You can refer this link as well more details:

https://engineering.careers360.com/articles/gujcet

yes you can apply for Btech and BE courses into all the 112 colleges across the state of Gujarat.

the application mode is online and the mode of examination is offline.

the candidate must be of the Indian nationality 

• All candidates should be bonafide residents of Gujarat. Bonafide residents of Gujarat who are residing in other states of the country will also be eligible for GUJCET 2018.

• Should have qualified 10+2 (or equivalent) examination from Gujarat Secondary and Higher Secondary Education Board, Gandhinagar/CBSE, Delhi/CISCE, New Delhi/NIOS/International School Board.

• Candidates who will be completing their 10+2 (or equivalent) examination in 2018 will also be eligible for admission.

Minimum score of 45% has to be secured by the candidates in the qualifying exam. The reserved category candidates will have to score 40% marks.

for further details one can go to the link

https://engineering.careers360.com/articles/gujcet