SZF IOM 2023 previous year paper practice · PYQ-pattern set

SZF IOM 2023 PYQ-pattern questions

Showing 10 of the 18 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 · Linear Equations in Two Variables

   A pair of linear equations 2x + 3y = 7 and 4x + ky = 14 will have infinitely many solutions if the value of k is:

   • A. 3
   • B. 6
   • C. 8
   • D. 12
   Answer and solution

   Answer: B

   For infinitely many solutions, a₁/a₂ = b₁/b₂ = c₁/c₂. Here, 2/4 = 3/k = 7/14, which simplifies to 1/2 = 3/k. Solving gives k = 6.

2. Q2 · Lines and Angles

   Two parallel lines are cut by a transversal. If one interior angle on the same side of the transversal is 65°, what is the measure of the other interior angle on the same side?

   • A. 65°
   • B. 115°
   • C. 125°
   • D. 135°
   Answer and solution

   Answer: B

   Co-interior angles (also called consecutive interior angles) formed by parallel lines and a transversal are supplementary. Therefore, the other angle = 180° - 65° = 115°.

3. Q3 · Circles

   A chord of length 16 cm is at a distance of 6 cm from the center of a circle. What is the radius of the circle?

   • A. 8 cm
   • B. 10 cm
   • C. 12 cm
   • D. 14 cm
   Answer and solution

   Answer: B

   Half the chord length is 8 cm. Using Pythagoras theorem: r² = 8² + 6² = 64 + 36 = 100, so r = 10 cm.

4. Q4 · Probability

   A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a blue ball?

   • A. 1/2
   • B. 3/10
   • C. 1/5
   • D. 2/5
   Answer and solution

   Answer: B

   Total balls = 5 + 3 + 2 = 10. Probability of blue ball = 3/10.

5. Q5 · Verbal Reasoning

   In a certain code language, 'PENCIL' is written as 'QFODJM'. How is 'MARKER' written in that code?

   • A. NBSLFS
   • B. NBSLFR
   • C. NARLFS
   • D. MBSLFS
   Answer and solution

   Answer: A

   Each letter is shifted one position forward in the alphabet. Applying the same rule: M→N, A→B, R→S, K→L, E→F, R→S, giving NBSLFS.

6. Q6 · Higher Order Thinking

   A clock shows 3:00. What is the angle between the hour hand and the minute hand?

   • A. 75°
   • B. 90°
   • C. 105°
   • D. 120°
   Answer and solution

   Answer: B

   At 3:00, the minute hand is at 12 and the hour hand is at 3. Each hour represents 30° (360°/12). The angle is 3 × 30° = 90°.

7. Q7 · Case Study and Application

   A shopkeeper marks up the price of an item by 60% above cost price. During a festival sale, he offers a 25% discount on the marked price and still makes a profit of ₹280 on selling the item. What was the cost price of the item?

   • A. ₹1,200
   • B. ₹1,400
   • C. ₹1,600
   • D. ₹2,000
   Answer and solution

   Answer: B

   Let CP = x. Marked price = 1.6x. Selling price after 25% discount = 1.6x × 0.75 = 1.2x. Profit = 1.2x - x = 0.2x = 280. Therefore x = 1400.

8. Q8 · Lines and Angles

   Two supplementary angles are in the ratio 7:5. Find the measure of the smaller angle.

   • A. 60°
   • B. 75°
   • C. 80°
   • D. 90°
   Answer and solution

   Answer: B

   Let angles be 7x and 5x. Since supplementary: 7x + 5x = 180°, so x = 15°. Smaller angle = 5×15° = 75°.

9. Q9 · Mensuration

   A cylindrical tank has a radius of 3.5 m and height 8 m. Find the volume of the tank in cubic meters. (Use π = 22/7)

   • A. 308 m³
   • B. 616 m³
   • C. 154 m³
   • D. 224 m³
   Answer and solution

   Answer: A

   Volume = πr²h = (22/7) × 3.5 × 3.5 × 8 = (22/7) × 12.25 × 8 = 308 m³.

10. Q10 · Probability

    A bag contains 5 red balls, 4 blue balls, and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are of the same color?

    • A. 19/66
    • B. 13/66
    • C. 17/66
    • D. 23/66
    Answer and solution

    Answer: A

    P(both same) = P(both red) + P(both blue) + P(both green) = (5/12)(4/11) + (4/12)(3/11) + (3/12)(2/11) = 20/132 + 12/132 + 6/132 = 38/132 = 19/66.