Dear aspirant hope you are doing well. It's difficult to predict because cut keep changing every year depends on various factors  like no  of seat available , difficulty level of exam and noo of student appear in exam.

As you secured 36.67 in jee mains. Your rank lies in between 1025009-334080   . You can check the using the given link below

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile/amp

From previous years trends and analysis, it has observe that all the seats are filled up by  candidates in between 15k to 25k rank in colleges NITs , IIITs, GIFTs . So its difficult to get any any  NITs , IIITs, and GIFTs . According to your rank you will get some of private colleges are listed.

yes you can get private engineering colleges in Maharashtra. Some are listed below.

• - Konkan Gyanpeeth College of Engineering, Karjat
• Jaywant Shikshan Prasarak Mandal's,Rajarshi Shahu College of Engineering, Tathawade, Pune
• Janata Shikshan Prasarak Mandal’s Babasaheb Naik College Of Engineering, Pusad

More

For best results, please must use jee main college predictor tool, so you can get best college according to your rank and category.

To know the list of engineering colleges , you have chances to get admission, you can also use JEE MAINS college predictor tool. Link is given below. .

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Pervious years percentile to qualify the jee advance is given

General : - 87.8992241 percentile

EWS:- 66.2214845 percentile

OBC-NCL :- 68.0234447 percentile

SC :- 46.8825338 percentile

ST:- 34.6728999 percentile

PWD :- 0.0096375 percentile

you can use this cut off as a reference for jee advance 2022. you can also check the same using the link given below..

https://engineering.careers360.com/articles/jee-main-cutoff

Hope it's helpful thank