India · IITs (JAM 2026 organised by IIT Bombay) · pg
Computer-based, 3 hours, 60 questions, 100 marks, English. Section A 30 MCQs (10 x 1 mark, 20 x 2 marks); Section B 10 MSQs (2 marks, no negative or partial marking); Section C 20 NAT (10 x 1, 10 x 2, no negative). MCQ wrong answers lose 1/3 or 2/3 mark.
Admission to MSc Statistics and joint MSc-PhD programmes at IITs (89 programmes across 22 IITs for 2026-27 across all JAM papers). Pattern read on the JAM 2026 syllabus page; the 30/70 mathematics-statistics split is as Laisha knows it and was not on the page read.
Official source: https://jam2026.iitb.ac.in/Syllabus.html
Original questions written to this exam's published syllabus and pattern. Not past papers.
1. Which of these sets is uncountable?
A. The real numbers in (0, 1)
Cantor's diagonal argument shows (0, 1) is uncountable. Q and Z are countable, and finite subsets of N can be listed by size and largest element.
Real Analysis for Statistics · Sets, countability and the real number system
2. Which subset of R³ is a subspace?
B. The plane x + y + z = 0
A subspace must contain 0 and be closed under addition and scaling; x + y + z = 1 misses 0, x ≥ 0 fails under negation, and the union of two axes is not closed under addition.
Linear Algebra & Matrix Theory for Statistics · Vector spaces, subspaces, linear independence, basis and dimension
3. The integrating factor of dy/dx + y/x = x (x > 0) is:
B. x
e^(∫(1/x)dx) = e^(ln x) = x.
Differential Equations, Finite Differences & Numerical Analysis · Ordinary differential equations of first order: exact, linear and Bernoulli equations
4. A collection 𝓕 of subsets of Ω contains Ω. Which further pair of closure properties makes 𝓕 a σ-field?
B. Closure under complements and under countable unions
A σ-field needs Ω, complements and countable unions; countable intersections then follow by De Morgan. Closure under complements and finite unions only defines a field (algebra), which is weaker. Arbitrary uncountable unions are not required, and without complements the collection need not be a σ-field.
Probability Theory · Sample spaces, sigma-fields and the axioms of probability
5. A geometric variable X counts the failures before the first success in independent trials with success probability 0.25. What is E(X)?
A. 3
For the failures-before-first-success version, E(X) = q/p = 0.75/0.25 = 3. The trials-until-success version has mean 1/p = 4; 12 is the variance q/p².
Probability Distributions & Sampling Distributions · Discrete distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric and multinomial
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