With a GATE XL (Life Sciences) rank of 6000, getting admission in Biochemical Engineering at top IITs may be difficult because competition is high and cutoffs are usually lower ranks. However, you might have a chance in some NITs or newer IITs with higher rank limits. It’s good to check each college’s previous year cutoff for Biochemical Engineering and apply through CCMT counseling. Also, consider private universities that accept GATE scores for better chances.