Hello student,
Yes, With a rank of 11,680 in St category, you can procure a seat in the good IHM's. The following are those, which you can get when comparing the results of previous years

• IHM Bengaluru
• IHM Bhopal
• IHM Srinagar
• IHM Shillong
• IHM Gurdaspur
• IHM Guwahati
• IHM Gwalior
• IHM Kolkata
• IHM Lucknow
• IHM. Hajipur
• IHM Shimla
• IHM Thiruvananthapuram
• IHM Jaipur
• IHM Chennai
• IHM Bhubaneshwar

The above mentioned colleges are central government IHM's which you can get in the first round. But, one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
https://hospitality.careers360.com/nchm-jee-college-predictor
Good luck

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