1. The cost (in Rs.) of a watermelon is proportional to the square root of its weight (in pounds). If a watermelon weighing 16 pounds costs Rs.50, how much will a watermelon costing Rs.37.5 weigh, in pounds?
2. One morning, Govind Lal, the owner of the local petrol bunk, was adulterating petrol that he sells with kerosene. He had two identical tanks - the first being full of pure petrol, and the second being empty. First, he transferred an arbitrary amount of petrol from the first tank into the second and then replaced the petrol removed from the first tank with kerosene. He then repeated this process one more time but this time he ensured that by the end of the process the second tank was exactly full.
Which of the following statements is/are not true regarding the concentration
of petrol in the second tank?
I. It cannot be more than 75%
II. It cannot be less than 75%
III. It is at most 50%
a) Only I and III
b) Only I and II
c) Only II
d) Only III
3. Two identical conical containers, C1 and C2, each of volume V litres, contain exactly v litres of water each. Initially both the containers are resting on their
bases. If C2 is now inverted and made to rest on its vertex, the water level in it becomes twice as high as that in C1. If v/V = p, then which of the following is true of p?
4. An odd number of stones were lying all along a straight road, with any pair of adjacent stones being separated by a distance of 10 m. Ajay was assigned the task of removing all the stones, excluding the middle stone, and assembling them around it. He was allowed to carry only one stone at a time. He started the job with a stone at one end and carried the stones in succession. If he had to travel a total distance of 8.2 km before he could assemble all the stones, find the total number of stones on the road
5. There are two flagpoles, A and B, of heights 15√3 m and 30√3 m respectively. If there is only one point on the ground from where both the flagpoles subtend an angle of 60° each, find the maximum possible distance between the tops of the two flagpoles.
a) 30√3 m
b) 15 m
c) 15√3 m
d) 45 m
6. There are 51 coins in a bag. The coins are first divided into two separate bags, after which the coins in one of the two bags are taken and again divided into two separate bags and then from out of the three bags present, the coins in one of the bags are taken and divided into two separate bags, and so on until we are left with 51 bags containing one coin each. If after every division of the coins in a bag into two bags, the product of the number of coins in the two bags is written down, what is the sum of all the numbers written down?
7. There are three drain pipes P1, P2 and P3, all of equal capacity, fitted to a cylindrical tank of height 6 metres. P1 is fitted at the bottom of the tank, while P3 is fitted at a height of 5 m above P1, and P2 is fitted in between P3 and P1. P1 alone can empty the full tank in T minutes and if all the three pipes are in operation, the full tank can be emptied in 2T/3 minutes. What is the height (above P1) at which P2 is fitted to the tank?
a) 10/3 min
b) 8/3 min
c) 7/3 min
d) 11/3 min
8. A sum was invested under compound interest, interest being compounded annually. If it fetches Rs.2880 as interest in the second year and Rs.3456 as interest in the third year, find the annual rate of interest.
9. Find the value of