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If you enjoy maths for its own sake, the JEE is not the only road after Class 12. The Indian Statistical Institute (ISI) and the Chennai Mathematical Institute (CMI) run undergraduate programmes built around mathematics, and both admit students through their own entrance tests. This post explains how each admission works, using the institutes' own 2026 documents, shows two problems of the kind these tests reward, and gives a plan for the 2027 cycle.
What does ISI offer after Class 12?
The ISI Admission Notice for 2026-27 lists two three-year degrees for school leavers who studied Mathematics and English in Class 12:
B Stat (Hons), offered at Kolkata.
B Math (Hons), offered at Bengaluru.
Both carried a stipend of ₹5,000 a month in 2026-27 for students who meet the academic requirements. The ISI Prospectus 2026-27 listed 63 gender-neutral seats and 16 supernumerary seats for female candidates in each programme, plus up to 5 supernumerary seats for INMO awardees.
ISI also runs a four-year B SDS (Statistical Data Science) programme with different rules, including at least 75% in Class 12 and tuition fees, so read its section separately.
How is the ISI admission test structured?
According to the prospectus, B Stat and B Math applicants sit two papers in Class 12 level mathematics on the same day:
Forenoon, test code UGA: multiple-choice questions.
Afternoon, test code UGB: descriptive questions, where you write full solutions.
The 2026 business rules for B Stat and B Math say admission is on the basis of the written tests, with merit lists built from scores in both. Students selected for the International Mathematical Olympiad Training Camp after INMO can apply through a separate INMO channel, where selection is by interview, not the written test. An INMO certificate of merit alone does not qualify.
In 2026, applications ran from 12 February to 26 March and the test was on 10 May. The 2027 dates were not out when this was written, so watch admission.isical.ac.in.
How does CMI admission work?
CMI's information brochure for 2026-27 describes three B.S. (Honours) programmes: Mathematics, Mathematics and Computer Science, and Mathematics and Physics. From 2026 the old three-year B.Sc. became a four-year B.S., with an exit option after three years.
The CMI admissions page says:
There is one common entrance exam for all B.S. programmes, and you choose your programme after admission.
The exam for 2027-28 admissions is on Saturday, 15 May 2027, and applications open around 1 March 2027.
Students who reached certain olympiad camps in Class 11 or 12, such as IMOTC in maths or OCSC in physics, get direct admission. The page lists the exact cases.
The CMI syllabus page describes the exam as a test of aptitude for mathematics with objective questions and longer problems, based mostly on material up to Class 12, and posts past papers with solutions.
What kind of problem do these tests reward?
Here are two short problems in the style of the descriptive papers.
Example 1. How many positive divisors does 720 have, and how many of them are perfect squares?
Factorise: 720 = 2⁴ × 3² × 5.
A divisor is 2ᵃ × 3ᵇ × 5ᶜ with a from 0 to 4, b from 0 to 2, c from 0 to 1. That gives 5 × 3 × 2 = 30 divisors.
A square divisor needs every exponent even: a in {0, 2, 4}, b in {0, 2}, c = 0. That gives 3 × 2 × 1 = 6 square divisors (1, 4, 9, 16, 36, 144).
Example 2. Prove that n³ − n is divisible by 6 for every integer n.
Factorise: n³ − n = (n − 1) n (n + 1), a product of three consecutive integers.
Among any three consecutive integers, one is a multiple of 3.
Among any two consecutive integers, one is even, so the product is even.
Being divisible by both 2 and 3, and since 2 and 3 share no factor, the product is divisible by 6.
A full-credit UGB answer looks like Example 2: each step stated, each reason given. Our post on counting with permutations and combinations covers the counting ideas in Example 1.
Common mistakes
Practising only MCQs. UGB and CMI's longer problems need written arguments. A correct answer with no reasoning earns little.
Skipping number theory and inequalities. These are thin in board exams but common in proof-style papers. Olympiad material helps; see our guide to the maths olympiad and IOQM.
Missing deadlines. ISI and CMI have separate portals and dates, both earlier than many families expect.
A practice routine from now to May
Each week: one past paper section from ISI or CMI, untimed, writing full solutions.
Then: compare with the official solutions and rewrite any step you skipped.
From March: two timed full papers a month, plus a log of topics that keep costing you marks.
When a concept such as modular arithmetic or the AM-GM inequality is shaky, the Fermi Concept Library has a lesson for each concept in mathematics, so you can fix the idea before going back to the problem.
This week, download one CMI past paper and one ISI sample paper and try a single problem from each with a full written proof.
