GATE XE study plan

Derive and apply the rank-nullity theorem to solve systems of linear equations, distinguishing consistent, inconsistent and underdetermined cases

Compute eigenvalues and eigenvectors of 3x3 matrices by hand and use them to diagonalise a matrix where possible

Build a one-page formula sheet covering vector calculus identities, matrix operations and Taylor/Maclaurin expansions

Solve 25 mixed linear algebra and calculus problems under timed conditions without notes

Evaluate double and triple integrals in Cartesian, polar, cylindrical and spherical coordinates, choosing the coordinate system that simplifies the region

Apply Green's, Stokes' and Gauss divergence theorems to convert line, surface and volume integrals

Solve first-order ODEs by separation of variables, integrating factors and exact differentials

Solve second-order linear ODEs with constant coefficients including both homogeneous and particular solutions

Compute partial derivatives, gradients, directional derivatives, Jacobians and Hessians for multivariable functions

Classify stationary points of two-variable functions using the second-derivative test

Apply Lagrange multipliers to constrained optimisation problems

Evaluate complex integrals using Cauchy's integral theorem and residue calculus

Determine convergence of series using ratio, root, comparison and integral tests

Solve first-order and second-order linear and non-linear partial differential equations for common engineering boundary conditions

Apply Fourier series expansion to periodic functions and identify symmetry shortcuts

Compute Laplace and Fourier transforms of standard functions and use them to solve initial-value problems

Solve probability problems involving conditional probability, Bayes' theorem and standard distributions

Map the XE sectional syllabus to identify which two optional sections you will attempt and confirm the exact topic list for each

Derive and apply the core governing equations of your chosen first section to standard textbook problems

Build a concept map linking the key formulas of the chosen section to typical question patterns

Solve 20 previous-style problems in the chosen section with a target of 70 percent accuracy

Derive and apply the core governing equations of your chosen second section to standard problems

Work through numerical methods or material and energy balance problems typical of the section, showing every step

Compare and contrast the two chosen sections to decide the attempt strategy for the exam

Solve 20 problems in the second section with a target of 70 percent accuracy

Integrate mathematics techniques into XE section problems by solving mixed sets that require both

Complete two full-length mixed mock papers under strict exam timing

Audit every wrong answer and classify errors as conceptual, calculation or time-management

Rebuild the formula sheets from memory and check them against the originals

Re-solve every previously missed problem until each is correct without reference material

Run three timed sectional sprints of 45 minutes each, alternating Mathematics and the XE section

Finalise the exam-day plan covering question order, time per section and skip criteria

Rest and taper: reduce study volume in the final three days and protect sleep