INMO is the Indian National Mathematical Olympiad. Practise sustained proof work across algebra, number theory, combinatorics and geometry. Allow time to explore, choose a promising representation and turn your ideas into a complete proof.
Paper format: 6 questions · 270 minutes · Written proofs.
These five original sample mocks follow the response format and duration shown below. They are practice material, not official papers, endorsed tests, selection predictions or a calibrated replica of any particular year’s difficulty.
INMO mock paper 1
6 questions with hints and complete worked solutions.
Read online or print a question-only copy.
INMO mock paper 2
6 questions with hints and complete worked solutions.
Read online or print a question-only copy.
INMO mock paper 3
6 questions with hints and complete worked solutions.
Read online or print a question-only copy.
INMO mock paper 4
6 questions with hints and complete worked solutions.
Read online or print a question-only copy.
INMO mock paper 5
6 questions with hints and complete worked solutions.
Read online or print a question-only copy.
From answers to proofs
Before a full mock, work through direct proof and contradiction and modular arithmetic and valid cancellation. For geometry, review triangle correspondence and similarity.
Readiness check: Can you explain why the difference of the squares of two consecutive integers is odd for every integer, and not just for the examples you tried? Write the two integers as n and n + 1, expand their square difference to 2n + 1, then explain why that expression is odd. A proof states the domain, gives a reason for each step and covers every permitted case. If that structure is unfamiliar, practise with the worked examples in the proof lesson before using a timer.
Before you start
Practise sustained proof work across algebra, number theory, combinatorics and geometry. Allow time to explore, choose a promising representation and turn your ideas into a complete proof.
Try mixed preparation through the concept lessons and use the India official past-paper guide to compare the real contest format and demands.
Format source and selection rules
Official INMO programme and current notices. Format checked 27 September 2026. Eligibility, regional quotas, qualification and registration requirements are set by the organisers; completing these mocks does not qualify you for a selection stage.