India, June 8 -- By the time she was in the ninth grade, Arohi Deshpande had decided she wanted to study engineering, and not just at any college but at India's top-ranked engineering college, the Indian Institute of Technology.

She had a role model at home. Her mum Amita, a civil engineer with a specialisation in environmental engineering, had done her M.Tech at IIT, Kanpur and works at a private company.

Her dad Prasad is an electrical engineer with a master's degree from the University of South Florida. A maternal uncle as well as a maternal great-aunt are in the sciences.

So, when Arohi spoke about wanting to get into IIT, of course the family rallied behind her.

That support extended to relocating from Pune to Kota, India's best-...