51). Let A be a pyramid on a square base and B be a cube. It a, b and c denote the number of edges, number of faces and number of corners, respectively. Then, the result a = b + c is true for
| A). only A |
| B). only 3 |
| C). both A and B |
| D). neither A nor 8 |
|
52). Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid.
| A). 750 sq cm |
| B). 1500 sq cm |
| C). 2250 sq cm |
| D). 700 sq cm |
|
53). A hemispherical basin of 150 cm diameter holds water 120 times as much as a cylindrical tube. If the height of the tube is 15 cm, then the diameter of the tube is
| A). 27 cm |
| B). 24 cm |
| C). 25 cm |
| D). 26 cm |
|
54). A well of inner diameter 14 m is dug to a depth of 15 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of embankment so formed.
| A). 7 m |
| B). 5 m |
| C). 14 m |
| D). None |
|
55). In a shower, 10 cm of rain falls. What will be the volume of water that falls on 1 hect area of ground?
| A). 500 \( \Large cm^{3} \) |
| B). 650 \( \Large cm^{3} \) |
| C). 1000 \( \Large cm^{3} \) |
| D). 750 \( \Large cm^{3} \) |
|
56). A large solid metallic cylinder whose radius and height are equal to each other is to be melted and 48 identical solid falls are to be recast from the liquid metal so formed. What is the ratio of the radius of a ball to the radius of the cylinder?
| A). 1 ; 16 |
| B). 1 : 12 |
| C). 1 : 8 |
| D). 1 : 4 |
|
57). What is the volume of the largest sphere that can be curved out of a cube of edge 3 cm?
| A). 9 \( \Large \pi cm^{3} \) |
| B). 6 \( \Large \pi cm^{3} \) |
| C). 4.5 \( \Large \pi cm^{3} \) |
| D). 3 \( \Large \pi cm^{3} \) |
|
58). A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere?
| A). 2 cm |
| B). 3 cm |
| C). 4 cm |
| D). 5 cm |
|
59). Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. Let C and S denote the volume of cone and volume of sphere respectively, then which one of the following is correct?
| A). C = 2S |
| B). S = 2C |
| C). C = S |
| D). C = 3S |
|
60). 10 circular plates each of thickness 3 cm, each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed?
| A). 264 \( \Large \pi cm^{3} \) |
| B). 252 \( \Large \pi cm^{3} \) |
| C). 236 \( \Large \pi cm^{3} \) |
| D). None of these |
|
