SOF IMO 2024 previous year paper practice · PYQ-pattern set

SOF IMO 2024 PYQ-pattern questions

Showing 10 of the 16 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 · Number and Alphabet Series

   Complete the number series: 3, 9, 27, 81, ?

   • A. 162
   • B. 243
   • C. 216
   • D. 324
   Answer and solution

   Answer: B

   Each term is obtained by multiplying the previous term by 3. So, 81 × 3 = 243.

2. Q2 · Direction Sense Test

   Ravi walks 8 m towards North, then turns right and walks 6 m, then turns right again and walks 8 m. How far is he from the starting point?

   • A. 6 m
   • B. 8 m
   • C. 10 m
   • D. 14 m
   Answer and solution

   Answer: A

   After the movements, Ravi ends up 8 m North and 8 m South (canceling out), leaving only 6 m East displacement. So, he is 6 m from the starting point.

3. Q3 · Ranking and Arrangement

   In a row of 50 students, Priya is 18th from the left end. What is her position from the right end if she and the student at the 25th position from the left exchange their positions?

   • A. 26
   • B. 25
   • C. 33
   • D. 27
   Answer and solution

   Answer: A

   After exchange, Priya takes the position 25th from the left. From the right, her position = 50 − 25 + 1 = 26.

4. Q4 · Mirror and Water Images

   Select the correct mirror image of the given figure (containing the letters 'MNP' arranged horizontally), if the mirror is placed vertically to the right.

   • A. PNM (letters reversed but not flipped)
   • B. Laterally inverted PNM
   • C. MNP upside down
   • D. Laterally inverted MNP
   Answer and solution

   Answer: B

   When a mirror is placed vertically on the right, the image is laterally inverted (horizontally flipped) and the order reverses, giving laterally inverted PNM.

5. Q5 · Matrix and Pattern Completion

   Complete the series of numbers in the matrix: 1st row: 4, 9, 16 2nd row: 9, 16, 25 3rd row: 16, 25, ? What is the missing number?

   • A. 30
   • B. 34
   • C. 36
   • D. 40
   Answer and solution

   Answer: C

   The pattern shows perfect squares: 2², 3², 4² in the first row; 3², 4², 5² in the second row; 4², 5², 6² in the third row. So the missing number is 6² = 36.

6. Q6 · Circles

   Two chords AB and CD of a circle intersect at point P inside the circle. If AP = 6 cm, PB = 4 cm, and CP = 3 cm, what is the length of PD?

   • A. 6 cm
   • B. 8 cm
   • C. 9 cm
   • D. 12 cm
   Answer and solution

   Answer: B

   By the intersecting chords theorem, AP × PB = CP × PD. Therefore, 6 × 4 = 3 × PD, giving 24 = 3 × PD, so PD = 8 cm.

7. Q7 · Quadrilaterals

   In a parallelogram PQRS, if ∠P = 65°, what is the measure of ∠R?

   • A. 65°
   • B. 115°
   • C. 125°
   • D. 130°
   Answer and solution

   Answer: A

   In a parallelogram, opposite angles are equal. Therefore, ∠R = ∠P = 65°.

8. Q8 · Areas of Parallelograms and Triangles

   The base of a parallelogram is 15 cm and its height is 8 cm. What is its area?

   • A. 90 cm²
   • B. 100 cm²
   • C. 120 cm²
   • D. 140 cm²
   Answer and solution

   Answer: C

   Area of parallelogram = base × height = 15 × 8 = 120 cm².

9. Q9 · Arithmetic Progressions (Class 10)

   The 10th term of an AP is 47 and the first term is 2. What is the common difference?

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

   Answer: A

   Using a_n = a + (n-1)d: 47 = 2 + 9d, so 9d = 45, d = 5.

10. Q10 · Probability

    A die is rolled once. What is the probability of getting a number divisible by 3?

    • A. 1/2
    • B. 1/3
    • C. 2/3
    • D. 1/6
    Answer and solution

    Answer: B

    Numbers divisible by 3 on a die are 3 and 6. So there are 2 favorable outcomes out of 6, giving probability 2/6 = 1/3.