The nose required sutures, and may need some corrective surgeries later, the doctors said.
CSE said: "Cyclists in Indian cities are being edged out systematically to make way for cars - sometimes literally so."
"Narain and CSE have been vocal supporters of people's right to walk and cycle on the roads of urban India," it said.
The 2005 Padma Shri awardee, Narain has also received the World Water Prize for work on rainwater harvesting and for its policy influence in building paradigms for community based water management.
She is also the director of the Society for Environmental Communications and publisher of the fortnightly magazine, Down To Earth.
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