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IOQM · Previous year papers · 2024

IOQM 2024 previous year paper · official paper and PYQ-pattern practice

6 PYQ-pattern questions modelled on the 2024 paper (which had 30) · 180 min

Every question here is freshly worded in the pattern of the 2024 paper — same topics, style and difficulty — not the original questions, which Shishya does not reproduce.

The original 2024 paper, as HBCSE-TIFR (Mathematical Olympiad Cell) published it

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6 PYQ-pattern questions modelled on the 2024 paper (which had 30) · instant scoring · topic-wise analysis. Sign up with Google, free, to attempt and track your progress.

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IOQM 2024 PYQ-pattern questions

Showing 6 of the 6 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

  1. Q1 · Basic Preliminaries

    What is 40% of 60% of 250?

    • A. 50
    • B. 60
    • C. 75
    • D. 90
    Answer and solution

    Answer: B

    40% of 60% of 250 = (40/100) × (60/100) × 250 = 0.4 × 0.6 × 250 = 60.

  2. Q2 · Combinatorics

    In how many ways can 5 boys and 4 girls be arranged in a row such that no two girls sit together?

    • A. 43200
    • B. 86400
    • C. 2880
    • D. 1440
    Answer and solution

    Answer: A

    Arrange 5 boys in 5! = 120 ways. This creates 6 gaps; place 4 girls in these gaps so no two are adjacent: 6P4 = 360. Total = 120 × 360 = 43200.

  3. Q3 · Geometry

    A circle with center O has radius 10 cm. Two chords AB and CD intersect at point P inside the circle such that AP = 8 cm, PB = 6 cm, and CP = 12 cm. Find the length of PD in cm.

    • A. 3
    • B. 4
    • C. 5
    • D. 6
    Answer and solution

    Answer: B

    By the intersecting chords theorem, when two chords intersect inside a circle, AP × PB = CP × PD. Substituting: 8 × 6 = 12 × PD, so 48 = 12 × PD, giving PD = 4 cm.

  4. Q4 · Trigonometry

    If sin θ + cos θ = 7/5, where 0 < θ < π/2, find the value of 100 × sin θ × cos θ.

    • A. 12
    • B. 24
    • C. 48
    • D. 36
    Answer and solution

    Answer: C

    Squaring both sides: sin²θ + cos²θ + 2sinθcosθ = 49/25. Since sin²θ + cos²θ = 1, we get 1 + 2sinθcosθ = 49/25, so 2sinθcosθ = 24/25, hence 100 × sinθcosθ = 12. [Correction 2026-08-31: answer key corrected to C after student report + independent re-verification. Squaring sin θ + cos θ = 7/5 gives 1 + 2sin θ cos θ = 49/25, so sin θ cos θ = 12/25. Therefore 100 × sin θ × cos θ = 100 × 12/25 = 48.]

  5. Q5 · Number Theory

    How many positive integers less than or equal to 120 are divisible by exactly one of 4 or 6 (but not both)?

    • A. 30
    • B. 32
    • C. 34
    • D. 36
    Answer and solution

    Answer: A

    Multiples of 4 up to 120: 30; of 6: 20; of LCM 12: 10. Exactly one = (30+20) - 2*10 = 30.

  6. Q6 · Algebra

    Let x and y be real numbers satisfying x + y = 7 and x² + y² = 29. Find the value of x³ + y³.

    • A. 91
    • B. 133
    • C. 147
    • D. 161
    Answer and solution

    Answer: B

    Using the identity x³ + y³ = (x + y)³ - 3xy(x + y), first find xy from (x + y)² = x² + y² + 2xy, so 49 = 29 + 2xy giving xy = 10. Then x³ + y³ = 7³ - 3(10)(7) = 343 - 210 = 133.

Breakdown by subject

  • Mathematics

    6 questions

IOQM 2024 previous year paper — frequently asked questions

Where can I solve the IOQM 2024 previous year paper (PYQ) free online?
At https://shishya.in/exams/IOQM/pyq/2024 you can solve IOQM 6 PYQ-pattern questions modelled on the 2024 paper free. Shishya does not reproduce the original paper: every question is freshly worded in that year's pattern — same topics, style and difficulty, new wording and numbers, and this set holds 6 questions, not the whole paper. They run as a timed mock with instant scoring, step-by-step solutions and topic-wise weak-area analysis. No fee and no coaching enrolment needed. The original 2024 paper is published by HBCSE-TIFR (Mathematical Olympiad Cell): https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2025/04/ioqm-2024-english.pdf
Are these the actual IOQM 2024 paper questions?
No. They are PYQ-pattern questions modelled on the IOQM 2024 paper — freshly worded practice questions in the same pattern, not the original questions, which Shishya does not reproduce. This set holds 6 questions. The original 2024 paper is published by HBCSE-TIFR (Mathematical Olympiad Cell): https://olympiads.hbcse.tifr.res.in/wp-content/uploads/2025/04/ioqm-2024-english.pdf For a whole paper in one sitting, Shishya has a free full-length mock in the real pattern (30 questions, 180 minutes): the "Full-Length Mock (Real Pattern)" tile at https://shishya.in/exams/IOQM
Do these IOQM 2024 pattern questions come with solutions and analysis?
Yes — every question carries a worked solution, and on submitting you get an instant score with a topic-wise breakdown showing exactly which areas to revise. Wrong answers are auto-collected into a free Mistake Notebook for one-tap re-practice until cleared.
Are previous year papers enough to crack IOQM?
Previous-year papers are the best signal of what the exam actually tests, but they work best with targeted practice and a plan. On Shishya (all free): solve PYQ-pattern sets year-wise, drill weak topics via the Mistake Notebook, follow a day-by-day plan from the Personal Coach at https://shishya.in/coach and sit the Sunday live test at https://shishya.in/live-test to see where you stand nationally.