Ofcourse you can give both the exam JEE and GUJCET as JEE exam give admission to IIT, NIT, and GFTIs for B. Tech courses and GUJCET offers seats in the universities situated in Gujarat.by giving two exams you have more options of colleges to choose from for your b.tech course.

If you see Engineering Admission Process are like this

Josaa: This is JEE counselling process. This would Only admitted students on the basis of JEE Mains marks and would be considered for your rank.

ACPC: This is your state admission process which GUJCET marks along with PCM boards theory marks would be considered. 50% of college seats are given to ACPC.

Since you are interested in both JEE as well as GUJCET, I'd advice you to enroll through both the processes for good colleges and good branches.

Best of luck!!!