.careers360.com/university/national-institute-of-technology-goa/btech-mechanical-engineering-course

Hope it helps

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