Hey,

Unfortunately you cannot get a btech degree within 3 years. You are required to study 4 years to complete your btech degree. Though some colleges like iits gives an opportunity to weaker students to opt out after 3 years with a Bsc degree instead. Also,there are some colleges that offers a one year betch programme. You may go through that as well.

Also once you get a complete graduation degree you may apply for any civil services exams given you fulfill other requirements.

Kindly let me know you have any further doubts.