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 Mathematics MAT Feb 2006 Back to MAT Home

# Quantitative Aptitude MAT

1. There are 4 candidates for the post of a lecturer in Mathematics and is to be selected by votes of 5men. The number of ways in which the votes can be given is:

(A) 1048

(B) 1072

(C) 1024

(D) None of these

2. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by:

(A) 6! X 5!

(B) 5! X 4!

(C) 30

(D) 7! X 5!

3. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is:

(A) 140

(B) 280

(C) 196

(D) 346

4. A club consists of members whose ages are in A.P., the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 years, then the numbers of members in the club are:

(A) 15

(B) 20

(C) 25

(D) 30

5. A metal cube of edge 12cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6cm and 8cm, find the edge of the third smaller cube.

(A) 10cm

(B) 14cm

(C)12cm

(D) 16cm

6. A well has to be dug out that is to be 22.5m deep and of diameter 7m. Find the cost of plastering the inner curved surface at Rs. 3 per sq. meter.

(A) Rs. 1465

(B)Rs. 1485

(C) Rs. 1475

(D) Rs. 1495

7. Water flows out through a circular pipe whose internal diameter is 2cm, at the rate of 6 meters per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?

(A) 2m

(B) 4m

(C) 3m

(D) 5m

8. A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12m high. Find the width of the street.

(A) 19m

(B) 21m

(C) 20m

(D) 22m

9. The horizontal distance between two trees of different heights is 60m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.

(A) 20m

(B) 22m

(C) 18m

(D) 16m

10. The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is:

(A) 1960

(B) 3240

(C) 1540

(D) None of these

11. An aero plane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45°,respectively.Thenthe height of the lower plane from the ground, in metres, is:

(A)

(B) 50

(C)

(D)

12. A person standing on the bank of river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 metres away from the tree the angle of elevation becomes 30°.The breadth of the river is:

(A) 40m

(B) 20m

(C) 30m

(D) 60m

13. A room has 3 lamps .From a collection of 10 light bulbs of which are 6 are not good, a person selects 3 at random and puts them in a socket. The probability that he will have light, is:

(A) 5/6

(B) 1/2

(C) 1/6

(D) None of these

14. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected person will be a woman is:

(A) 25/39

(B) 5/13

(C) 14/39

(D) 10/13

15. The probability that a certain electronic component fails when first used is 0-10.If it does not fails immediately, the probability that it lasts for one year is 0-99.The probability that a new component will last for one year is:

(A) 0.89

(B) 0.92

(C) 0.692

(D) None of these

16. A circular grassy plot of land,42m in diameter, has a path 3.5 m wide running around it on the outside. The cost of gravelling the path at Rs.4 per square metre is:

(A) Rs.1002

(B) Rs.3002

(C) Rs.2002

(D) Rs.1802

17. A plot of land in the form of a rectangle has a dimension 240m X 180m.A drain let 10m wide is drug all around it(on the outside) and the earth dug all around it over the plot, increasing its surface level by 25cm.The depth of the drain let is:

(A) 1.225m

(B) 1.229m

(C) 1.227m

(D) 1.223m

18. A rectangle tank is 225m by 162m at the base. With what speed must water flow into it through an aperture 60cm by 45cm that the level may be raised 20cm in 5 hours?

(A) 5000m/hr

(B) 5400m/hr

(C) 5200m/hr

(D) 5600m/hr

19. An iron pipe 20cm long has exterior diameter equal to 25cm.If the thickness of the pipe is 1 cm ,the whole surface of the pipe is:

(A) 3068cm²

(B) 3268cm²

(C) 3168cm²

(D) 3368cm²

20. At appoint on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12.On walking 192 metres towards the tower, the tangent of the angle of elevation is 3/4.The height of the tower is:

(A) 160m

(B) 180m

(C) 0170m

(D) 190m

21. A man on the top of vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the tower?

(A) 14minutes 23 seconds

(B) 16minutes 2 3seconds

(C) 15 minutes 23 seconds

(D) 17minutes 23 seconds

22. A school has 4 sections of chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.

(A) 50.25

(B) 52.25

(C) 51.25

(D) 53.25

23. The average score of boys in an examination of a school is 71 and that of girls is 73.The average score of the school in that examination is 71.8.Find the ratio of the number of boys to the number of girls that appeared in the examination.

(A) 2:2

(B) 4:2

(C) 3:2

(D) 1:2

24. Company C sells a line of 25 products with an average retail price of Rs.1, 200. If none of these products sells for less than Rs 420 and exactly 10 of the products sell for less than Rs.1, 000, what is the greatest possible selling price of the most expensive products?

(A) Rs.2, 600

(B) Rs.7, 800

(C) Rs.3, 900

(D) Rs.11, 800

25. A sink contains exactly 12litres of water. If water is drained from the sink until it holds exactly 6 litres of water less than the quantity drained away, how many litres of water were drained away?

(A) 2

(B) 6

(C) 3

(D) 9

26. A chemist has 10litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many liters of water must be added?

(A) 15

(B) 20

(C) 18

(D) 25

27. A company received two shipments of ball bearings. In the first shipment,1 per cent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 per cent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, how many ball bearings were there in the first shipment?

(A) 990

(B) 2,000

(C) 1,000

(D) 3,000

28. In a certain laboratory, chemicals are identified by a color coding system. These are 20 different chemicals. Each one is coded with either a single color or a unique two color pair. If the order of colors in the pairs doesn’t matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of color?

(A) 5

(B) 7

(C) 6

(D) 20

29. Population of a district is 2, 96,000 out of which1, 66,000 are male.50% of the population is literate. If 70% male are literate, the number of women who are literate, is?

(A) 32,200

(B) 31,800

(C) 66,400

(D) 48,000

30. A train covers 180km distance in 4hours. Another train covers the same distance in 1 hour less. What is the difference covered by these trains in one hour?

(A) 45km

(B) 9km

(C) 40 km

(D) None of these

31. Speed of a speed –boat when moving in the direction perpendicular to the direction of the current is 16km/hr, speed of the current is 3km/hr. So the speed of the boat against the current will be (km/hr)?

(A) 22

(B) 9.5

(C) 10

(D) None of these

32. R and S start walking towards each other at 10 A.M. at speed of 3 km/hr and 4km/hr respectively. They were initially 17.5 km apart. At what time do they meet?

(A) 2:30P.M.

(B) 11:30P.M.

(C) 1:30P.M.

(D) 12:30P.M.

33. A shopkeeper marks up his goods to gain 35%.But he allows 10% discount for cash payment .His profit on the cash transaction therefore, in percentage, is:

A.

B. 25

C.

D.

34. A can do 50% more as B can do in the same time .B alone can do a piece of work in 20 hours. A, with the help of B can finish the same work in how many hours?

A. 12

B. 8

C.

D.

35. Profits of a business are distributed among three partners A, B and C in such a way that 4 times that amount received by A is equal to 6 times the amount received by B and 11 times the amount received by C. The ratio in which the three received the amount is:

A. 4:6:11

B. 11:6:4

C.

D. 66:44:24

36. A train covered a certain distance at uniform speed. If the train had been 6 km/h faster. It would have taken 4 hours less than the scheduled time. And, if the train were slower by 6km/h. the train would have taken 6 hours more than the scheduled time. The length of the journey is:

(A) 700km

(B) 740km

(C) 720km

(D) 760km

37. Students of a class are made to stand in rows. If 4 students are extra in each row, there would be 2row less. If 4 students are less in each row, there would be 4 more rows. The number of students in the class is:

(A) 90

(B) 94

(C) 92

(D) 96

38. A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs.250 a quintal, the total monthly expenses of the family are Rs.1000 and when it is Rs.240 a quintal, the total monthly expenses are Rs.980.Find the total monthly expenses of the family when the cost of wheat is Rs.350 a quintal.

(A) Rs.1000

(B) Rs.1400

(C) Rs.1200

(D) Rs.800

39. A plane left 30minutes later than the scheduled time and in order to reach the destination 1500km away in time, it had to increase the speed by 250km/h from the usual speed. Find its usual speed:

(A) 720km/h

(B) 740km/h

(C) 730km/h

(D) 750km/h

40. A metallic sheet is of rectangular shape with dimensions 48cm x 36 cm. From each one of its corners, a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box.

(A) 5110cm³

(B) 5130cm³

(C) 5120cm³

(D)5140cm³