Jammu and Kashmir Board of Professional Entrance Examination conduct JKCET Entrance Exam for the admission to various B.tech programmes offered by different institutes in Jammu and Kashmir. You can take an Idea of the No. of seats of the of Jammu & Kashmir Engineering colleges with the given below link from the page No. 48 to 50.

http://jkbopee.gov.in/Pdf/Downloader.ashx?nid=31&type=1

Good Luck!