CAT Previous Paper 2009 Online Test

1. In triangle ABC, angle B is a right angle. If AC is 6cm, and D is the mid-point of side AC, the length of BD is:

2. Among the four infants, who grew the least in the first five months of life?

3. A, S, M and D are functions of x and y, and they are defined as follows:
A (x, y) = x + y
S (x, y) = x - y
M (x, y) = xy
D (x, y) = x/y, where y ? 0
What is the value of S(M(D(A(a, b), 2), D(A(a, b), 2)), M(D(S(a, b), 2), D(S(a, b), 2)))

4. Given the quadratic equation x² - (A -3) x² - (A - 2), for what value of A and B will the sum of the squares of the roots be zero?

5. Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE.
BOLT

6. A watch dealer incurs an expense of Rs 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs 250. If he fails to do so, he has to sell each watch for Rs. 100.
If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of:

7. A man has nine friends, four boys and five girls. In how many ways can he invite them. if there have to be exactly three girls in the invitees?

8. A watch dealer incurs an expense of Rs 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs 250. If he fails to do so, he has to sell each watch for Rs. 100.
If he produces 1500 watches, what is the number of watches that he must sell during the season in order to break even, given that he is able to sell all the watches produced?

9. If f(x) = x³ - 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?

10. A man travels from A to B at a speed of x kmph. He then rests at B or x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be:

11. If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be:

12. In a mile race Akshay can be given a start of 128 metres by Bhairav. If Bhairav can given Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser? (One mile is1600 metres).

13. Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE.
PASSING

14. Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries; textile, cement and steel.

An investor wants to buy stock of only steel or cement companies with a turnover more than 1000 and

15. A, S, M and D are functions of x and y, and they are defined as follows:
A (x, y) = x + y
S (x, y) = x - y
M (x, y) = xy
D (x, y) = x/y, where y ? 0
What is the value of M(M(A(M(x, y), S(x, y)), x), A (y, x)) for x = 2, y = 3

16. Companies that try to improve employees performance by _______ rewards encourage negative kinds of behaviour instead of _____ a genuine interest in doing the work well.

17. Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries; textile, cement and steel.

For how many steel companies with a turnover of more than 2000 is the profit less than 300?

18. Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash payment, what is his overall percent profit?

19. A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is r during the first 30 seconds, r/2 during next one minute, r/4 during next 2 minutes, r/8 during next 4 minutes, ans so on. What is the ratio of the time taken for the nth round to that for the previous round?

20. The length of an infant is one of the measures of his/her development in the early stages of his/her life. The figure below shows the growth chart of four infants in the first five months of life.

Who grew at the fastest rate in the first two months of life?

21. A closed wooden box of thickness 0.5 cm and length 31 cm, width 11 cm, and height 6 cm, is panted on the inside. The cost of painting is Rs. 70. What is the rate of painting in rupees per sq.cm?

22. A growing number of these expert professionals ________ having to train foreigners as the students end up _______ the teachers who have no then unhappily contend with no jobs at all or new jobs with drastically reduced pay packets.

23. Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE.
FALLOUT

24. In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs 18 min 15 seconds of watch time. What is the time gained or lost by this watch in one day?

25. The ________ regions of Spain all have unique cultures, but the _____ views within each region make the issue of an acceptable common language of instruction an even more contentious one.

26. The length of an infant is one of the measures of his/her development in the early stages of his/her life. The figure below shows the growth chart of four infants in the first five months of life.

The rate of growth during the third month was the lowest for

27. Let f(x) = ax² - b |x|, where a and bare constants. Then at x = 0, f(x) is

28. The length of an infant is one of the measures of his/her development in the early stages of his/her life. The figure below shows the growth chart of four infants in the first five months of life.

After which month did Rita's rate of growth start to decline?

29. Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries; textile, cement and steel.

For how many companies does the profit exceed 10% of turnover?