Singh is a Fellow of the Indian National Science Academy (INSA), India's apex body of scientists and technologists.
Her dissertation titled 'Contributions to the Theory of Linear Operators in Locally Convex Spaces', was supervised by Frank Smithies.
[6] Singh began teaching immediately after completing her master's degree, as faculty at Indraprastha College, Delhi University.
In 1974, Singh was appointed reader in mathematics at Delhi University South Campus and continued on as professor from 1984 to 2008.
[2][6] Singh was awarded the Rai Bahadur Brij Mohan Lal Saheb Memorial Gold Medal and the Ravi Kanta Devi Prize from Delhi University.