# June 2016: Life Sciences and Physical Sciences

June 2016

1. An infinite number of identical circular discs each of radius ½ are tightly packed such that the centres of the discs are at integer values of coordinates x and y. The ratio of the area of the uncovered patches to the total area is

2. It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B (all speeds stay constant)?

3. How many times starting at 1:00 pm would the minute and hour hands of a clock make an angle of 40o with each other in the next 6 hours?

4. Of the following which is the odd one out?

5. “My friend Raju has more than 1000 books”, said Ram. “Oh no, he has less than 1000 books”, said Shyam. “Well, Raju certainly has at least one book”, said Geeta. If only one of these statements is true, how many books does Raju have?

6. Which of the following best approximates sin (0.5o)?

7. Find the next figure “D” 8. The diagram shows a block of marble having the shape of a triangular prism. What is the maximum number of slabs of 10 × 10 × 5 cm3 size that can be cut parallel to the face on which the block is resting? 9. Fill in the blank: F2, __, D8, C16, B32, A64

10. A student appearing for an exam is declared to have failed the exam if his/her score is less than half the median score. This implies

11. Which of the following statements is logically incorrect?

12. What comes next in the sequence?  13. Which of the following inferences can be drawn from the graph? 14. The relationship among the numbers in each corner square is the same as that in the other corner squares. Find the missing number. 15. The set of numbers (5, 6, 7, m, 6, 7, 8, n) has an arithmetic mean of 6 and mode (most frequently occurring number) of 7. Then m × n =

16. N is a four-digit number. If the leftmost digit is removed, the resulting three-digit number is 1/9th of N. How many such N are possible?

17. Brothers Santa and Chris walk to school from their house. The former takes 40 minutes while the latter, 30 minutes. One day Santa started 5 minutes earlier than Chris. In how many minutes would Chris overtake Santa?

18. AB and CD are two chords of a circle subtending 60o and 120o respectively at the same point on the circumference of the circle. Then AB:CD is

19. What is the minimum number of moves required to transform Figure 1 to Figure 2? A move is defined as removing a coin and placing it such that it touches two other coins in its new position. 20. A solid contains a spherical cavity. The cavity is filled with a liquid and includes a spherical bubble of gas. The radii of cavity and gas bubble are 2 mm and 1 mm, respectively. What proportion of the cavity is filled with liquid?

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