With a rank above 5000, it would be a bit difficult to get offers from govt. colleges. Still, you might have fair chances in some of the new govt. engineering colleges. However, you have a very good chance at some of the top private engineering colleges in WB.

Dear Shaleen,

you choose a correct plateform for Knowing about the detail of WBJEE,

Firstly if u score more mark that is to be better chances to the better collages of wbjee.

there are the previous report of the cutoff and rank detail of WBJEE for his first priyority of collages.

Very few Government engineering institutes are there in West Bengal for getting in through WBJEE.

The best and famous Government Engineering colleges of West Bengal,which conducts admission through WBJEE are as (Rank wise) follows:-

Jadavpur University:1-500 (However,last year closing rank was 365 in construction engineering).

Bengal Engineering and Science University (BESU):Rank in WBJEE- 1-800.(However,last year closing rank was 637).

Kalyani Government Engineering college:1-750.

Jalpaiguri Government Engineering college:1-3,000 (IAF also conducts campusing here Under Fast Track entry Scheme). 

Netaji Subhash Engineering College: Any rank within 17,000.

Government Engineering College : Any rank within 22,000.

Murshidabad College of Engineering & Technology : Any rank within 25,000.

Bardawan Engineering college: Any rank within 2,000.

Bankura Engineering college: Any rank within 20,000.

Asansol Engineering College:Any rank within 20,000.

Kindly note the whole answer was given by analysing previous years councelling and admission method. Nobody can tell the exact (100% sure) that's because this year number of seats has also been increased.

Best of Luck!!