With Open General category JEE rank of 11973 where can I get CSE. Home state J&K.

Congratulations for your result. You know the cutoffs varies every year as it depends on various factors. Also you have not mentioned the home state you belong to as the cutoffs also depend on them. Now as a general category student, you can expect Commputer Science and Engineering in NIT Uttarakhand, Sikkim, Meghalaya, Manipur, Mizoram, Arunachal Pradesh, Patna, Srinagar, Pondicherry, Nagaland, Silchar, Goa, Raipur, Agartala, Andhra Pradesh etc under All India Quota. You can check the cutoffs of various NITs here http://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches
http://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits
We have Jee Main College Predictor tool to help the aspirants to get the best colleges based on their rank and percentile http://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer