SOF IMO 2021 previous year paper practice · PYQ-pattern set

SOF IMO 2021 PYQ-pattern questions

Showing 10 of the 17 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 · Blood Relations

   Pointing to a photograph, Meera says, 'He is the son of my grandfather's only daughter.' How is the boy related to Meera?

   • A. Brother
   • B. Cousin
   • C. Uncle
   • D. Nephew
   Answer and solution

   Answer: A

   Meera's grandfather's only daughter is Meera's mother. So, the son of Meera's mother is Meera's brother.

2. Q2 · Analogy and Classification

   Choose the group of letters that is different from the others.

   • A. AEIOU
   • B. BCDFG
   • C. HJKLM
   • D. PQRST
   Answer and solution

   Answer: A

   AEIOU consists of all vowels, while all other options contain consonants.

3. Q3 · Direction Sense Test

   A man walks 3 km South, then turns East and walks 4 km, then turns North and walks 3 km, then turns West and walks 2 km. How far is he from the starting point and in which direction?

   • A. 2 km East
   • B. 2 km West
   • C. 4 km East
   • D. 4 km West
   Answer and solution

   Answer: A

   North-South movements cancel (3 km S and 3 km N). East-West: 4 km E − 2 km W = 2 km East from the starting point.

4. Q4 · Matrix and Pattern Completion

   Complete the matrix pattern: Row 1: 2, 4, 8 Row 2: 3, 6, 12 Row 3: 5, 10, ? What number should replace the question mark?

   • A. 15
   • B. 20
   • C. 25
   • D. 30
   Answer and solution

   Answer: B

   In each row, the pattern is: first number × 2 = second number, second number × 2 = third number. So 5 × 2 = 10, and 10 × 2 = 20.

5. Q5 · Mirror and Water Images

   Choose the correct water image of the given figure showing an arrow pointing upward and to the right.

   • A. Arrow pointing downward and to the right
   • B. Arrow pointing downward and to the left
   • C. Arrow pointing upward and to the left
   • D. Arrow pointing upward and to the right (same)
   Answer and solution

   Answer: A

   A water image is obtained by flipping the figure vertically (upside down). The upward arrow becomes downward, while left-right orientation remains the same.

6. Q6 · Polynomials

   If α and β are the zeroes of the polynomial x² - 7x + 10, find the value of (1/α) + (1/β).

   • A. 7/10
   • B. 10/7
   • C. 3/5
   • D. 5/3
   Answer and solution

   Answer: A

   For polynomial ax² + bx + c, (1/α) + (1/β) = (α+β)/(αβ). Here α+β = 7 and αβ = 10, so (1/α) + (1/β) = 7/10.

7. Q7 · Quadrilaterals

   ABCD is a rhombus with diagonals AC = 16 cm and BD = 12 cm. What is the perimeter of the rhombus?

   • A. 40 cm
   • B. 36 cm
   • C. 32 cm
   • D. 28 cm
   Answer and solution

   Answer: A

   Diagonals of a rhombus bisect at right angles. So each side = √[(16/2)² + (12/2)²] = √[64 + 36] = √100 = 10 cm. Perimeter = 4 × 10 = 40 cm.

8. Q8 · Lines and Angles

   In the figure, lines AB and CD intersect at O. If ∠AOC = 3x + 10° and ∠BOD = 5x - 30°, what is the value of x?

   • A. 15°
   • B. 20°
   • C. 25°
   • D. 30°
   Answer and solution

   Answer: B

   Vertically opposite angles are equal. So ∠AOC = ∠BOD gives 3x + 10 = 5x - 30, which yields 40 = 2x, so x = 20°.

9. Q9 · Real Numbers (Class 10)

   The HCF and LCM of two numbers are 12 and 420 respectively. If one of the numbers is 60, what is the other number?

   • A. 84
   • B. 72
   • C. 96
   • D. 108
   Answer and solution

   Answer: A

   Using the relation: HCF × LCM = Product of two numbers. So 12 × 420 = 60 × other number. Other number = 5040/60 = 84.

10. Q10 · Surface Areas and Volumes

    A cylinder has radius 7 cm and height 10 cm. What is its curved surface area? (Take π = 22/7)

    • A. 440 cm²
    • B. 220 cm²
    • C. 154 cm²
    • D. 308 cm²
    Answer and solution

    Answer: A

    Curved surface area = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².