SZF IOM 2021 previous year paper practice · PYQ-pattern set

SZF IOM 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 · Arithmetic Progression

   The 10th term of the arithmetic progression 7, 11, 15, 19, ... is:

   • A. 39
   • B. 41
   • C. 43
   • D. 45
   Answer and solution

   Answer: C

   First term a = 7, common difference d = 4. Using the formula aₙ = a + (n-1)d, the 10th term = 7 + (10-1)×4 = 7 + 36 = 43.

2. Q2 · Coordinate Geometry

   The coordinates of the point which divides the line segment joining points A(4, -6) and B(-2, 8) in the ratio 1:2 internally are:

   • A. (2, -4/3)
   • B. (2, 0)
   • C. (8/3, -8/3)
   • D. (10/3, -4/3)
   Answer and solution

   Answer: A

   Using section formula for ratio m:n=1:2: x=(1·(-2)+2·4)/3=(-2+8)/3=6/3=2. y=(1·8+2·(-6))/3=(8-12)/3=-4/3. So point is (2, -4/3).

3. Q3 · Mensuration

   A cylindrical tank has a radius of 7 m and a height of 10 m. What is the total surface area of the tank? (Use π = 22/7)

   • A. 528 m²
   • B. 748 m²
   • C. 440 m²
   • D. 660 m²
   Answer and solution

   Answer: B

   Total surface area = 2πr(h + r) = 2 × (22/7) × 7 × (10 + 7) = 44 × 17 = 748 m².

4. Q4 · Circles

   The area of a circle is 616 cm². What is its circumference? (Use π = 22/7)

   • A. 88 cm
   • B. 44 cm
   • C. 66 cm
   • D. 110 cm
   Answer and solution

   Answer: A

   Area = πr² = 616, so r² = 616 × 7/22 = 196, thus r = 14 cm. Circumference = 2πr = 2 × (22/7) × 14 = 88 cm.

5. Q5 · Spatial and Visual Reasoning

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

   • A. 12
   • B. 20
   • C. 24
   • D. 32
   Answer and solution

   Answer: C

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

6. Q6 · Case Study and Application

   A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the journey. What is the original speed of the train?

   • A. 40 km/h
   • B. 45 km/h
   • C. 50 km/h
   • D. 60 km/h
   Answer and solution

   Answer: A

   Let speed = x km/h. Then 360/x - 360/(x+5) = 1. Solving: 360(x+5) - 360x = x(x+5), giving 1800 = x² + 5x, or x² + 5x - 1800 = 0. Factoring: (x-40)(x+45) = 0, so x = 40 km/h.

7. Q7 · Advanced Algebra

   If α and β are the roots of the equation 3x² - 7x + 2 = 0, what is the value of 1/α + 1/β?

   • A. 2/7
   • B. 7/2
   • C. 3/2
   • D. 2/3
   Answer and solution

   Answer: B

   Using Vieta's formulas: α + β = 7/3 and αβ = 2/3. Therefore 1/α + 1/β = (α + β)/(αβ) = (7/3)/(2/3) = 7/2.

8. Q8 · Quadrilaterals

   A rhombus has diagonals of lengths 16 cm and 12 cm. What is its area?

   • A. 96 cm²
   • B. 192 cm²
   • C. 84 cm²
   • D. 48 cm²
   Answer and solution

   Answer: A

   Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 16 × 12 = 96 cm².

9. Q9 · Triangles

   In triangle PQR, PQ = 15 cm, QR = 20 cm and ∠Q = 90°. If a perpendicular is drawn from Q to PR, what is the length of this perpendicular?

   • A. 10 cm
   • B. 12 cm
   • C. 9 cm
   • D. 8 cm
   Answer and solution

   Answer: B

   First, PR = √(15² + 20²) = 25 cm. Area = (1/2)×15×20 = 150 cm². Also Area = (1/2)×PR×h, so h = 300/25 = 12 cm.

10. Q10 · Applied Mathematics

    A rectangular garden is 25 m long and 18 m wide. A path of uniform width 2 m runs around the outside of the garden. What is the area of the path?

    • A. 180 m²
    • B. 188 m²
    • C. 196 m²
    • D. 204 m²
    Answer and solution

    Answer: B

    Outer rectangle including path: (25+2×2)×(18+2×2)=29×22=638 m². Garden area=25×18=450 m². Path area=638-450=188 m².