Hi

This is a bit difficult to predict as your marks vs percentile vs rank in JEE main depends upon a number of factors like

-------------------------) number of students that appeared in the  jee main exam,

-------------------------) kind of marks obtained by them ,

-------------------------) toughness level of the jee main examination for different shift etc.

But yes ,

As per past year trends,

>>>>>>>> With    137 marks

--------------------) your percentile will be roughly around   96.65 - 98.05 considering paper of moderate level

--------------------)  considering the worst case if we go with   96.65 percentile then your  rank would be roughly around 34270 - 38525

To help you get the complete list of colleges that you can get, we have JEE main college predictor, the link for the same is given below:-

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

To help you  further,

To give an idea of jee main 2022 qualifying cut off to be eligible for jee advanced 2022.

Minimum percentile in jee main 2021 to qualify it to  be eligible for jee advanced 2021 is given below :-

--------) 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 check the same at our page the link is provided below

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

Regards

ADITYA KUMAR