GATE Statistics (ST)

Your paper has no Engineering Mathematics section. Its mathematics is Sections 1 and 2, Calculus and Matrix Theory, asked at the depth of a first course in real analysis and linear algebra rather than as engineering technique. Limits, continuity, derivatives, maxima and minima and definite integrals are in the borrowed limits, derivatives and integration chapters; partial derivatives, saddle points and multiple integrals in the Multivariable Calculus chapter; rank, eigenvalues and Cayley–Hamilton in the Linear Algebra chapter; and rank–nullity, quadratic forms and singular values in the Vector Spaces chapter. Three chapters are written for this paper alone, because no shared chapter teaches what they do at your depth: countable sets, sequences, series and their convergence tests, power series, uniform continuity, Taylor’s theorem and the Riemann and improper integrals; several-variable limits, directional derivatives and the gradient, Taylor’s theorem, Lagrange multipliers and the Jacobian; and subspaces and row reduction, trace, determinant and inverse, inner products and Gram–Schmidt, Hermitian and unitary matrices, similarity, positive semidefinite matrices and the SVD. The Vector Calculus chapter is deliberately left off your list — your syllabus names the gradient and nothing after it. All ten discipline sections — Probability through Regression Analysis — have chapters of their own.