Hello Isha

You wont be able to participate in JoSAA as 78.7 percentile is not enough for you to qualify JEE Mains as per oyur category. However you can participate in state level counselling,and not to worry you are going to get a decent branch in a  SGFTIs(State Government Funded Technical Institute)and many other good colleges.

However, to help you find a college as per your rank,I suggest you to go through this,

Hope this will help you find a suitable college

Hello there,

78.7 percentile in jee mains is not a good percentile so be sure that you are not going to get any top engineering college or govt. college. You can apply for private colleges in your state or if you had given your state's entrance exam then you can use that too to get admission in engineering colleges under state quota.

Since you belong from himachal pradesh, there's a state exam called HPCET, which i guess you should've given so try applying using your hpcet exam marks.

to see engineering colleges available in your state visit the following link:
https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-himachal-pradesh-accepting-jee-main

since, as you haven't passed the cut off you won't be able to participate in JoSAA counselling. and about the branches, you won't get top branches like CSE,ECE,BIOTECH, Civil. you can try for metallurgy, Industrial, petroleum branches.

Hope it helps!
AND BEST OF LUCK FOR YOUR FUTURE!