SSC Mains Test- 13 - SSC Exam Tutornotes.sscexamtutor.com/Maths/Questions/SSC MAINS MOCK...The LCM...
Transcript of SSC Mains Test- 13 - SSC Exam Tutornotes.sscexamtutor.com/Maths/Questions/SSC MAINS MOCK...The LCM...
Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR ��������DILSHAD GARDEN ���� ROHINI ����BARDARPUR BORDER
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1. If the fractions 7
5,
11
8,
3
2,
13
9 are arranged
in ascending order, then the correct
sequence is
(A)7
5,
11
8,
3
2,
13
9(B)
7
5,
11
8,
13
9,
3
2
(C) 13
9,
7
5,
11
8,
3
2(D)
13
9,
3
2,
11
8,
7
5
2.1/2 1/2(28 10 3) (7 4 3)�� � � is equal to
(A) 1074 (B) 1075
(C) 1000 (D) None of these
3. If x is a positive number, then which of the
following fractions has the greatest value?
(A) x
x(B)
x
x )1( �
(C) )1( �x
x(D)
)3(
)2(
�
�
x
x
4. One of a group of swans, 7/2 times the
square root of the number are playing on
the shore of the pond. The two remaining
are inside the pond. What is the total
number of swans?
(A) 10 (B) 14
(C) 12 (D) 16
5. The remainder when 784 is divided by 342
is
(A) 0 (B) 1
(C) 49 (D) 341
6. Students of a class are preparing for a drill
and are made to stand in a row. If 4
students are extra in a row, then there
would be 2 rows less. But there would be 4
more rows if 4 students are less in a row
The number of students in the class is
(A) 96 (B) 56
(C) 69 (D) 65
7. The LCM and HCF of two numbers are 84
and 21 respectively. If the ratio of the two
numbers is 1 : 4, then the larger of the two
number is
(A) 12 (B) 48
(C) 84 (D) 108
8. A printer numbers the pages of a book
starting with I and uses 3189 digits in all.
How many pages does the book have?
(A) 1074 (B) 1075
(C) 1000 (D) None of these
9. The sum of 40 terms of an AP whose firstterm is 4 and common difference is 4, will be(A) 3200 (B) 1600
(C) 200 (D) 280010. In a GP the first term is 5 and the common
ratio is 2. The eighth term is(A) 640 (B) 1280
(C) 256 (D) 16011. Out of 80 students in a class, 25 are studying
commerce, 15 Mathematics and 13 Physics.3 are studying Commerce and Mathematics,4 are studying Mathematics and Physics
and 2 are studying Commerce and Physics.1 student Commerce and Physics. 1commerce and Physics. 1 student is
studying all the three subjects together.How many students are not studying any ofthe three subjects?
(A) 35 (B) 40(C) 20 (D) 15
12. A batsman has a certain average of runs
for 12 innings. In the 13th inning, he scores96 runs thereby increasing his average by5 runs. What is his average after the 13th
innings?(A) 64 (B) 48(C) 36 (D) 72
13. The average monthly salary of employees,consisting of officers and workers of an
organization is 3000. The average salary
of an officer is 10000 while that of a worker
is 2000 per month. If there are total 400employees in the organization, find the
number of officers and workers separately.(A) 50, 350 (B) 350, 450(C) 50, 275 (D) 325, 350
14. The sum of the reciprocals of the ages oftwo brothers is five times the difference ofthe reciprocals of their ages. If the ratio of
the product of their ages to the sum of theirages is 14.4 : 1, find their ages.(A) 36 and 24 yr (B) 24 and 20 yr
(C) 18 and 15 yr (D) 12 and 9 yr15. A trader has 50 kg of rice, a part of which
he sells at 10% profit and the rest at 5%
loss. He gain 7% on the whole. How muchwas sold at 10% gain and how much wassold at 5% loss?
(A) 40 kg and 15 kg(B) 30 kg and 10 kg(C) 35 kg and 40 kg
(D) 40 kg and 10 kg
SSC Mains Test- 13
2
7
5,
11
8,
3
2,
13
9
(A)9 2 8 5
, , ,13 3 11 7
(B) 7
5,
11
8,
13
9,
3
2
(C) 13
9,
7
5,
11
8,
3
2(D)
13
9,
3
2,
11
8,
7
5
1/2 1/2(28 10 3) (7 4 3)�� � �
(A) 1074 (B) 1075
(C) 1000 (D)
x
(A) x
x(B)
x
x )1( �
(C) )1( �x
x(D)
)3(
)2(
��
x
x
2
7
(A) 10 (B) 14
(C) 12 (D) 16
(A) 0 (B) 1
(C) 49 (D) 341
(A) 96 (B) 56
(C) 69 (D) 65
(A) 12 (B) 48
(C) 84 (D) 108
(A) 1074 (B) 1075
(C) 1000 (D)
SSC Mains Test- 13
AP
(A) 3200 (B) 1600
(C) 200 (D) 2800
GP
(A) 640 (B) 1280
(C) 256 (D) 160
(A) 35 (B) 40
(C) 20 (D) 15
(A) 64 (B) 48
(C) 36 (D) 72
(A) 50, 350 (B) 350, 450
(C) 50, 275 (D) 325, 350
(A) 36 24 (B) 24 20
(C) 18 15 (D) 12 9
(A) 40 15
(B) 30 10
(C) 35 40
(D)40 10
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16. A chemist has 10 L of a solution that has
10% nitric acid by volume. He wants to
dilute the solution to 4% strength by adding
water. How many litres of water must he
add?
(A) 15 (B) 20
(C) 18 (D) 25
17. A pilot flies an aircraft at a certain speed
for a distance of 800 km. He could have
saved 40 min by increasing the average
speed of the plane by 40 km/h. Find the
average speed of the aircraft.
(A) 200 km/h (B) 300 km/h
(C) 240 km/h (D) None of these
18. Mohan and Puran are running towards
each other, each one from his own house.Mohan can reach Puran’s house in 25 minof running, which is half the time Puran
takes to reach Mohan’s house. If the twostarted running at the same time, howmuch more time will it take Puran to reach
the middle than Mohan?
(A) 35 min (B) 25 min
(C) 12.5 min (D) 50 min
19. X runs 1
12
times as fast as Y. If X gives Y a
start of 300 m, how far must X run beforehe catches up with Y?
(A) 450 m (B) 400 m
(C) 1 km (D) 900 m
20. Two shopkeepers announce the same price
of 700 for a shirt. The first offerssuccessive discounts of 30% and 6% whilethe second offers successive discounts of
20% and 16%. The shopkeeper that offersbetter discount is more of
(A) 22.40 (B) 16.80
(C) 9.80 (D) 36.40
21. Sita buys a fridge at 15
16 of its original value
and sells it for 10% more than its value.Then, gain per cent is
(A) 15.55 (B) 11.67
(C) 16.67 (D) None of these
22. A motor boat can travel at 10 km/h in still
water. It travelled 91 km downstream in ariver and then returned, taking altogether
20 hrs. . Find the rate of flow of the river.
(A) 6 km/h (B) 5 km/h
(C) 8 km/h (D) 3 km/h
23. A booster pump can be used for filling aswell as for emptying a tank. The capacity of
the tank is 2400 m3. The emptying capacity
of the tank is 10 m3 per minute higherthan its filling capacity and the pump needs
8 min lesser to empty the tank than itneeds to fill it. What is the filling capacity
of the pump?
(A) 50m3/min (B) 60m3/min
(C) 72m3/min (D) 36 m3/min
24. A tank is filled by three pipes . The first two
pipes operating simultaneously fill the tank
in the same time during which the tank is
filled by the third pipe alone. The second
pipe fills the tank 5 h faster than the first
pipe and 4 h slower than the third pipe. The
time required by the first pipe is
(A) 6 h (B) 10 h
(C) 15 h (D) 30 h
25. A contractor employed 25 labourers on a job.
He was paid 275 for the work. After
retaining 20% of this sum, he distributed
the remaining amount amongst the
labourers. If the number of men to women
labourers was in the ratio 2 : 3 and their
wages in the ratio 5 : 4, what wages did a
woman labourer get?
(A) 10 (B) 8
(C) 12 (D) 15
26. X contributes 1500 and Y 900 in a
business. X is a sleeping partner and Y gets
10% of the profit for management and the
rest of the profit is divided in the proportion
of their capital. If the profit is 800, what
is the share of Y?
(A) 375 (B) 360
(C) 350 (D) 450
27. Sumit lent some money to Mohit at 5% per
annum simple interest. Mohit lent the
entire amount to Birju on the same day
at 1
82
% per annum. In this transaction
after a year. Mohit earned a profit of 350.
Find the sum of money lent by Sumit to
Mohit.
(A) 10000 (B) 9000
(C) 10200 (D) None of these
28. A computer is available for 39000 cash
or 17000 as cash down payment followed
by five monthly instalments of 4800
each. What is the rate of interest per
annum under the instalment plan?
(A) 35.71% (B) 37.71%
(C) 36.71% (D) 38.71%
4
(A) 15 (B) 20
(C) 18 (D) 25
(A) 200 (B) 300
(C) 240 (D)
(A) 35 (B) 25
(C) 12.5 (D) 50
X, Y 2
11 X, Y
300 X Y
(A) 450 (B) 400
(C) 1 (D) 900
(A) 22.40 (B) 16.80
(C) 9.80 (D) 36.40
16
15
(A) 15.55 (B) 11.67
(C) 16.67 (D)
(A) 6 (B) 5
(C) 8 (D) 3
(A) 50 / (B) 60 /
(C) 72 / (D) 36 /
(A) 6 (B) 10
(C) 15 (D) 30
(A) ` 10 (B) ` 8
(C) ` 12 (D) ` 15
X, Y,
X Y
Y
(A) 375 (B) 360
(C) 350 (D) 450
%2
18
(A) 10000 (B) 9000
(C) 10200 (D)
(A) 35.71% (B) 37.71%
(C) 36.71% (D) 38.71%
Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR ��������DILSHAD GARDEN ���� ROHINI ����BARDARPUR BORDER
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5
29. Anu is a working partner and Bimla is a
sleeping partner in a business. Anu puts
in 5000 and Bimla puts in 6000. Anureceives 12.5% of the profit for managing
the business and the rest is divided in
proportion to their capital. What does each
get out of a profit of 880?
(A) 400 and 480
(B) 460 and 420
(C) 450 and 430
(D) 470 and 410
30. The population of a city increases at a rate
of 4% perannum. There is an additional
annual increase of 1% in the population due
to the influx of job seekers. The total
percentage increase in the population after 2 yr.
(A) 10.25% (B) 10%
(C) 10.50% (D) 10.75%
31. In an examination, 30% and 35% students
respectively failed in History and Geography
while 27% students failed in both the
subjects. If the number of students passing
the examination is 248, then find the totalnumber of students who appeared in the
examination.
(A) 425 (B) 400
(C) 380 (D) 725
32. In an examination, it is required to get 296
of the total maximum aggregate marks to
pass. A student gets 259 marks and is
declared failed. The difference of marks
obtained by the student and that required
to pass is 5%. What are the maximum
aggregate marks a student can get?
(A) 690 (B) 780
(C) 740 (D) Cannot be determined
33. Ram spends 20% of his monthly income on
his household expenditure, 15% of the rest
on books, 30% of the rest on clothes and
saves the rest. On counting, he comes to
know that he has finally saved 9520. Find
his monthly income.
(A) 15000 (B) 10000
(C) 20000 (D) None of these
34. In an examination, there were 2000
candidates, out of which 900 candidates
were boys and the rest were girls. If 32% of
the boys and 38% of the girls passed, then
the total percentage of failed candidates is
(A) 68.5% (B) 64.7%
(C) 35.3% (D) 70%
35. There were two candidates in an election,10% of the voters did not vote. 60 votes weredeclared invalid. The elected candidate got
308 votes more than his opponent. If theelected candidate got 47% of the total votes,how many votes did each candidate get?
(A) 2316 and 2012
(B) 2629 and 2324
(C) 2871 and 2575
(D) 2914 and 2606
36. A student purchased a computer system anda colour printer. If he sold the computer
system at 10% loss and the colour printerat 20% gain, he would not lose anything.But if he sells the computer system at 5%gain and the colour printer at 15% loss, he
would lose 800 in the bargain. How much
did he pay for the colour printer?
(A) 8000 (B) 16000
(C) 9000 (D) 5334
37. A man sells a book at a profit of 20%. If he
had bought it at 20% less and sold it for
18 less, he would have gained 25%. The
cost price of the book is
(A) 80 (B) 70
(C) 60 (D) 90
38. Even after reducing the marked price of a
transistor by 32, a shopkeeper makes a profit
of 15%. If the cost price be 320, whatpercentage of profit would he have made if he
had sold the transistor at the marked price?
(A) 25% (B) 20%
(C) 10% (D) None of these
39. A man buys apples at a certain price perdozen and sells them at eight times per
hundred. What is his gain or loss percent?
(A) 4% loss (B)1
84
% loss
(C) 4% gain (D)1
64
% gain
40. Two trains move from station A andstation B towards each other at the speedof 50 km/h and 60 km/h. At the meetingpoint, the driver of the second train foundthat the train has covered 120 km more.
What is the distance between A and B?
(A) 1320 km (B) 1100 km
(C) 1200 km (D) 960 km
41. A train overtakes two persons walkingalong a railway track. The first one walksat 4.5 km/h and the other one walks at 5.4km/h. The train needs 8.4 and 8.5 srespectively to overtake them. What is thespeed of the train if both the persons arewalking in the same direction as the train?
(A) 66 km/h (B) 72 km/h
(C) 78 km/h (D) 81 km/h
6
(A) 400 480
(B) 460 420
(C) 450 430
(D) 470 410
(A) 10.25% (B) 10%
(C) 10.50% (D) 10.75%
(A) 425 (B) 400
(C) 380 (D) 725
(A) 690 (B) 780
(C) 740 (D)
(A) 15000 (B) 10000
(C) 20000 (D)
(A) 68.5% (B) 64.7%
(C) 35.3% (D) 70%
(A) 2316 2012 (B) 2629 2324
(C) 2871 2575 (D) 2914 2606
(A) 8000 (B) 16000
(C) 9000 (D) 5334
(A) 80 (B) 70
(C) 60 (D) 90
(A) 25% (B) 20%
(C) 10% (D)
(A) 4% (B)1
84
%
(C) 4% (D)1
64
%
A B
A B
(A) 1320 (B) 1100
(C) 1200 (D) 960
(A) 66 (B) 72
(C) 78 (D) 81
7
42. Ashokan is thrice as good a workman as
Nitin and is therefore able to finish a piece
of work in 40 days less than Nitin. Find the
time in which they can do it working
together.
(A) 15 days (B) 7 days
(C) 16 days (D) 13 days
43. If 15 men or 24 women or 36 boys can do a
piece of work in 12 days, working 8 h a day,
how many men must be associated with 12
women and 6 boys to do another piece of
work 2.25 times in 30 days working 6 h in
a day?
(A) 9 (B) 7
(C) 5 (D) 8
44. A team of workers was employed by a
contractor who undertook to finish 360
pieces in a certain number of days. Making
four more pieces per day that was planned,
they could complete the job a day ahead of
schedule. How many days did they take to
complete the job?
(A) 8 days (B) 10 days
(C) 9 days (D) 12 days
45. The ratio of milk to water in three
containers of equal capacity is 3 : 2, 7 : 3
and 11 : 4 respectively. The three containers
are mixed together. What is the ratio of
milk to water after mixing?
(A) 38 : 8 (B) 21 : 9
(C) 61 : 29 (D) 41 : 18
46. The sum of money is to be divided amongst
A, B and C in the respective ratio of 3 : 4 : 5
and another sum of money is to be divided
between E and F equally. If F got 1050
less than A, how much amount did B
receive?
(A) 750 (B) 2000
(C) 1500 (D) Cannot be determined
47. Salaries of A, B and C are in the ratio 3:5:7,
respectively. If their salaries are increased
by 50%, 60% and 50% respectively, what will
be the new ratio of their respective
salaries?
(A) 4 : 5 : 7 (B) 3 : 6 : 7
(C) 4 : 15 : 18 (D) 9 : 16 : 21
48. Given that 24 carat gold is pure gold, 18
carat gold is 4
3gold and 20 carat gold is
5
6
gold, the ratio of the pure gold in 18 carat
gold to the pure gold in 20 carat gold is
(A) 5 : 8 (B) 9 : 10
(C) 15 : 24 (D) 8 : 5
49. The monthly incomes of two persons are in
the ratio of 4 : 5 and their monthly
expenditures are in the ratio of 7 : 9. If each
saves 50 a month, then what are their
monthly incomes?
(A) 100, 125 (B) 200, 250
(C) 300, 375 (D) 400, 500
50. What is the next number in the series
given below?
2, 5, 9 14, 20
(A) 25 (B) 26
(C) 27 (D) 28
51. If 23
242
��x , then
12
12
8
8
�
��
�
�
x
x
x
x will
be?
(A) 1 (B) 2
(C) 0 (D) –2
52. If 223 ��a , then the value of
3
246 1
a
aaa ���
(A) 204 (B) 212
(C) 192 (D) 240
53. If x = 997, y = 998, z = 999, then x2 + y2 + z2
– xy – yz – zx will be
(A) 3 (B) 9
(C) 16 (D) 4
54. If 53
15 ��
aa , the value of 2
2
25
19
aa � = ?
(A) 5
51(B)
5
29
(C) 5
52(D)
5
39
55. If 31
2
���
���
�
xx , then what will be the value
of x206 + x200 + x90 + x84 +x18 + x12 + x6 + 1?
(A) 84 (B) 206
(C) 0 (D) 1
56. If (a – b) = 3, (b – c) = 5 and (c – a) = 1, then
the cba
abccba
����� 3333
will be
(A) 17.5 (B) 20.5
(C) 10.5 (D) 15.4
57. What will be the value of t, if expression
4
2
2
2 ytx
y
x�� is a perfect square.
(A) 1 (B) 2
(C) 0 (D) 3
8
(A) 15 (B) 7
(C) 16 (D) 13
(A) 9 (B) 7
(C) 5 (D) 8
(A) 8 (B) 10
(C) 9 (D) 12
(A) 38 : 8 (B) 21 : 9
(C) 61 : 29 (D) 41 : 18
A, B C
E F
F A
B
(A) 750
(B) 2000
(C) 1500
(D)
A, B C
(A) 4 : 5 : 7 (B) 3 : 6 : 7
(C) 4 : 15 : 18 (D) 9 : 16 : 21
4
3
6
5
(A) 5 : 8 (B) 9 : 10
(C) 15 : 24 (D) 8 : 5
(A) 100, 125 (B) 200, 250
(C) 300, 375 (D) 400, 500
(A) 25 (B) 26
(C) 27 (D) 28
23
242
��x
12
12
8
8
�
��
�
�
x
x
x
x
B
C D
223 ��a 3
246 1
a
aaa ���
B
C D
; fn x = 997, y = 998, z = 999 x2 + y2 + z2
– xy – yz – zx
B
C D
53
15 ��
aa
2
2
25
19
aa �
5
51B
5
29
C5
52D
5
39
31
2
���
���
�
xx x206 + x200 + x90 + x84 +
x18 + x12 + x6 + 1
B
C D
(a – b) = 3, (b – c) = 5 (c – a) = 1
cba
abccba
����� 3333
B
C D
4
2
2
2 ytx
y
x�� t
1 B 2
C D 3
9
58. For what value of 'a' and 'b', (a>0, b<0) the
expression bxaxx ��� 548 23 is a perfect
cube?
(A) 27,18 ��� ba (B) 9,16 ��� ba
(C) 9,12 ��� ba (D) 27,36 ��� ba
59. If (a – b) and (a + 3, b + k) are co-ordinates of
two different points situated on the straight
line x = 3y – 7 in xy-co-ordinate system, then
the value of k will be ?
(A) 3
7(B) 1
(C) 9 (D) 3
60. Area enclosed by the equations y = |x| – 5
in xy-co-ordinates system is
(A) 50 sq. unit (B) 20 sq. unit
(C) 25 sq. unit (D) 52 sq. unit
61. A and B are the centres of two circles whose
radii are 5 cm and 2 cm respectively. The
common tangent to the circles meets AB
produced at the point P, then P divides AB –
(A) Externally in the ratio of 5 : 2
(B) Internally in the ratio of 2 : 5
(C) Interally in the ratio of 5 : 2
(D) Externally in the ratio of 7 : 2
62. D and E are two points on the sides AB and
AC of a triangle ABC in a such way that
DE||BC. DE, divides traingle ABC into two
parts of a equal area, then what is the ratio
between AD and BD?
(A) 2:1 (B) 12:1 �
(C) 1 : 1 (D) 12:1 �
63. There are two circles of radii 6 cm and 3
cm. There is a common tangent whose
length is 8 cm, then distance between their
centres will be –
(A) 150 cm (B) 135 cm
(C) 145 cm (D) 140 cm
64. Out of 5 angles of a polygon each one is 172º
and out of the remaining angles of the same
polygon each one is of 160º. The number of
sides of the polygon is –
(A) 20 (B) 21
(C) 22 (D) 23
65. Out of the line segments of length 2 cm,
3 cm, 5 cm and 6 cm, how many triangles
can be formed by using any three of them ?
(A) 4 (B) 3
(C) 2 (D) 1
66. ABCD is a rhombus. If AB is produced to F
and BA is produced to E in a such manner
that AB = AE = BF, then the result will be ?
ED || CF B ED > CF
C ED �CF D ED2 + CF2 = EF2
67. A boy is standing in a field. He observes abird flying in the north direction at anelevation of 30º. Two minutes later, heobserves the same bird flying in the southdirection at an elevation of 60º. If the bird is
flying at a height of 350 m in a straight line,
then the speed of the bird (in km/hr) is–
(A) 3 (B) 9
(C) 6 (D) 4.5
68. Rama owns a piece of land in the shape of aright triangle. Its hypotenuse is 3 m morethan twice the shortest side. If theperimeter of the piece of land is 6 timesthe shortest side, find the dimensions (in
meter) of the piece of land.
(A) 6, 15, 12 (B) 5, 12, 13
(C) 4, 9, 11 (D) None of these
69. If P and Q are the mid-points of the sidesCA and CB respectively of a triangle ABC,
right angled at C. Then, the value of
4 (AQ2 + BP2) is equal to
(A) 4BC2 (B) 5AB2
(C) 2AC2 (D) 2BC2
70. A rhombus OABC is drawn inside a circlewhose centre is at O in such a way that the
vertices A, B and C of the rhombus are on
the circle. If the area of the rhombus is
332 m2, then the radius of the circle is
(A) 64 m (B) 8 m
(C) 32 m (D) 46 m
71. If cba ���� cossin , then the value of
��� sincos ba will be ?
(A) 222 cba �� (B) 222 cba ���
(C) 222 cba �� (D) 222 cba ��
72. If )º90º0(4
1sec � ���
xx , then
��� tansec will be equal to?
(A) x (B) x2
1
(C) 2
x(D) 2x
73. The value of � , ]º90º0[ � for which
4sin1
cos
sin1
cos�
���
����
is –
(A) º45 (B) º60
(C) º30 (D) None of these
10
a b )0,0( � ba
bxaxx ��� 548 23
27,18 ��� ba B 9,16 ��� ba
C 9,12 ��� ba D 27,36 ��� ba
xy )( ba � (a + 3, b + k)
x = 3y – 7 k
3
7B
C D
y = |x| – 5
B
C D
A B
AB P P AB
B
C
D
ABC D E AB AC
DE || BC DE ABC
AD
BD
2:1 B 12:1 �
C D 12:1 �
150 B 135
C 145 D 140
B
C D
B
C D
ABCD AB F
BA E AB = AE =
BF
ED || CF B ED > CF
C ED �CF D ED2 + CF2 = EF2
350
B
C D
(A) 6, 15, 12 (B) 5, 12, 13
(C) 4, 9, 11 (D)
P Q ABC CA CB
C
4(AQ2 + BP2)
(A) 4BC2 (B) 5AB2
(C) 2AC2 (D) 2BC2
OABC O
A, B
C
332
(A) 64 (B) 8
(C) 32 (D) 46
cba ���� cossin ��� sincos ba
222 cba �� B 222 cba ���
C 222 cba �� D 222 cba ��
1sec ,(0º 90º )
4x
x� � � �
��� tansec
x Bx2
1
C2
xD 2x
� ]º90º0[ �
4sin1
cos
sin1
cos�
���
����
º45 B º60
C º30 D
Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR ��������DILSHAD GARDEN ���� ROHINI ����BARDARPUR BORDER
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11
74. If ���� nnnu sincos , then how much will
132 46 �� uu be ?
(A) 1 (B) 4
(C) 6 (D) 0
75. If 2222 cos2sin)( baabba ������ , then
what will be the value of �tan ?
(A) )(2
1 22 ba � (B) )(2
1 22 baab
�
(C) )(2
1 22 baab
� (D) )(2
1 22 baab
�
76. If 1sin
sin
cos
cos2
4
2
4
��
��
�
�, then
�
��
�
�2
4
2
4
sin
sin
cos
cos is
equal to –
(A) 4 (B) 0
(C) 8
1(D) 1
77. If 1cos
)1(coscossincos
2
2222
��
�������
ec
ecml ,
where º90º0 � , then ?tan ��
(A) 1
2
�
�
m
l(B)
m
l
�
�
2
1
(C) m
l
�
�
1
2(D)
m
l
�
�
1
2
78. If 3 3sin cos sin cos , 0x y� � � � � � � � and
0cossin ���� yx , then the value of
22 yx � is –
(A) 4 (B) 9
(C) 1 (D) 2
79. Two points are at a distance of x and y
respectively on the same side of the base
of a tower, if the angles of elevation of these
points with the top of the tower are
complementry. The height of the tower is –
(A) y
x(B) yx �
(C) xy (D) y
x
80. What will be the area of the trapezium
formed by x -axis, y-axis and the lines
3x + 4y = 12 and 6x + 8y = 60 ?
(A) 31.5 sq. units (B) 48 sq. units
(C) 36.5 sq. units (D) 37.5 sq. units
81. A reservoir is in the shape of a frustum of a
right circular cone. It is 8 m across at the
top and 4 m across the bottom. It is 6 m
deep. Find the area of its curved surface.
(A) 118.4 m2 (B) 162.3 m2
(C) 452 m2 (D) 181.6 m2
82. Two cans have the same height equal to
21 cm. One can is cylindrical, the diameter
of whose base is 10 cm. The other can has
square base of side 10 cm. What is the
difference in their capacities?
(A) 350 cm3 (B) 250 cm3
(C) 450 cm3 (D) 300 cm3
83. What is the total surface area of a
triangular prism whose height is 30 m and
the sides of whose base are 21 m, 20 m and
13 m, respectively?
(A) 1872 sq m (B) 1725 sq m
(C) 1652 sq m (D) 1542 sq m
84. A sector of a circle of radius 15 cm has the
angle 120°. It is rolled up so that two
bounding radii are joined together to form
a cone. The volume of the cone is
(A) 250 2 � cm3
(B) [(500 2 ) � /3] cm3
(C) [(250 2 ) � /3] cm3
(D) [(100 2 ) � /3] cm3
85. In measuring the sides of a rectangular
plot, one side is taken 5% in excess and
the other 6% in deficit. The error percent
in area calculated of the plot is
(A) 1 % (B) 1.3 %
(C) 1.5 % (D) 3 %
86. A cylindrical tub of radius 12 cm contains
water up to a depth of 20 cm. A spherical
iron ball is dropped into the tub and thus
the level of water is raised by 6.75 cm. The
radius of the ball is
(A) 7.25 cm (B) 6 cm
(C) 4.5 cm (D) 9 cm
87. A spherical ball of lead, 3 cm in diameter is
melted and recast into three spherical balls.
The diameter of two of these are 1.5 cm and
2 cm respectively. The diameter of the third
ball is
(A) 3 cm (B) 2.66 cm
(C) 2.5 cm (D) 3.5 cm
88. A 4 cm cube is cut into 1 cm cubes. Find
the percentage increase in surface area.
(A) 200% (B) 100%
(C) 400% (D) 300%
12
���� nnnu sincos 132 46 �� uu
B
C D
2222 cos2sin)( baabba ������
�tan
)(2
1 22 ba � B )(2
1 22 baab
�
C )(2
1 22 baab
� D )(2
1 22 baab
�
1sin
sin
cos
cos2
4
2
4
��
��
�
�
�
��
�
�2
4
2
4
sin
sin
cos
cos
B
C8
1D
1cos
)1(coscossincos
2
2222
��
�������
ec
ecml
º90º0 � ?tan ��
1
2
�
�
m
lB
m
l
�
�
2
1
Cm
l
�
�
1
2D
m
l
�
�
1
2
3 3sin cos sin cosx y�� �� � � , 0� �
0cossin ���� yx 22 yx �
B
C D
x y
y
xB yx �
C xy Dy
x
x y 3x + 4y = 12 6x + 8y = 60
B
C D
(A) 118.4 2 (B) 162.3 2
(C) 452 2 (D) 181.6 2
(A) 350 3 (B) 250 3
(C) 450 3 (D) 300 3
(A) 1872 (B) 1725
(C) 1652 (D) 1542
(A) (250 2 )� 3
(B) [(500 2 ) � /3] 3
(C) [(250 2 ) � /3] 3
(D) [(100 2 ) � /3] 3
(A) 1 % (B) 1.3 %
(C) 1.5 % (D) 3 %
(A) 7.25 (B) 6
(C) 4.5 (D) 9
(A) 3 (B) 2.66
(C) 2.5 (D) 3.5
(A) 200% (B) 100%
(C) 400% (D) 300%
Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR ��������DILSHAD GARDEN ���� ROHINI ����BARDARPUR BORDER
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13
89. The area of the largest circle, that can be
drawn inside a rectangle with side 18 cm
by 14 cm is
(A) 49 cm2 (B) 154 cm2
(C) 378 cm2 (D) 1078 cm2
90. Dimensions of a cuboid are 25 cm × 20 cm
× 4 cm. The volume of a cube is half the
volume of the cuboid. Total surface area of
such a cube is
(A) 400 cm2 (B) 600 cm2
(C) 800 cm2 (D) 1200 cm2
Directions (91-95) These questions are based
on the pie charts which represent the shift in
water usage between 2006 and 2009; based on
a survey conducted by Central Water
Commission.
Water usage in 2006 (In trillion litres)
Water usage in 2009 (In trillion litres)
91. If the ratio of processing cost for water for
industrial, energy and domestic usage is
3 : 5 : 2, what is the ratio of processing cost
for above mentioned usage in 2006 to that
in 2009?
(A) 0.68 (B) 0.72
(C) 0.60 (D) 0.77
92. What is the percentage increase in usage
in energy related sector from 2006 to 2009?
(A) 34.6% (B) 23.3%
(C) 15.4% (D) 17%
93. What is the irrigation usage as percentage
of total usage in 2009?
(A) 65.18% (B) 83.45%
(C) 77.9% (D) 69.6%
94. What is the difference in domestic usage
as percentage of total usage between 2006
and 2009?
(A) 3.16 (B) 2.08
(C) 2.26 (D) 1.82
95. Which one out of the four shows the highest
percentage increase in usage from 2006 to
2009?
(A) Domestic (B) Industrial
(C) Others (D) Energy
Directions (96-100) Study the following graph
and answer these questions following it.
96. By how much amount are the sales in 1989
more than that in 1987 ?
(A) 100 (B) 10000
(C) 100000 (D) 1000000
97. The sales in 1987 are how many times to
that in 1988 ?
(A) 0.8 (B) 1.25
(C) 8 (D) 0.25
98. In which year do the sales show the least
per cent increase over those in the
preceding year ?
(A) 1986 (B) 1988
(C) 1989 (D) 1990
99. The ratio of the number of years for which
the sales were above average to the number
of years for which the sales were below
average is
(A) 2 : 1 (B) 3 : 2
(C) 4 : 3 (D) 1 : 2
100. What are the approximate average sales
(in thousands) for the years 1988 to 1991 ?
(A) 420 (B) 425
(C) 430 (D) None of these
14
×
(A) 49 2 (B) 154 2
(C) 378 2 (D) 1078 2
× ×
(A) 400 2 (B) 600 2
(C) 800 2 (D) 1200 2
(A) 0.68 (B) 0.72
(C) 0.60 (D) 0.77
(A) 34.6% (B) 23.3%
(C) 15.4% (D) 17%
(A) 65.18% (B) 83.45%
(C) 77.9% (D) 69.6%
(A) 3.16 (B) 2.08
(C) 2.26 (D) 1.82
(A) (B)
(C) (D)
(A) 100 (B) 10000
(C) 100000 (D) 1000000
(A) 0.8 (B) 1.25
(C) 8 (D) 0.25
(A) 1986 (B) 1988
(C) 1989 (D) 1990
(A) 2 : 1 (B) 3 : 2
(C) 4 : 3 (D) 1 : 2
(A) 420 (B) 425
(C) 430 (D)