Yes, You are elegible for JEE, you can give JEE MAINS. Marks of Class 11 are never considered for JEE OR HPCET. You can give JEE MAINS or HPCET and can score good marks but here the major problem is for getting into NITs your minimum percentage should be 75% which is not satisfied. But after scoring good marks in JEE and with this percentage you can take various colleges like DTU or NSIT and even private colleges too. You are not elligible for JEE ADVANCED as minimum percentage needed there is also 75%. So there is no need to go for JEE ADVANCE. Yes, you can go for JEE MAINS or HPCET and can score good marks so as to ensure good college for BTech. After scoring 68.8% you can take admission into NSIT and some good private colleges like Thapar Engineering College.

You can even check for various colleges after applying your marks at the JEE College Predictor as being provided by Career 360.

https://engineering.careers360.com/jee-main-college-predictor?icn=jee-main-clgpd_landing-page&ici=prediction-section_c360-home