I have just completed my +2 in state board with 96% but failed in jee with 42.Can you please suggest me some jee institutions in chennai?

Chennai has many good coaching centres like :--

AAKASH :-- The teachers here are good, but it's very expensive if you compare other JEE Institutes some of which are better. It's good for medical preparations though.

FIITJEE :-- They take a test based on which they divide you into batches ,  the students performing better are given better batches which sometimes demoralises the students who didn't get into good batches. They only concentrate all attention and focus on these students which I personally disapprove of.

BRILLIANT TUTORIALS / CAREER LAUNCHER :--
Their performance has been disappreciating for a while , they provide you basic mentorship and have good test series, though there have many cases where people have paid the entire coaching amount but not received any coaching or refund.

BYJU'S  CLASSES :-- They have been doing really well in last couple of years. I have heard that they make classrooms a fun interactive session for their students which works in their favor. Also they have been known to return the entire fee amount if the student doesn't find them good for JEE . The only downside is that they accept only a certain no. of students and the batches fill up really fast .
Hope it helps :)