GATE XE case studies
GATE XE · Put your knowledge to work in context.
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. The GATE XE case studies are 5 cases and about 3,413 words.
1Recirculation Gain and the Limits of a Linear Stability Certificate
A two-tank thermal loop is linearised about a nominal operating point. The deviation state x = [T1, T2, T3]^T in kelvin satisfies dx/dt = A x, where A = [[0, 1, 0], [0, 0, 1], [-k, -3, -2]] and k 0 is the recirculation-valve gain in h^-1.
702 words, about 4 min2Stiff CSTR Integration: Stability Step Versus Accuracy Target
A lab-scale CSTR is modelled by dy/dt = -80(y - 1.02) + 0.4 sin(2t), y(0) = 0, where y is dimensionless concentration and t is in minutes. A student integrates with explicit Euler using h = 0.02 min and obtains a smooth response.
715 words, about 4 min3Pump Suction Lift, Cavitation Margin, and Where to Throttle
A centrifugal pump draws water at 60 °C from an open sump and delivers 45 m³/h to a header. The pump centreline is 4.2 m above the sump free surface.
660 words, about 3 min4Bracket Material Choice When Deflection Governs
A cantilever support bracket is a solid rectangular bar of width b = 40 mm and depth h = 80 mm, with length 1.2 m, loaded by a 2.0 kN point load at the free end. Two materials are stocked: hot-rolled steel with E = 200 GPa, ρ = 7850 kg/m³ and σ allow = 160 MPa; and 6061-T6 aluminium with E = 69 GPa, ρ = 2700 kg/m³ and σ allow = 110 MPa.
645 words, about 3 min5Two-Stage Air Compression and a Suspicious Discharge Temperature
A plant needs 1.2 kg/s of air at 700 kPa. Air is taken at 100 kPa and 300 K.
691 words, about 3 min