# June 2017: Mathematical Sciences, Chemical Sciences and Earth Sciences

1. If NET14 and NET15 are 5 digit numbers such that their sum = 157229, then N + E + T would be

2. A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it? (Earth’s circumference is roughly 40,000 km. The height of the human beings is between 1 and 2 m).

3. A cylindrical cake is to be cut into 16 equal pieces. What is the minimum number of cuts required to do so?

4. If  P+ 1/Q = 1 and Q + 1/R = 1 then what is PQR?

5. A, B and C are three distinct digits. If they are added as below,

A          B          C

+          A          B          C

+          A          B          C

C          C          C

Find out the value of A, B and C

6. N is a two digit number such that a product of its digits when added to their sum = N. The unit digit of N would be:

7. If equal weights of 22 carat gold (alloy of 22 parts gold and 2 parts copper by weight) and 24 carat gold (pure gold) are mixed to form an alloy, what will be the weight proportion of copper in the alloy?

8. A 4m x 4m floor needs to be covered by tiles of size 2m x 1m. Two diagonally opposite corners of size 1m x 1m should be left uncovered. How many tiles are required to complete the job without breaking the tiles or overlapping them?

9. A shopkeeper sells the file and a notebook for Rs.27 to the first customer, a notebook and a pen for Rs.31 to the second customer and a pen and file for Rs.29 to the third customer. The price of the items are rounded in rupees. Which of the following inferences is correct?

10. Pre-PhD exam score of 10 students are plotted against their M.Sc. m arks. Which of the following is true?

11. What is the reminder when 3256 is divided by 5?

12. If 42 → 26, 71 → 78, 33 →16 then 62 →

13. The diagram shows a cubic block of marbles (1 x 1 x 1 m3) having a planar fracture. What is the maximum number of slabs sized 20 x 20 x 5 cm3 that can be cut from this block avoiding the fracture?

14. A tall metal cylinder is filled end-to-end with n snugly fitting spherical wax balls of diameter d. If the balls melt completely, the volume fraction occupied by the melted wax is

15. With reference to the right angle triangle shown what is the value of sin (A)cos(B) + cos(A)sin(B)

16. Walking from my home, at a speed of 5 km/h I am 8 minutes late in reaching my office. If I walk at a speed of 8 km/h I reach 5 minutes late. How far is my office from the house?

17. Some fishermen caught some fish. No one caught more than 20 fish. a1 number of fishermen caught at least 1 fish among them, a2 number of fishermen caught at least 2 fish among them, and so on and a20 number of fisher men caught exactly 20 fishes among them. How many fishes were caught?

18. If the product of 3 consecutive positive integers is equal to their sum, then what would be the sum of their squares?

19. L is the tallest and eldest of a group of 5 people K, L, M, N and P. M is elder tot N and shorter than K. M and P are of same age and P is taller than K. N and K are of same height and K is younger to P. Which of the following inferences is certain?

20. Consider a square of side a. Fit the largest possible circle inside it and the largest possible square inside the circle. What is the side length of the innermost square?

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