Hi, since you have not mentioned the name if the exam but I can assume that your this question is of JEE Adavance so on behalf of your question below I'm mentioning the colleges under 10000 ranked best IIT with girl category;

• IIT, Bhilai
• IIT, Palakkad
• IIT, Bhubaneshwar
• IIT, Jodhpur
• IIT, Dhanbad
• IIT, Triupati
• IIT, Kharagpur
• IIT, Varanasi
• IIT, Ropar
• IIT, Guwahati
• IIT, Kanpur

Etc.

Hope this will help you.

Good Luck.