1. Two taps with emptying capacities in the ratio 1 : 2, empty a full tank in 2 hours when opened together. How much time does the first tap alone take to empty half the tank?
a) 3/2 hours
b) 2 hours
c) 3 hours
d) 6 hours
2. A mathematics teacher wrote n positive numbers on the black board and asked the students in her class to find the product of all the n numbers. One of her students, Rajith, randomly chose one of the nnumbers and increased it by a certain quantity and found that the original product increased by 9%. Two other students, Satish and Tarun, also carried out a similar calculation and found that the original product increased by 12% and 18% respectively. If all the three students increased the respective numbers that they chose by the same quantity, find the ratio of the respective numbers that they chose.
a) 3 : 4 : 6
b) 6 : 4 : 3
c) 4 : 3 : 2
d) 2 : 3 : 4
3. Sunder works for a multinational company and earns a 4-digit monthly salary. However, Sunder prefers to disclose his salary to his friends in the number system to the base 6 or base 9, as then his salary would, in either case, correspond to a 5-digit number. Find the difference (as a decimal number) between the maximum and minimum possible values of his salary.
4. Two equal circles, C1 and C2, are drawn, touching each other externally. Another larger circle, C3, is drawn, enveloping both C1 and C2, with the least possible radius, R. If two distinct small circles, C4 and C5, of equal size, are now drawn such that each of them touches C1 and C2 externally and C3 internally, find the area of the region inside C3 which is not common to any of C1, C2, C4 or C5.
5. A number when divided by 4, 5, 6 and 7 leaves a remainder of 2, 3, 4 and 5 respectively. What is the largest such number less than 3000?
6. Alok and Bijoy start a business with their capitals in the ratio of 1 : 2. Alok manages the business for which he is paid a part of the gross annual profit as his annual salary. At the end of the year, Bijoy gets half of the gross annual profit as his share of the profit. What part of Alok’s income is his annual salary?
7. There are two alloys, A and B, of copper and zinc. The ratio (by weight) of copper and zinc in alloy A is 8 : 1 and that in alloy B is 2 : 7. It is found that, if alloy A and alloy B are mixed in a certain ratio, the weights of copper and zinc in the resultant alloy are also in that ratio. What is that ratio?
a) 4 : 3
b) 3 : 2
c) 5 : 3
d) 2 : 1
8. Let S denote the sum of the squares of ten consecutive positive integers. Which of the following values represents a possible value of S?
9. Two men Sam and Jack, are initially standing at the two ends, P and Q, of a straight road, respectively. Both started running towards each other at the same time. Sam covered 2/5th of the distance PQ at a speed 2a and the remaining distance at a speed 3b, to reach Q. Jack ran at a speed 5c and by the time Sam reached from P to Q, Jack ran from Q to P and went back to Q, such that both of them reached Q simultaneously. Which of the following is true about a, b and c?
a) 1/a + 1/b = 1/c
b) a + b = c
c) 2a + 3b = 5c
d) 1/a + 1/b = 2/c
10. T is a right-angled triangle, whose perpendicular sides are a, b and hypotenuse is c. The minimum possible value of c/a + c/b is