Yes, you can apply for UPSC in your last year of B.E. 

UPSC Civil Services Examination is one of the toughest examinations to crack and a candidate requires a few specific traits, right attitude and temperament to get success in this coveted exam.

A systematic and regular 10-hours-a-day study for 10 months is sufficient to crack Prelimsand Mains rounds of the examination. You should have right study material is very important and it can help immensely in achieving success in PSC exams. 

You can refer NCERT books of 10th and 12th standards in order to buttress your basic concepts and knowledge. You must keep themselves abreast of current affairs and start making notes of every major happening around the world. 

Good Luck!!

Yes, in the final year of B.E you can apply for UPSC exam. Here are some of the preparation tips you can follow.

Go through with the previous year papers.
Prepare a suitable time table for the preparation

Study and revision should be part of your syllabus:

Focus on basic concepts: The preparation does not mean you should be a book-worm but an aspirant with the practical knowledge of his surroundings.
Make your own notes: As you go through the syllabus, make quick notes. This will help you in revision and better understanding of concerned topics.