Question : A piece of paper and a cricket ball are dropped from the same height. Under which of the following conditions do both reach the surface simultaneously?

Option 1: They must have the same volume.

Option 2: They must have the same density.

Option 3: They must have the same mass.

Option 4: They must be dropped in a vacuum.

Question : Two stones of different masses are dropped simultaneously from the top of the building:

Option 1: smaller stone reaches the ground earlier.

Option 2: larger stone reaches the ground earlier.

Option 3: both the stones reach the ground at the same time.

Option 4: depends on the composition of the stone.

Question : Which of the following statements is not correct?

Option 1: For a given radius and height, a right circular cone has a lesser volume than a right circular cylinder.

Option 2: If the side of a cube is increased by 10%, the volume will increase by 33.1%.

Option 3: If the radius of a sphere is increased by 20%, the surface area will increase by 40%.

Option 4: Cutting a sphere into 2 parts does not change the total volume.

Question : If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of the total surface area and the volume.

Option 1: 5 : 14

Option 2: 7 : 15

Option 3: 3 : 7

Option 4: 3 : 14

Question : The height of a cylinder is $\frac{2}{3}$rd of its diameter. Its volume is equal to the volume of a sphere whose radius is 4 cm. What is the curved surface area (in cm²) of the cylinder?

Option 1: $\frac{112}{3} \pi$

Option 2: $32 \pi$

Option 3: $\frac{128}{3} \pi$

Option 4: $40 \pi$

Question : If $h, C$, and $V$ are respectively the height, the curved surface, and the volume of a cone, then $3\pi Vh^{3} -C^{2}h^{2} + 9V^{2} =?$

Option 1: $0$

Option 2: $3$

Option 3: $\frac{1}{2}$

Option 4: $11$