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Directions for Questions 68–69: Match Column I and Column II based on the given questions. Column I (i) \(X\) = Cone, volume of cone = \(1232\text{ m}^3\) (ii) \(Y\) = Cylinder, volume of cylinder = \(1848\text{ m}^3\) (iii) \(S\) = Square, which is inscribed in a circle Column II (A) Radius = 14 m (B) Radius = 7 m (C) Circumference of circle = 44 m 68. If the difference between the height of \(Y\) and the side of \(S\) is greater than 20 m, then which option is correct?

1. (a) Only A, either B or C (ii) Only A (iii) Only A
2. (b) Only C (ii) Only B (iii) Only A
3. (c) Only B (ii) Only A (iii) Only A
4. (d) Only C (ii) Only B (iii) Only B

Correct answer: (b) Only C (ii) Only B (iii) Only A

Solution

Using the cylinder volume and the given radius options, the height of \(Y\) matches the case with radius 7 m. For the square inscribed in a circle, the side is determined from the circle radius, and only the option with circumference 44 m satisfies the condition that the height difference is greater than 20 m. Hence the correct matching is option (b).

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