IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Concept:Use the volume formulas for a cylinder and a sphere, then express all quantities in terms of the unknown variables $h$ and $k$.Explanation:Let the cylinder radius be $2k$ and the sphere radius be $3k$.Volume of sphere $= \frac{4}{3}\pi (3k)^3 = 36\pi k^3 = 88y$.Therefore, $y = \frac{36\pi k^3}{88} = \frac{9\pi k^3}{22}$.Quantity I $=$ Volume of cylinder $= \pi(2k)^2 h = 4\pi k^2 h$.Quantity II $= \frac{y}{4} = \frac{9\pi k^3}{88}$.Quantity III $= h \times y = \frac{9\pi k^3 h}{22}$.Comparing Quantity I and Quantity II depends on the ratio of $h$ and $k$, which is not provided.Comparing Quantity II and Quantity III also depends on the unknown value of $h$.Hence, no definite relationship can be established among the quantities.Answer:Relationship between Quantity I and Quantity II cannot be determined, and Relationship between Quantity II and Quantity III cannot be determined.Therefore, the correct option is D.