GATE XE study guide
GATE XE · Work through your exam, one topic at a time.
GATE 2025 (Graduate Aptitude Test in Engineering) is a national-level computer-based examination organised by Indian Institute of Technology Roorkee on behalf of the National Coordination Board – GATE, Department of Higher Education, Ministry of Education, Government of India. It primarily tests comprehensive understanding of undergraduate-level subjects in Engineering, Technology, Architecture, Science, Commerce, Arts and Humanities. GATE 2025 has 30 test papers comprising full papers and sectional papers; candidates may appear for one or two papers from the allowed two-paper combinations. The XE (Engineering Sciences) paper is a sectional paper: it pairs a compulsory Engineering Mathematics section with a chosen optional engineering-sciences section, which makes it attractive to candidates from science backgrounds or those whose discipline does not map neatly onto a single full paper. Topics on this exam: Engineering Mathematics and Engineering Sciences sectional paper (XE). The GATE XE study guide has 2 sections and about 717 words.
01Engineering Mathematics (XE Section A, compulsory)
Engineering Mathematics is Section A of GATE XE and is compulsory for every candidate regardless of the sectional paper chosen. It rewards computational accuracy, not proof-writing: short questions on linear algebra, calculus and vector calculus, complex variables, ordinary and partial differential equations, probability and statistics, and numerical methods. Consistency of Ax = b requires rank(A) = rank([A b]); for square systems a nonzero determinant is the quick sufficient check. For a 2×2 matrix, λ² − (trace)λ + det = 0.
361 words, about 2 min02Engineering Sciences Sectional Paper (XE Section B)
Section B of XE is one sectional paper chosen at application stage: XE-A Materials Science, XE-B Solid Mechanics, XE-C Thermodynamics, XE-D Polymer Science and Engineering, XE-E Food Technology, or XE-F Atmospheric and Oceanic Sciences. All Section B questions come from that single paper, and they test numerical application of standard formulae rather than derivations. Solid Mechanics: principal stresses σ₁,₂ = (σx+σy)/2 ± √[((σx−σy)/2)² + τxy²]; torsion τ = Tr/J; Euler buckling Pcr = π²EI/(KL)² holds only above the critical slenderness ratio. Thermodynamics: entropy balance on a control volume; Rankine pump work ≈ v(P₂−P₁); Brayton efficiency 1 − rp^(−(γ−1)/γ).
356 words, about 2 min