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:
(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!
(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:
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:
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.
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
(A) Rs. 1465
(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
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.
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.
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:
(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,
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:
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:
(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:
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:
(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:
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:
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?
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:
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:
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
(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
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.
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?
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?
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?
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?
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?
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?
(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)?
(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?
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
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?
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:
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:
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:
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.
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:
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.