As high as 99% and as low as 40%, depending upon course and your category.
If you are from general category and want to pursue economics hons than in top colleges like st. Stephans, srcc and hindu the cutoff is generally above 98% in best of four including one language subject.
If you want to pursue bachelors in commerce (hons) than in top 5 colleges, srcc, hansraj, hindu, lsr and kmc the cutoff is generally above 97%.
On the other hand cutoff for courses like Hindi (hons) and sanskrit (hons) the cutoff is very low. For sanskrit hons you can take admission in st. Stephans college by just scoring 66% marks. And for hindi hons the cutoff in top colleges are between 85–92%.