GATE Physics (PH)

Your paper has no Engineering Mathematics section. Its mathematics is Section 2, Mathematical Physics, one of eleven physics sections, and it is asked the way physics uses it. Linear vector spaces and basis are in the Vector Spaces chapter (its rank–nullity section; its decompositions and quadratic forms go beyond your list); eigenvalues, eigenvectors and diagonalisation are in the Linear Algebra chapter. Your linear differential equations are the first-order linear form in the borrowed first-order chapter and the second-order equations in the Differential Equations chapter — its Laplace and PDE sections are beyond your list. Complex analysis — Cauchy–Riemann, Cauchy’s theorem, residues — is the Complex Variables chapter; Fourier analysis starts in the first two sections of the Transforms chapter, and you can skip its z-transform. Two chapters are written for this paper alone, because no shared chapter teaches what they do: inner products, orthogonality, Gram–Schmidt and completeness, similarity transformations with Hermitian and unitary matrices, and tensors; and the classification of singularities, real integrals by contour integration, Parseval’s theorem, the Fourier transform of a Gaussian and the Dirac delta. Vector calculus is not named in Section 2, but the electromagnetic-theory chapter uses it throughout, and the Vector Calculus chapter is there if you need it. All ten discipline sections — Measurements and Error Analysis through Electronics — have chapters of their own.