Hi Shreya, since you have general category rank 38548 as well as you have 7780 girls rank so absolutely  there are chances that you can get into  any of the government college based on you rank you have scored. Also for your better convenience I'm mentioning some of the government colleges in which you may try for admission;

• Dr. Ram Manohar Lohia Awadh University
• VBSPU, Jaunpur
• Universiy of Engineering and Technology, Kanpur
• Dr. Shakuntala Mishra National Rehabilitation University, Lucknow
• MJPRU, Bareilly
• Feroz Gandhi Institute of Engineering and Technology, Raebareli
• Lucknow University

Etc.