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  1. Prepare for an exam
  2. /Olympiads
Exam preparation

Olympiads preparation

Hard problems for the national and international olympiads. Think first, then calculate.

48 mock tests · 16 questions · 16 problems

Paper pattern

Our full olympiad papers follow this pattern.

  • Physics, Chemistry, Mathematics and Biology

    Each subject: 15 questions, 30 minutes

    Correct answer +3, wrong answer −1

Timed mock tests

Chapter tests and full papers. You get your score as soon as you finish.

  • MathematicsIntroduction to Trigonometry: Olympiad Style Test 10 questions · 20 minStart now
  • MathematicsArithmetic Progressions: Olympiad Style Test 10 questions · 20 minStart now
  • BiologyPlant Kingdom: Challenge Paper 10 questions · 20 minStart now
  • MathematicsThe Quadratic Formula: Olympiad Style Test 10 questions · 20 minStart now
  • BiologyControl and Coordination: Challenge Paper 10 questions · 20 minStart now
  • BiologyRespiration: Challenge Paper 10 questions · 20 minStart now
  • All Physics papers16
  • All Chemistry papers15
  • All Mathematics papers9
  • All Biology papers8

Question sets

No timer. Work at your own pace.

  • PhysicsJEE Advanced Physics: Gravitation10 questions
  • PhysicsJEE Advanced Physics: Rotational Motion9 questions

All Olympiads question sets →

Practice questions and problems

Hardest first. Try each one on paper before you see the answer.

Physics

Questions

  • AdvancedA satellite moves in a circular orbit of radius r round a planet. Its rocket fires for a very short time along its direction of motion and raises its speed by 10%. Which of the following statements are correct?
  • AdvancedA small moon goes round a planet in a circular orbit with a period of 32 days. Suppose the moon were suddenly stopped in its orbit. Treating the planet and the moon as points, how long would the moon take to fall into the planet?

All problems for this exam

  • Olympiad problems →

The full list, by topic and level, each with a worked solution.

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Advanced
Three stars, each of mass 2.0 × 10³⁰ kg, sit at the corners of an equilateral triangle of side 1.0 × 10¹¹ m. They move together in one circle round the centre of the triangle, under their own gravity alone, so that the triangle keeps its shape, as shown in the figure. Take G = 6.67 × 10⁻¹¹ N m²/kg². What is the period of their motion?
  • AdvancedA thin uniform spherical shell has mass M, radius R and centre O. A small hole is cut in it at a point H, as shown in the figure. Which of the following statements are correct?
  • AdvancedA planet moves round the Sun in an ellipse of eccentricity 0.50, with a period of 12 years. B and B' are the two ends of the minor axis, and P is the point nearest the Sun, as shown in the figure. How long does the planet take to go from B to B' through P?
    • More Physics questions for Olympiads →

    Problems with worked solutions

    • AdvancedTwo stars, A of mass 2M and B of mass M, where M = 1.0 × 10³⁰ kg, move in circular orbits about…
    • AdvancedA planet is a uniform sphere of radius R = 3200 km and centre O.
    • AdvancedA projectile is fired from the Earth's surface with a speed v₀ = √gR = 8.0 km/s, in a direction 30°…
    • AdvancedA satellite moves in a circular orbit of radius 2R round the Earth, where R = 6400 km is the…
    • AdvancedA plank of mass 4.0 kg and length 1.5 m lies on a smooth horizontal floor.
    More Physics problems for Olympiads →