As per your BITSAt scores you can convert BiTs Goa and Hyderabad for Chemical engineering & Pilani campus for Manufacturing engineering.

• For Mechanical engineering you can check following permutations and combination :
  

From your JEE Main scores you can get NIT Sikkim, Manipur, Durgapur, Hamirpur, raipur, Arunachal pradesh, Mizoram, Agartala, Nagland. Also IIITs like Sonepat, Una and Bhagalpur.
From MHTCET scores you can get SPCE, DJ Sanghvi, Kj Somaiya Vidyavihar and Sion, Thakur Kandivali, Father Agnel Bandra, Rajiv Gandhi Andheri, Thadomal Shahani Bndra.
https://engineering.careers360.com/articles/mht-cet-cutoff

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