Hello Preet

As you have not clearly mentioned that on basis of which exam you are asking for engineering admissions in Maharashtra State .But i will answered your query for both JEE Mains and MHTCET

JEE Mains: As NTA conducted jee mains this year twice once in January and then in April and released qualifying cutoff to sit for Jee Advanced . JEE advanced is conducted on 27 May this year all over India and Ranks will be declared soon.

Once Ranks are declared then JOSSA will start counselling probably on last week of June and First week of July .JOSSA conduct counselling in many stages and each stage seat is alloted 

For eligible to get admissions in IIT you want to qualify for Advance.And you can sit for NIT , IIIT and other centrally funded Engineering Colleges .

SO wait for last week of JUNE.

MHTCET : As mentioned on official website of Maharashtra DTE counselling will start on First Week of june. so get ready for it if you sit for MHTCET.

Most private colleges and many state government colleges give admissions on basis of MHTCET.

Hello!
     Please be clear while posting your query. If you can specify us a few cities you would like to gain admissions, then it will be easy for us to help you. Kindly do post your question in the comments section below.
Thank you!