SZF IOM 2024 previous year paper practice · PYQ-pattern set

SZF IOM 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 · Polynomials

   If p(x) = x³ - 6x² + 11x - 6, and one of its zeros is 1, then what is the product of the other two zeros?

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

   Answer: B

   Using Vieta's formulas, the product of all three zeros equals the constant term divided by the leading coefficient: 6/1 = 6. Since one zero is 1, the product of the other two zeros is 6/1 = 6.

2. Q2 · Coordinate Geometry

   If the distance between points (3, k) and (7, 2) is 5 units, then the positive value of k is:

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

   Answer: C

   Using distance formula: √[(7-3)² + (2-k)²] = 5. This gives 16 + (2-k)² = 25, so (2-k)² = 9, yielding k = 5 or k = -1. The positive value is k = 5.

3. Q3 · Quadrilaterals

   The diagonals of a rhombus are 24 cm and 18 cm. What is the area of the rhombus?

   • A. 216 cm²
   • B. 432 cm²
   • C. 108 cm²
   • D. 324 cm²
   Answer and solution

   Answer: A

   The area of a rhombus is (1/2) × d₁ × d₂ = (1/2) × 24 × 18 = 216 cm².

4. Q4 · Statistics

   The mean of five numbers is 18. If four numbers are 15, 20, 22, and 13, what is the fifth number?

   • A. 20
   • B. 18
   • C. 25
   • D. 30
   Answer and solution

   Answer: A

   Sum of five numbers = 18 × 5 = 90. Sum of four known numbers = 15 + 20 + 22 + 13 = 70. Fifth number = 90 − 70 = 20.

5. Q5 · Mental Aptitude

   If 15th August 2024 is a Thursday, what day of the week will be 15th September 2024?

   • A. Friday
   • B. Saturday
   • C. Sunday
   • D. Monday
   Answer and solution

   Answer: C

   From 15th August to 15th September is 31 days (August has 31 days). 31 days = 4 weeks + 3 days. Thursday + 3 days = Sunday.

6. Q6 · Case Study and Application

   A water tank has two inlet pipes A and B. Pipe A can fill the tank in 8 hours and pipe B in 12 hours. There is an outlet pipe C that can empty the full tank in 6 hours. If all three pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank completely?

   • A. 16 hours
   • B. 24 hours
   • C. Cannot be filled
   • D. 48 hours
   Answer and solution

   Answer: B

   Pipe A fills 1/8 per hour, B fills 1/12 per hour, C empties 1/6 per hour. Net rate = 1/8 + 1/12 - 1/6 = (3 + 2 - 4)/24 = 1/24 per hour. Time = 24 hours.

7. Q7 · Coordinate Geometry

   The distance between points A(3, 4) and B(7, 1) is:

   • A. 4 units
   • B. 5 units
   • C. 6 units
   • D. 7 units
   Answer and solution

   Answer: B

   Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.

8. Q8 · Area of Triangles, Parallelograms and Circles

   The area of a circle with radius 7 cm is: (Use π = 22/7)

   • A. 154 cm²
   • B. 144 cm²
   • C. 196 cm²
   • D. 176 cm²
   Answer and solution

   Answer: A

   Area = πr² = (22/7) × 7 × 7 = 154 cm².

9. Q9 · Non-Verbal Reasoning

   A cube is painted red on all faces and then cut into 64 smaller equal cubes. How many of the smaller cubes have exactly two faces painted?

   • A. 12
   • B. 24
   • C. 32
   • D. 48
   Answer and solution

   Answer: B

   A cube cut into 64 smaller cubes means 4×4×4 division. Cubes with exactly two painted faces lie along the edges but not at corners. Each edge has 4-2=2 such cubes, and there are 12 edges, giving 12×2 = 24 cubes.

10. Q10 · Mental Aptitude

    A series is given: 2, 6, 12, 20, 30, ?. What number should come next?

    • A. 40
    • B. 42
    • C. 38
    • D. 36
    Answer and solution

    Answer: B

    The differences between consecutive terms are 4, 6, 8, 10, which form an arithmetic sequence increasing by 2. The next difference should be 12, so 30 + 12 = 42.