SSC Mains Test- 13 - SSC Exam Tutornotes.sscexamtutor.com/Maths/Questions/SSC MAINS MOCK...The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers

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1

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


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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3

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


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%


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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


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


=============================================================

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%


=============================================================

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


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)

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SSC Mains Test- 13 - SSC Exam Tutornotes.sscexamtutor.com/Maths/Questions/SSC MAINS MOCK...The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers