“June 2017: Life Sciences and Physical Sciences”

1. A bread contains 40% (by volume) edible matter and the remaining space is filled with air. If the density of edible matter is 2 g/cc, what will be the bulk density of the bread (in g/cc)?

 
 
 
 

2. An ant starts at the origin and moves along the y-axis and covers a distance l. This is its first stage in its journey. Every subsequent stage requires the ant to turn right and move a distance which is half of its previous stage. What would be its coordinates at the end of its 5th stage?

 
 
 
 

3. A job interview is taking place with 21 male and 17 female candidates. Candidates are called randomly. What is the minimum number of candidates to be called to ensure that at least two males or two females have been interviewed?

 
 
 
 

4. The graph shows cumulative frequency % of research scholars and the number of papers published by them. Which of the following statements is true?

 
 
 
 

5. A board has 8 rows and 8 columns. A move is defined as two steps along a column followed by one step along a row or vice-versa. What is the minimum number of moves needed to go from one comer to the diagonally opposite comer?

 
 
 
 

6. A fair die was thrown three times and the outcome was repeatedly six. If the die is thrown again what is the probability of getting six?

 
 
 
 

7. Consider a circle of radius r. For the largest possible square inside it and the largest possible circle inside the square. What is the radius of the innermost circle?

 
 
 
 

8. In a group of siblings there are seven sisters, and each sister has one brother. How many siblings are there in total?

 
 
 
 

9. Which is the odd one out based on a divisibility test? 154, 286, 363, 474, 572, 682

 
 
 
 

10. A tells only lies on Monday, Tuesday and Wednesday and speaks only the truth for the rest of the week. B tells only lies on Thursday, Friday and Saturday and speaks only the truth for the rest of the week. If today both of them state that they have lied yesterday, what day is it today?

 
 
 
 

11. What is the average value of y for the range of x shown in the following plot?

 
 
 
 

12. In how many ways can you place N coins on a board with N rows and N columns such that every row and every column contains exactly one coin?

 
 
 
 

13. In ΔABC, AB = AC and ∠ BAC = 90°; EF||AB and DF||AC. The total area of the shaded region is?

 
 
 
 

14. A 100 m long train crosses a 200 m long and 20 m wide bridge in 20 seconds. What is the speed of the train in km/hr?

 
 
 
 

15. Two identical wheels B and C move on the periphery of circle A. Both start at the same point on A and return to it, B moving inside A and C outside it. Which is the correct statement?

 
 
 
 

16. A square is drawn with one of its sides as the hypotenuse of a right angled triangle as shown in the figure. What is the area of the shaded circle?

 
 
 
 

17. Which of the following is the odd one out?

 
 
 
 

18. What should be added to the product of the two numbers 983713 and 983719 to make it a perfect square?

 
 
 
 

19. Find the missing word: A, AB, __, ABBABAAB

 
 
 
 

20. My birthday is in January. What would be a sufficient number of questions with ‘Yes/No’ answers that will enable one to find my birth date?

 
 
 
 

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