IIT JAM MS case studies
IIT JAM MS · Put your knowledge to work in context.
JAM MS is the Mathematics and Statistics paper of the Joint Admission Test for Masters (JAM), conducted by the GATE/JAM Office at IIT Madras on behalf of all IITs, as stated on the official JAM site. It is a postgraduate entrance examination for candidates seeking admission to M.Sc. and related master's programmes in mathematics, statistics, and allied areas at participating IITs and other institutions. The paper is split evenly between two subject domains: Mathematics (50%) and Statistics (50%). Topics on this exam: Mathematics and Statistics. The IIT JAM MS case studies are 5 cases and about 1,869 words.
1Uniform convergence and the limit of an integral
During a revision session on sequences of functions, a student considers f n(x) = n x(1 − x²)^n on [0,1], n ≥ 1. The student computes the pointwise limit: at x=0, f n(0)=0; for 0<x≤1, the factor (1−x²)^n decays exponentially while n grows linearly, so f n(x)→0; at x=1, f n(1)=0.
442 words, about 2 min2A parameterised matrix that is never diagonalisable
A student is given A a = [[2,1,0],[0,2,1],[0,0,a]] with real parameter a. They compute the characteristic polynomial det(A a − λI) = (2−λ)²(a−λ).
396 words, about 2 min3Uniqueness failure in an initial-value problem
A student studies the initial-value problem y′(t) = √ y(t) , y(0)=0. The right-hand side f(y)=√ y is continuous everywhere, including at y=0.
305 words, about 2 min4One-sided and two-sided p-values after seeing the data
A researcher observes 218 successes in 400 independent Bernoulli trials. Before data collection, the alternative was H1: p 0.5, with α=0.05.
370 words, about 2 min5t-interval versus z-interval near a decision threshold
A nutrition study measures a biomarker in n=16 adults. The sample mean is 12.4 mg/L and the sample standard deviation is 3.2 mg/L.
356 words, about 2 min