Dr. Nadeem Rao's research interests lie primarily in "Approximation Theory", with a specific focus on the "convergence properties of sequences of positive linear operators". His work involves constructing and analyzing modified operator families (e.g., Szász, Bernstein, Baskakov, Schurer, Kantorovich types) often incorporating special polynomials (like Appell, Bernoulli, Hermite) and shape parameters to improve approximation accuracy. His academic interests are broad, encompassing the teaching of a wide range of pure and applied mathematics at both undergraduate and postgraduate levels, including Real Analysis, Complex Analysis, Linear Algebra, Abstract Algebra, Numerical Analysis, Measure Theory, and Differential Equations. He is also actively involved in research supervision, editorial board memberships, and peer review for major international journals.