Question : A tap is dripping at a constant rate into a container. The level L cm of the water in the container is given by the equation L = $2-2^t$, where t is the time taken in hours. What is the level of water in the container at the start?

Option 1: 0 cm

Option 2: 1 cm

Option 3: 2 cm

Option 4: 4 cm

Question : Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of a mixture of spirit and water. In the 1st container, the ratio of spirit and water is 4 : 1, in the second container the ratio is 11 : 4 and in the 3rd container the ratio is 7 : 3. All three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is:

Option 1: 4 : 9

Option 2: 11 : 4

Option 3: 5 : 10

Option 4: 9 : 5

Question : Some ice pieces, spherical in shape, of diameter 6 cm are dropped in a cylindrical container containing some juice and are fully submerged. If the diameter of the container is 18 cm and the level of juice rises by 40 cm, then how many ice pieces are dropped in the container?

Option 1: 95

Option 2: 85

Option 3: 80

Option 4: 90

Question : A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.

Option 1: 8 cm

Option 2: 6 cm

Option 3: 8.75 cm

Option 4: 6.75 cm

Question : Directions: A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours. If all three taps are opened simultaneously, then how much time will it take to fill the tank?

Option 1: 4.2 Hours

Option 2: 5 Hours

Option 3: 4.5 Hours

Option 4: 4.8 Hours

Question : Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?

Option 1: 76

Option 2: 72

Option 3: 70

Option 4: 75