[2] Sinha is married to Kapil Hari Paranjape, who is a professor of mathematics at the Indian Institute of Science Education and Research, Mohali.
Her maternal grandfather was Dr. Prabodh Chandra Bagchi, formerly the vice-chancellor of Viswa Bharati University and historian.
Sinha holds a Master of Science (Five Years Integrated Programme in Physics) from the Indian Institute of Technology, Kanpur, in 1985.
[4] Sinha is currently a professor at the Indian Institute of Science Education and Research, Mohali and works in the field of nonlinear physics.
[5] Her research areas include nonlinear dynamics, chaos, complex systems, networks, and computation.