SOF IMO 2025 previous year paper practice · PYQ-pattern set

SOF IMO 2025 PYQ-pattern questions

Showing 10 of the 13 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 · Verbal and Non-Verbal Reasoning

   Find the odd one out from the given options.

   • A. Triangle, Square, Pentagon
   • B. Rose, Lotus, Tulip
   • C. Car, Bus, Train
   • D. Dog, Cat, Table
   Answer and solution

   Answer: D

   Dog and Cat are animals, while Table is a non-living thing. All others in option D are not from the same category, making it the odd group.

2. Q2 · Coding-Decoding

   If in a certain code 'TIGER' is written as 'UJHFS', how is 'LION' written in that code?

   • A. MJPO
   • B. MJPN
   • C. LIPO
   • D. MJQO
   Answer and solution

   Answer: A

   Each letter in 'TIGER' is shifted one position forward to get 'UJHFS'. Applying the same rule, L→M, I→J, O→P, N→O, giving 'MJPO'.

3. Q3 · Mathematical Operations

   If '×' means '+', '+' means '÷', '÷' means '−', and '−' means '×', find the value of 20 − 5 + 10 × 15.

   • A. 25
   • B. 27
   • C. 125
   • D. 115
   Answer and solution

   Answer: A

   Substituting: − becomes ×, + becomes ÷, × becomes +. So 20×5÷10+15 = 100÷10+15 = 10+15 = 25.

4. Q4 · Number Systems

   If 3⁴ × 27 = 3ˣ, then find the value of x.

   • A. 5
   • B. 6
   • C. 7
   • D. 8
   Answer and solution

   Answer: C

   Since 27 = 3³, we have 3⁴ × 3³ = 3⁽⁴⁺³⁾ = 3⁷. Therefore x = 7.

5. Q5 · Linear Equations in Two Variables

   The sum of two numbers is 45 and their difference is 9. What are the two numbers?

   • A. 27 and 18
   • B. 24 and 21
   • C. 30 and 15
   • D. 28 and 17
   Answer and solution

   Answer: A

   Let the numbers be x and y. Then x + y = 45 and x - y = 9. Adding both equations: 2x = 54, so x = 27. Substituting back: y = 18.

6. Q6 · Triangles

   In triangle ABC, AB = AC and ∠BAC = 40°. If D is a point on BC such that AD bisects ∠BAC, what is the measure of ∠ADB?

   • A. 90°
   • B. 100°
   • C. 110°
   • D. 120°
   Answer and solution

   Answer: A

   In an isosceles triangle with AB=AC, the angle bisector from apex A to base BC is also perpendicular to BC. Thus AD is perpendicular to BC, making ∠ADB = 90°.

7. Q7 · Constructions

   To construct an angle of 67.5°, which of the following constructions is most efficient?

   • A. Bisect an angle of 135°
   • B. Bisect an angle of 120°
   • C. Trisect an angle of 202.5°
   • D. Add 60° and 7.5°
   Answer and solution

   Answer: A

   67.5° = 135°/2. We can construct 135° (90° + 45°) and then bisect it to get 67.5°.

8. Q8 · Heron's Formula

   The sides of a triangle are 13 cm, 14 cm and 15 cm. What is the area of the triangle?

   • A. 84 cm²
   • B. 90 cm²
   • C. 96 cm²
   • D. 105 cm²
   Answer and solution

   Answer: A

   Using Heron's formula: s = (13+14+15)/2 = 21 cm. Area = √[21(21-13)(21-14)(21-15)] = √[21×8×7×6] = √7056 = 84 cm².

9. Q9 · Quadratic Equations (Class 10)

   If the roots of the equation x² - 7x + k = 0 are equal, what is the value of k?

   • A. 49/4
   • B. 49/2
   • C. 7
   • D. 14
   Answer and solution

   Answer: A

   For equal roots, discriminant = 0. Thus, b² - 4ac = 0: 49 - 4k = 0, so k = 49/4.

10. Q10 · Statistics

    The median of the data 15, 12, 18, 21, x, 24 arranged in ascending order is 19. What is the value of x?

    • A. 20
    • B. 19
    • C. 18
    • D. 22
    Answer and solution

    Answer: A

    Sorted data: 12,15,18,x,21,24. Median = average of 3rd and 4th terms = (18+x)/2 = 19, giving 18+x=38, so x=20.