Your girls' quota rank of 15,000 is significantly better, and you'd have a much higher chance of getting into a college with that rank. However, the question specifically asks about colleges accessible based on your *general* rank.
To find out which colleges *might* be accessible with your general rank, you'd need to:
* Check the UPSEE cutoff ranks from previous years: Look at the closing ranks of different colleges from the previous year's UPSEE results. This will give you an indication of what ranks were successful in securing admission.
* Consider less popular branches: You might have a better chance of getting into less sought-after branches of engineering (like some less-popular specializations) even in a college that's otherwise highly competitive.
* Explore private colleges: Private colleges often have their own admission processes and may have higher cutoffs than government-aided institutions.
In short: Don't rely on securing a seat in Ghaziabad or Greater Noida with a general rank of 87,000. Your options are significantly better using your girls' quota rank. It's strongly recommended to focus your efforts on applying through the girls' quota.