Indian National Mathematical Olympiad Past Year Papers (Updated for 2026)

 

INMO (Indian National Mathematical Olympiad) is the third stage in the Indian Mathematical Olympiad programme that leads to the IMO (International Mathematical Olympiad). Students who qualify for INMO can become eligible for the International Mathematical Olympiad Training Camp (IMOTC), subject to the applicable selection and eligibility criteria. INMO is a four-and-a-half-hour written examination that includes 6 questions, with each question requiring a detailed proof. Students of Classes 8 to 12 can participate in the Mathematical Olympiad programme if they fulfil the prescribed eligibility criteria. For the 2025-2026 cycle, INMO 2026 was held on January 18, 2026, from 12:00 noon to 4:30 p.m. The top-performing students are considered for further training and selection for the International Mathematical Olympiad. 

 

At askIITians, you can find the past year's papers for INMO and practice for this olympiad. We have provided year-wise papers for INMO for your reference along with their stepwise solutions. Practising these papers can help you understand the level, format and proof-oriented nature of INMO problems and improve your mathematical problem-solving skills. 

 

Year-wise Past Papers for INMO (Indian National Mathematical Olympiad)
 

Year-wise INMO Papers
INMO Paper 2021	INMO Paper 2020
INMO Paper 2019	INMO Paper 2018
INMO Paper 2017	INMO Paper 2016
INMO Paper 2015	INMO Paper 2014
INMO Paper 2013	INMO Paper 2012
INMO Paper 2011	INMO Paper 2010
INMO Paper 2009	INMO Paper 2008
INMO Paper 2007	INMO Paper 2006
INMO Paper 2005	INMO Paper 2004
INMO Paper 2003	INMO Paper 2002
INMO Paper 2001	INMO Paper 2000

 

Benefits of Past Papers for INMO (Indian National Mathematical Olympiad)

 

1. Sharpen your skills for INMO: The more questions you practise for INMO, the more you can strengthen your mathematical problem-solving skills. Solving past papers helps you revise important concepts and understand how to apply them to challenging, proof-based problems. 

 

2. Prepare yourself psychologically for INMO: Many students who participate in olympiads may find the difficulty level challenging. Solving past papers gives you familiarity with the nature of INMO problems and can help build confidence before the examination. 

 

3. Enhance your time management skills: Time management is crucial for INMO. The examination consists of 6 advanced-level questions and lasts four and a half hours. As you practise past papers under timed conditions, you can learn how to allocate sufficient time to different problems and develop a suitable examination strategy. 

 

4. Understand your areas of weaknesses: Solving past papers helps you identify your strengths and areas that need improvement. This allows you to focus your preparation on topics and problem-solving techniques that require more practice. 

 

5. Understand the pattern of the exam: Past year papers familiarise you with the examination pattern and the types of proof-based questions asked in INMO. This helps you understand how to approach mathematical arguments, present detailed solutions and manage the examination effectively. 

 

Frequently Asked Questions 
 

1. Which topics are included in the INMO syllabus?

The Mathematical Olympiad syllabus includes topics from school mathematics along with additional olympiad-level areas. The major areas from which problems are posed are algebra, combinatorics, geometry and number theory. Important topics include inequalities, progressions, systems of linear equations, theory of equations, binomial coefficients, complex numbers, polynomials, functional equations, sequences, plane geometry, coordinate geometry, basic combinatorics, the pigeonhole principle, recursion, elementary graph theory, divisibility, congruences, the Chinese Remainder Theorem, Fermat's Little Theorem, Wilson's Theorem, Euler's phi function, Pythagorean triples and Diophantine equations. The difficulty level increases from RMO to INMO to IMO. 

 

2. How many students from Class 12 are chosen for INMO? 

For INMO 2026, students in Classes 8 to 11 were classified as Category A and students in Class 12 as Category B. From each region, the top 30 Category A students and the top 6 Category B students from RMO 2025 qualified for INMO 2026, along with 5 additional Category A girls under the Girls' quota. On the basis of INMO 2026, the selection criteria for further training included category-wise cutoffs and awardee selection. 

 

3. What is the benefit of giving olympiad exams in India? 

Olympiads provide students with opportunities to develop mathematical reasoning, analytical thinking, creativity and advanced problem-solving skills. They also expose students to challenging non-conventional problems and provide a pathway for students interested in participating in the national and international Mathematical Olympiad programme. 

 

4. What is the first stage of IMO?

In the Indian Mathematical Olympiad programme, the first stage is the Indian Olympiad Qualifier in Mathematics (IOQM). The current selection pathway is IOQM followed by the Regional Mathematical Olympiad (RMO) and then the Indian National Mathematical Olympiad (INMO). For the 2026-2027 cycle, IOQM 2026 is the first stage, RMO 2026 is the second stage and INMO 2027 is the third stage. INMO 2026 belonged to the 2025-2026 cycle and was held on January 18, 2026.