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

June 2016

1. The diagram (not to scale) shows the top view and cross section of a pond having a square outline and equal sized steps of 0.5 m width and 0.1 m height. What will be the volume of water (in m3) in the pond when it is completely filled?

2. What will be the next figure in the following sequence

3. D is a point on AC in the following triangle such that ∠ADB = ∠ABC. Then BD (in cm) is

4. When a polynomial f(x) is divided by x-5 or x-3 or x-2 it leaves a remainder of 1. Which of the following would be the polynomial?

5. A notebook contains only hundred statements as under:

1. This notebook contains 1 false statement.
2. This notebook contains 2 false statements.

.

.

1. This notebook contains 99 false statements.
2. This notebook contains 100 false statements.

Which of the statement is correct?

6. A, B, C, D are points on a circle with AB = 5 cm, BC = 12 cm, AC = 13 cm and AD = 7 cm. Then, the closest approximation of CD is

7. A frog hops and lands exactly 1 meter away at a time. What is the least number of hops required to reach a point 10 cm away?

8. A person paid income tax at the rate of R% for the first Rs. 2 lakhs, and at the rate of (R+10)% for income exceeding Rs. 2 lakhs. If the total tax paid is (R+5)% of the annual income, then what is the annual income?

9. Water is slowly dripping out of a tiny hole at the bottom of a hollow metallic sphere initially full of water. Ignoring the water that has flowed away, the centre of mass of the system

10. The function f(x) is plotted against x as shown. Extrapolate and find the value of the function at x = -1

11. The difference between the squares of the ages (in complete years) of a father and his son is 899. The age of the father when his son was born

12. Equilateral triangles are drawn one inside the other as shown.

What is the ratio of the two shaded areas?

13. It takes 2 hours for Tiwari and Deo to do a job. Tiwari and Hari take 3 hours to do the same job. Deo and Hari take 6 hours to do the same job. Which of the following statements is incorrect?

14. An experiment leads to the following set of observations of the variable ‘v’ at different times ‘t’.

 t 0 1 2 3 4 5 6 v 5 6.1 9.1 13.7 20.6 30.8 41.4

Allowing for experimental errors, which of the following expressions best describes the relationship between t and v?

15. A train running at 36 km/h crosses a mark on the platform in 8 seconds and takes 20 seconds to cross the platform. What is the length of the platform?

16. For a certain regular solid: number of faces + number of vertices = number of edges + 2. For three such distinct (not touching each other) objects, what is the total value of faces + vertices – edges?

17. Abdul travels thrice the distance Catherine travels, which is also twice the distance that Binoy travels. Catherine’s speed is 1/3 of Abdul’s speed, which is also ½ of Binoy’s speed. If they start at the same time, then who reaches first?

18. A chocolate bar having m × n unit square tiles is given. Calculate the number of cuts needed to break it completely, without stacking, into individual tiles.

19. A bicycle tube has a mean circumference of 200 cm and a circular cross section of diameter 6 cm. What is the approximate volume of water (in cc) required to completely fill the tube, assuming that it does not expand?

20. Choose the four-digit number, in which the product of the first & fourth digits is 40 and the product of the middle digits is 28. The thousands digit is as much less than the unit digit as the hundreds digit is less than tens digit.

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