# December 2016: Mathematical Sciences, Chemical Sciences and Earth Sciences

1. The houses of three sisters lie in the same row, but the middle sister does not live in the middle house. In the morning , the shadow of the eldest sister’s house falls on the youngest sister’s house. What can be concluded for sure?

2. A woman starts shopping with Rs. X and Y paise , spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The amount she started with is ?

3. A mine supplies 10000 tons of copper ore, containing an average of 1.5 wt% copper, to a smelter every day. The smelter extracts 80% of the copper from the ore on the same day. What is the production of copper in tons/day?

4. Wheat production of a country over a number of years is shown. Which year recorded highest percent reduction in production over the previous year?

5. What is the next pattern in the given sequence?

6. A person completely under sea water tracks the Sun. Compared to an observer above water, which of the following observations would be made by the underwater observer?

7. A man sells three articles A, B, C and gains10% on A, 20% on B and loses 10% on C. He breaks even when combined selling prices of A and C are considered, whereas he gains 5% when combined selling prices of B and C are considered. What is his net loss or gain on the sale of all the articles?

8. Based on the distribution of surface area of the Earth at different elevations and depths (with reference to sea- level) shown in the figure, which of the following is FALSE?

9. Time-distance graph of two objects A and B are shown. If the axes are interchanged, then the same information is shown by:

10. A chocolate salesman is travelling with 3 boxes with 30 chocolates in each box. During his journey he encounters 30 toll booths. Each tollbooth inspector takes one chocolate per box that contains chocolate(s), as tax. What is the largest number of chocolates he can be left with after passing through all tollbooths?

11. A milkman adds 10 litres of water to 90 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he has sold. The proportion of water to milk he sells now would be

12. Two coconuts have spherical space inside their kernels, with the first having an inner diameter twice that of the other. The larger one is half filled with liquid, while the smaller is completely filled. Which of the following statements its correct?

13. Which of the following graphs represents a stable fresh water lake? (i.e., vertical motion of water)

14. A tiger usually stalks its prey from a direction that is upwind of the prey. The reason for this is

15. A cellphone tower radiates 1 W power while the handset transmitter radiates 0.1 mw power. The correct comparison of the radiation energy received by your head from a tower 100m away (Er) and that from a handset held to your ear (E2) is

16. The pitch of a spring is 5 mm. The diameter of the spring is 1 cm. The spring spins about its axis with a speed of 2 rotations/s. The spring appears to be moving parallel to its axis with a speed of

17. The dimensions of a floor are 18 × 24. What is the smallest number of identical squares tiles that will pave the entire floor without the need to break any tile?

18. To determine the number of parrots in a sparse population, an ecologist captures 30 parrots and puts rings around their necks and releases them. After a week he captures 40 parrots and finds that 8 of them have rings on their necks. What approximately is the parrot population?

19. The mid-point of the arc of a semicircle is connected by two straight lines to the ends of the diameter as shown. What is the ratio of the shaded area to the area of the triangle?

20. Why is there low fish population in takes that have large hyacinth growth?

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