Question : Two equal maximum-sized circular plates are cut off from a circular paper sheet of circumference 352 cm. Then the circumference of each circular plate is:

Option 1: 176 cm

Option 2: 150 cm

Option 3: 165 cm

Option 4: 180 cm

Question : 24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.

Option 1: 4 cm

Option 2: 8 cm

Option 3: 6 cm

Option 4: 3 cm

Question : Two circles of radii 9 cm and 4 cm, respectively, touch each other externally at point $A. PQ$ is the direct common tangent of those two circles of centres $O_1$ and $O_2$, respectively. The length of $PQ$ is equal to:

Option 1: 13 cm

Option 2: 11 cm

Option 3: 10 cm

Option 4: 12 cm

Question : If a right circular cone of height 24 cm has the circumference of its base 42$\pi$ cm, then the volume of the cone is: (Use $\pi=\frac{22}{7}$)

Option 1: 15211 cm³

Option 2: 11088 cm³

Option 3: 12034 cm³

Option 4: 21011 cm³

Question : The area of two similar triangles TUV and PQR are $18 \ \text{cm}^2$ and $32 \ \text{cm}^2$, respectively. If $TU=6\ \text{cm}$, then PQ is equal to:

Option 1: 4 cm

Option 2: 8 cm

Option 3: 2 cm

Option 4: 64 cm

Question : A plate on the square base made of brass is of length $x$ cm and width 1 mm. The plate weighs 4725 g. If 1 cm³ of brass weighs 8.4 g, then the value of $x$ is:

Option 1: 75 cm

Option 2: 76 cm

Option 3: 72 cm

Option 4: 74 cm