GATE MA case studies
GATE MA · Put your knowledge to work in context.
GATE 2026 is a national-level examination that assesses candidates on undergraduate-level subjects across Engineering, Technology, Science, Commerce, Arts, Architecture and Humanities. It is being organised by IIT Guwahati, working in collaboration with IISc Bengaluru and the other 22 IITs on behalf of the National Coordination Board, Department of Higher Education, Ministry of Education, Government of India. The GATE MA case studies are 5 cases and about 1,981 words.
1Diagonalisability and a Krylov basis in a parametrised vibration model
A three-degree-of-freedom vibration model is reduced, after nondimensionalisation, to the real matrix A(α) = [[1,1,0],[0,2,α],[0,0,2]], with α real. The engineer needs to know whether the modes can be decoupled by a change of basis, and how the system behaves at the critical parameter value α=1.
440 words, about 2 min2Pointwise versus uniform convergence of a quadrature sequence
On [0,1] define f n(x)=n x (1-x²)^n for n≥1. A numerical analyst uses ∫ 0^1 f n(x) dx as a quadrature weight and observes that the computed values approach 0.5, while pointwise values appear to vanish.
406 words, about 2 min3Counting zeros of a polynomial on and between two circles
A control engineer needs the number of unstable modes, which are the zeros of p in the annulus 1< z <2, and must also confirm that no zero lies exactly on the unit circle, the stability boundary. Direct root finding is unreliable at this scale, so Rouché's theorem is to be used.
370 words, about 2 min4Resonant boundary-value problem and the Fredholm alternative
Consider the boundary-value problem y''+y=f(x), 0<x<π, y(0)=y(π)=0. A mechanical model is driven at frequency 1, exactly the first natural frequency of the homogeneous problem.
402 words, about 2 min5Choosing between unbiased estimators of a uniform endpoint
A reliability laboratory observes n=10 independent lifetimes, in hundreds of hours, from a uniform model on (0,θ), with θ 0 unknown. The sample mean is 4.2 and the sample maximum is 9.1.
363 words, about 2 min