Decemeber 2015: Life Sciences and Physical Sciences

December 2015

1. A bird leaves its nest and flies away. Its distance x from the nest is plotted as a function of time t. Which of the following plots cannot be right?

 
 
 
 

2. Statement A: The following statement is true. Statement B: The preceding statement is false.

Choose the correct inference from the following.

 
 
 
 

3. The number of squares in the figure is

 
 
 
 

4. The triangle formed by the lines y = x, y = 1 – x and x = 0 in a two dimensional plane is (x and y axes have the same scale)

 
 
 
 

5. Five congruent rectangles are drawn inside a big rectangle of perimeter 165 as shown. What is the perimeter of one of the five rectangles?

 
 
 
 

6. Four circles of unit radius each are drawn such that each one touches two others and their centres lie on the vertices of a square. The area of the region enclosed between the circles is

 
 
 
 

7. A vessel is partially filled with water. More water is added to it at a rate directly proportional to time [ a t]. Which of the following graphs depicts correctly the variation of total volume V of water with time t?

 
 
 
 

8. A shopkeeper purchases a product for Rs.100 and sells it making a profit of 10%. The customer resells it to the same shopkeeper incurring a loss of 10%. In these dealings the shopkeeper makes

 
 
 
 

9. A living cell has a protoplasm which is water based and demarcated by a lipid bilayer membrane. If a cell is pierced to 1/5th of its diameter with a very sharp needle, after taking the needle out

 
 
 
 

10. In each of the following groups of words is a hidden number, based on which you should arrange them in descending order. Pick the correct answer:

E. Papers I Xeroxed    F. Wi–Fi veteran      G. Yourself ourselves     H. Breaks even

 
 
 
 

11. A person walks downhill at 10 km/h, uphill at 6 km/h and on the plane at 7.5 km/h. If the person takes 3 hours to go from a place A to another place B, and 1 hour on the way back, the distance between A and B is

 
 
 
 

12. If       D + I + M = 1501         C + I + V + I + L = 157           L + I + V + I + D = 557

C + I + V + I + C = 207

What is V + I + M = ?

 
 
 
 

13. There are two buckets A and B. Initially A has 2 litres of water and B is empty. At every hour 1 litre of water is transferred from A to B followed by returning ½ litre back to A from B half an hour later. The earliest A will get empty is in:

 
 
 
 

14. Secondary colours are made by a mixture of three primary colours: Red, Green and Blue in different proportions; each of the primary colours comes in 8 possible levels. Grey corresponds to equal proportions of Red, Green and Blue. How many shades of grey exist in this scheme?

 
 
 
 

15. A car is moving at 60 km/h. The instantaneous velocity of the upper most points of its wheels is

 
 
 
 

16. A turtle starts swimming from a point A located on the circumference of a circular pond. After swimming for 4 meters in a straight line it hits point B on the circumference of the pond. From there it changes direction and swims for 3 meters in a straight line and arrives at point D diametrically opposite to point A. How far is point D from A?

 
 
 
 

17. A film projector and microscope give equal magnification. But a film projector is not used to see living cells because

 
 
 
 

18. At one instant, the hour hand and the minute hand of a clock are one over the other in between the markings for 5 and 6 on the dial. At this instant, the tip of the minute hand

 
 
 
 

19. A cubical cardboard box made of 1 cm thick card board has outer side of 29 cm. A tight-fitting cubical box of the same thickness is placed inside it, then another one inside it and so on. How many cubical boxes will be there in the entire set?

 
 
 
 

20. Density of a rice grain is 1.5 g/cc and bulk density of rice heap is 0.80 g/cc. If a 1 litre container is completely filled with rice, what will be the approximate volume of pore space in the container?

 
 
 
 

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