Hello Pranay,
With a rank of 16k you can get the following NIT colleges through home state quota as per previous year cutoff marks. But you will not get core branches such as CSE and E&C :

• NIT Hamirpur
• NIT Srinagar
• NIT Silchar
• NIT Puducherry
• NIT Mizoram
• NIT Sikkim
• NIT Arunachal Pradesh

You can take admission in IIIT colleges where  jee main percentile is considered for admission. Also there are several colleges which accept jee main percentile for admission such as BITS, MIIT, SCIT, Amity university and so on. Also RV,KIIT, VIT and other colleges accept jee main percentile for admission.
Since you have rank of 16k you can easily get admission in one of the above colleges. You can also try for NIT in 2nd or 3rd during  jee main counselling process. If you have any queries comment below so I can solve the same.
To know more about which college to join try our new college predictor link below :
https://engineering.careers360.com/jee-main-college-predictor

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