Last year cut off for JMI for CSE was 240+ for general candidates( are those excluding Muslims, Muslim women, jamia internal) in first list. This year first list will be selected on first week of July. Since you know that CSE is the top demanding branch that's why it gets filled first with high cutoff. But I will suggest you to apply. Because this time jee rank calculation has been changed so it might effect the cut offs.

Wish you a good luck.