Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR �������� DILSHAD GARDEN�������� ROHINI �������� BADARPUR BORDER

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1

ARITHMETICARITHMETICARITHMETICARITHMETIC

1. There are 50 boxes and 50 persons. Person

1 keeps 1 marble in every box. Person 2

keeps 2 marbles in every 2nd box and person

3 keeps 3 marbles in every third box. This

process goes on till person 50 keeps 50

marbles in the 50th box. Find the total no.

of marbles kept in the 50th box.

(A) 43 (B) 78

(C) 6 (D) 93

2. A number is divided into two parts in such

a way that 80% of 1st part is 3 more than

60% of 2nd part and 80% of 2nd part is 6

more than 90% of the 1st part. Then the

number is

(A) 125 (B) 130

(C) 135 (D) 145

3. If the digits in the unit and the ten's places

of a three digit number are interchanged, a

new number is formed, which is greater

than the original number by 63. Suppose

the digit in the unit place of the original

number be x. Then, all the possible values

of x are

(A) 7, 8, 9 (B) 2, 7, 9

(C) 0, 1, 2 (D) 1, 2, 8

4. If 1! + 2! + 3! + 4! + ........+ 100! is divided by

8 then the remainder is

(A) 1 (B) 2

(C) 3 (D) 5

5. If A and B are the H.C.F. and L.C.M.

respectively of two algebraic expressions x

and y, and A + B = x + y, then the value of A³

+ B³ is

(A) x³-y³ (B) x³

(C) y³ (D) x³ + y³

6. If the square root of x is the cube root of y,

then the relation between x and y is

(A) x³ = y² (B) x² = y³

(C) x = y (D) x6 = y5

7. Average age of 8 men is increased by 3 years

when two of them whose ages are 30 and

34 years are replaced by 2 persons. What is

the average age of the 2 persons ?

(A) 24 years (B) 32 years

(C) 44 years (D) 48 years

8. The average age of a family of 10 members

is 20 years. If the age of the yourngest

member of the family is 10 years, then the

average age of the members of the family

just before the birth of the youngest member

was approximately

(A) 27.14 years (B) 12.5 years

(C) 14.28 years (D) 14.01 years

9. 5 members of a team are weighedconsecutively and their average weightcalculated after each member is weighed.If the average weight increases by one kgeach time, how much heavier is the lastplayer than the first one ?(A) 4 kg (B) 20 kg(C) 8 kg (D) 5 kg

10. A train travels 6 km in the first quarter ofan hour, 8 km in the second quarter and40km in the third quarter. Find the averagespeed of the train per hour over the entirejourney.(A) 72 km/h (B) 18 km/h(C) 77.33 km/h (D) 78.5 km/h

11. The average age of the Indian football teamis 30 years. The average age of 5 of theplayers is 29 years and that of another setof 5 players, totally different from the firstfive, is 27 years. If it is the captain who wasnot included in either of these tow gorups,then find the age of the captain(A) 75 years (B) 55 years(C) 50 years (D) 58 years

12. 2 men and 4 boys can do a piece of work in10 days, while 4 men and 5 boys can do it in6 days. Men and boys are paid wagesaccording to their output. If the daily wageof a man is ̀ 40, then the ratio of daily wagesof a man and a boy will be(A) 5 : 3 (B) 5 : 2(C) 4 : 7 (D) 7 : 3

13. A person ordered 4 shirts of brand A andsome shirts of brand B. The price of one shirtof brand A was twice that of brand B. Whenthe order was executed, it was found thatthe numbers of the two brands has beeninterchanged. This increased the bill by40%. The ratio of the number of brand Ashirts to that of brand B shirts in the originalorder was(A) 1 : 2 (B) 1 : 3(C) 1 : 4 (D) 1 : 5

14. If three numbers are in the ratio of 1 : 2 : 3and half the sum is 18, then the ratio ofsquares of the numbers is :(A) 6 : 12 : 13 (B) 1 : 2 : 3(C) 36 : 144 : 324 (D) 3 : 5 : 7

15. Rs. 2250 is divided among three friendsApurva, Jitendra and Rajiv in such a waythat 1/6th of Apurva's share, 1/4th ofJitendra's share and 2/5th of Rajiv's shareare equal. Find Apurva's share.(A) Rs. 720 (B) Rs. 1080(C) Rs. 450 (D) Rs. 1240

2

1

(A) 43 (B) 78

2.

80%, 60% 3

80%, 90% 6

(A) 125 (B) 130

3.

63

x x

(A) 7, 8, 9 (B) 2, 7, 9

4. 1! + 2! + 3! + 4! + ........+ 100! 8

(A) 1 (B) 2

5. x y

A B A + B

= x + y A³ + B³ ?

(A) x³-y³ (B) x³x³ + ³

6. x y x y

(A) x³ = y² (B) x² = y³x6 = 5

7. 30 34

(A) 24 (B) 32

(C) 44 (D) 48

8. 10 20

10

(A) 27.14 (B) 12.5

(C) 14.28 (D) 14.01

9. 5

1

(A) 4

10. 6

8

40

(A) 72 (B) 18

11. 30

5 29 5

27

(A) 75 (B) 55

12. 2 4 10

4 5

6

` 40

(A) 5 : 3 (B) 5 : 2

13. A 4 B

A

B

40% A

B (A) 1 : 2 (B) 1 : 3

14. 1 : 2 : 3

18 (A) 6 : 12 : 13 (B) 1 : 2 : 3

15. ` 2250

6

1

4

1

5

2

(A) ` 720 (B) ̀ 1080

(C) ` 450 (D) ̀ 1240

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16. A milkman makes 20% profit by sellingmilk mixed with water at ` 9 per litre. If thecost price of 1 litre pure milk is ` 10, thenthe ratio of milk and water in the saidmixture is(A) 3 : 1 (B) 4 : 1(C) 3 : 2 (D) 4 : 3

17. A, B and C started a business by investingRs. 40500, Rs. 45000 and Rs. 60000respectively. After 6 months C withdrew Rs.15000 while A invested Rs. 4500 More. Inannual profit of Rs. 56100, the share of Cwill exceed that of A by(A) Rs. 900 (B) Rs. 1100(C) Rs. 3000 (D) Rs. 3900

18. The cost of an apple is twice that of a bananaand the cost of a banana is 25% less thanthat of an orange. If the cost of each type offruit increases by 10%, then the percentageincrease in the cost of 4 bananas, 2 applesand 3 orange is(A) 10% (B) 12%(C) 16% (D) 18%

19. A number is mistakenly divided by 5 insteadof being multiplied by 5. Find the percentagechange in the result due to this mistake.(A) 96% (B) 95%(C) 2400% (D) 200%

20. The price of sugar falls by 20%. How muchsugar can be bought now with the moneythat was sufficient to buy 20 kg of ricepreviously ?(A) 5 kg (B) 15 kg(C) 25 kg (D) 30 kg

21. 4/5th of the voters in Amethi promised tovote for Rahul Gandhi and the rest promisedto vote for Varun Gandhi. Of these voters,10% of the voters who had promised to votefor Rahul Gandhi, did not vote on theelection day, while 20% of the voters whohad promised to vote for Varun Gandhi didnot vote on the election day. What is thetotal no. of votes polled if Rahul Gandhi got216 votes?(A) 200 (B) 300(C) 264 (D) 100

22. A reduction of 10% in the price of wheatenables a man to buy 50 gram of wheat morefor a rupee. How much wheat couldoriginally be had for a rupee ?(A) 400 grams (B) 500 grams(C) 450 grams (D) 350 grams

23. A publisher printed 2000 copies of a book ata cost of ̀ 70,000. He distributes 400 copiesfree as specimen copies. He gave 30%discount on printed price and the printedprice of each book is ` 75. What is his gainor loss percentage ?(A) 20% gain (B) 20% loss(C) 10% loss (D) 10% gain

24. A trader purchases a watch and a wall clockfor ` 390. He sells them making a profit of10% on the watch and 15% on the wall clock.He earns a profit of ` 51.50. The differencebetween the original prices of the wall clockand the watch is equal to(A) ` 80 (B) ̀ 120(C) ` 110 (D) ` 100

25. A fruit seller makes a profit of 20% byselling mangoes at a certain price. If hecharges ` 1 more for each mango, he canmake a profit of 40%. Find the selling priceof a mango in the first case.(A) ` 6 (B) ` 5(C) ` 5.50 (D) ` 7

26. A shopkeeper allows a discount of 12.5% onthe marked price of a certain article andmakes a profit of 20%. If the article cost theshopkeeper Rs. 210, what price must bemarked on the article?(A) ` 280 (B) ̀ 288(C) ` 300 (D) ` 312

27. A man sells an article at 5% above its costprice. If he had bought it at 5% less thanwhat he paid for it and sold it for Rs. 2 less,he would have gained 10%. Find the costprice of the article.(A) ` 500 (B) ̀ 360(C) ` 425 (D) ` 400

28. A sells a scooter priced Rs. 36,000. He givesa discount of 8% on the first Rs. 20,000 and5% on the next Rs. 10,000. How muchdiscount can he afford on the remaining Rs.6,000 if he is to get as much as when 0.7%discount is allowed on the total(A) 5% (B) 6%(C) 7% (D) 8%

29. Two dealers A and B selling the same modelof fan mark them under the same sellingprice. A gives successive discounts of 5%and 25% and B gives successive discountsof 16% and 12%. From whom is it moreprofitable to purchase the fan?(A) From B(B) From A(C) Indifferent between the two(D) Cannot be determined

30. Successive discounts of p% and q% on thecatalogue price of an article is equivalentto a single discount of :

(A) %100

��

���

���

pqqp

(B) %100

��

���

���

pqqp

(C) %100

��

���

���

pqqp

(D) %100

��

���

���

pqqp

4

16. ` 9

20%

` 10 ,

(A) 3 : 1 (B) 4 : 1

17. A, B C ` 40500, ` 45000 `

60000

C ` 15000

A ` 4500 `

56100 C A

(A) ` 900 (B) ̀ 1100` 3900

18.

25%

10%

4 3

(A) 10% (B) 12%

19. 5

5

(A) 96% (B) 95%

20. 20% 20

(A) 5 (B) 15

(C) 25 (D) 30

21.5

4

10%

20%

216

(A) 200 (B) 300

22. 10%

50

(A) 400 (B) 500

23. 2000 `

400

30% ` 75

(A) 20% (B) 20%

(C) 10% (D) 10%

24.

` 390 10%

15%

` 51.50

(A) ` 80 (B) ` 120` 100

25.

20%

` 1 40%

(A) ` 6 (B) ` 5` 7

26. 12.5%

20%

` 210 (A) ` 280 (B) ` 288

` 312

27. 5%

5% ` 2

10%

(A) ` 500 (B) ` 360` 400

28. ` 36,000

` 20,000 8%

` 10,000 5%

0.7% (A) 5% (B) 6%

29. A B

A 5% 25%

B, 16% 12%

(A) B

(C)

30.

(A) %100

��

���

���

pqqp

(B) %100

��

���

���

pqqp

(C) %100

��

���

���

pqqp

(D) %100

��

���

���

pqqp

Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR �������� DILSHAD GARDEN�������� ROHINI �������� BADARPUR BORDER

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31. If there is a reduction in the number ofworkers in a factory in the ratio 15 : 11 andan increment in their wages in the ratio

22 : 25, then the ratio by which the totalwages of the workers should be decreased is(A) 6 : 5 (B) 5 : 6

(C) 3 : 7 (D) 3 : 532. What quarterly payment will discharge a

debt of Rs. 2280 due in two years at 16% perannum simple interest ?

(A) Rs. 500 (B) Rs. 450(C) Rs. 550 (D) Rs. 250

33. A sum of ̀ 3310 is to be paid back in 3 equalannual instalments. How much is eachinstalment if the interest is compounded

annually at 10% per annum ?(A) Rs. 1321 (B) Rs. 1343(C) Rs. 1325 (D) Rs. 1331

34. A sum of money at compound interestamounts to thrice itself in 3 years. In howmany years will it be 9 times itself?

(A) 9 (B) 27(C) 6 (D) 3

35. Sanjay purchased a refrigerator on the

terms that he is required to pay Rs. 1500cach down payment followed by Rs. 1020 atthe end of first year, Rs. 1003 at the end of

second year and Rs. 990 at the end of thirdyear. Interest is charged at the rate of 10%per annum compound interest. What is the

cash price of the refrigerator ?(A) Rs. 4000 (B) Rs. 4100(C) Rs. 4150 (D) Rs. 4200

36. A and B together can complete a work in 12days. A alone can complete in 20 days. If Bdoes the work only half a day daily, then in

how many days A and B together willcomplete the work ?(A) 10 days (B) 20 days

(C) 11 days (D) 15 days37. A takes 10 days less than the time taken

by B to finish a piece of work. If both A and B

can do it in 12 days, then the time takenby B alone to finish the work is(A) 30 days (B) 27 days

(C) 20 days (D) 25 days38. A takes 5 days more than B to do a certain

job and 9 days more than C; A and B together

can do the job in the same time as C. Howmany days A would take to do it ?(A) 16 days (B) 10 days

(C) 15 days (D) 20 days39. A pipe of diameter d can drain a certain

water tank in 40 minutes. The time taken

by a pipe of diameter 2d for doing the samejob in :(A) 5 minutes (B) 10 minutes

(C) 20 minutes (D) 80 minutes

40. Two pipes A and B can fill a water tank in

20 and 24 minutes respectively and a third

pipe C can empty at the rate of 3 gallons per

minute. If A, B and C opened together fill

the tank in 15 minutes, the capacity (in

gallons) of the tank is:

(A) 180 (B) 150

(C) 120 (D) 60

41. Two bullets were fired at a place at an

interval of 28 minutes 30 seconds. A person

approaching the firing point in his car hears

the two sounds at an interval of 27 minutes.

The speed of sound is 330 m/sec. What is

the speed of the car ?

(A) 44 km/hr (B) 66 km/hr

(C) 64 km/hr (D) 54 km/hr

42. In a race of 600 metres, Sonu beats Monu

by 60 metres and in a race of 500 metres,

Monu beats Bablu by 25 metres. By how

many metres will Sonu beat Bablu in a 400

metre race ?

(A) 48 m (B) 52 m

(C) 56 m (D) 58 m

43. Two trains are running on parallel lines in

the same direction at speeds of 40 kmph

and 20 kmph respectively. The faster train

crosses a man in the second trains in 36

seconds. The length of the faster train is

(A) 200 metres (B) 185 metres

(C) 225 metres (D) 210 metres

44. A boat goes down stream at x km/h and

upstream at y km/h. The speed of the boat

in still water is

(A) 0.5 (x + y) (B) 0.5 (x - y)

(C) x + y (D) x - y

45. If 1 + 10 + 10² + ............. upto n terms =

9

110 �n

, then the sum of the series 4 + 44 +

444 + ......... upto n term is

(A) 9

4)110(

9

4 nn �� (B) 9

4)110(

81

4 nn ��

(C) 9

4)110(

81

40 nn �� (D) 9

4)110(

9

40 nn ��

46. If a³b = abc = 180. a, b, c are positive

integers, then the value of c is

(A) 110 (B) 1

(C) 4 (D) 25

47. If a + b + c = 0, then the value of

2 2 2

2 –

a b c

a bc

� � is

(A) 0 (B) 1

(C) 2 (D) 3

6

31. 15 : 11

22 : 25

(A) 6 : 5 (B) 5 : 6

32.

16% 2

` 2280 (A) ` 500 (B) ` 450(C) ` 250

33. ` 3310 3

10%

(A) ` 1321 (B) ` 1343` 1331

34. 3

(A) 9 (B) 27

35. `

1500 ` 1020

` 1003

` 990

10%

(A) ` 4000 (B) ` 4100` 4200

36. A B 12

A 20

B A B

(A) 10 (B) 20

(C) 11 (D) 15

37. A B 10

A B 12

B

(A) 30 (B) 27

(C) 20 (D) 25

38. A, B C

5 9 A B

C

A

(A) 16 (B) 10

(C) 15 (D) 20

39. d

40 2d

(A) 5 (B) 10

(C) 20 (D) 80

40. A B 20

24 C, 3

A, B C

15

(A) 180 (B) 150

(C) 120 (D) 160

41. 28 30

27

330

(A) 44 (B) 66

(C) 64 (D) 54

42. 600 60

500 25

400

(A) 48 (B) 52

(C) 56 (D) 58

43.

40 20

36

(A) 200 (B) 185

(C) 225 (D) 210

44. x

y

(A) 0.5 (x + y) (B) 0.5 (x - y)(C) x + y (D) x - y

45. 1 + 10 + 10² + ............. n = 9

110 �n

,

4 + 44 + 444 + ......... n

(A) 9

4)110(

9

4 nn �� (B) 9

4)110(

81

4 nn ��

(C) 9

4)110(

81

40 nn �� (D) 9

4)110(

9

40 nn ��

46. a³b = abc = 180 a, b c

c

(A) 110 (B) 1

(C) 4 (D) 25

47. a + b + c = 0

2 2 2

2 –

a b c

a bc

� �

(A) 0 (B) 1

(C) 2 (D) 3

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48. If a & b are rational numbers and

aba ��� 232)1( , the value of )( ba � is

(A) -5 (B) 3

(C) -3 (D) 5

49. The graph of the linear equation

2443 � yx is a straight line intersecting

x-axis and y-axis at the points A and B

respectively. P(2, 0) and Q ��

���

�

2

3,0 are two

points on the sides OA and OB respectively

of OAB, where O is the origin of the co-

ordinate system. Given that AB = 10 cm,

then PQ =

(A) 20 cm (B) 2.5 cm

(C) 40 cm (D) 5 cm

50. The length of the intercept of the graph of

the equation 9x - 12y = 108 between the

two axes is

(A) 15 units (B) 9 units

(C) 12 units (D) 18 units

51. If 31

2

��

���

��

xx , then the value of x206 + x200 +

x90 + x84 + x18 + x12 + x6 + 1 is

(A) 0 (B) 1

(C) 84 (D) 206

52. The value of 76167616

7

���

(A) 2

1(B) 2

(C) 4

1(D)

2

3

53. If 12

12

�

�x and 1xy then find the value

of ²23²2

²23²2

yxyx

yxyx

��

��

(A) 7

72(B)

65

71

(C) 71

65(D)

72

7

54. If )(4

baba

abx �

� then find the value of

bx

bx

ax

ax

2

2

2

2

�

��

�

�

(A) 1 (B) 4

(C) 1/2 (D) 2

55. The numerical value of

��

���

���

�

���

��

���� cot

1

cos

1

cot

1

cos

1 is

(A) 0 (B) –1(C) +1 (D) 2

56. The numerical value of

��

� 22

2 tan1

5cos4

cosec

9

��� is :

(A) 4 (B) 5(C) 9 (D) 1

57. The angles of elevation of the top of a towerfrom the points P and Q at distances of 'a'and 'b' respectively from the base of thetower and in the same straight line with itare complementary. The height of the tower is

(A) ab (B) b

a

(C) ab (D) a²b²58. Two posts are x metres apart and the height

of one is double that of the other. If from themid-point of the line joining their feet, anobserver finds the angular elevations oftheir tops to be complementary, then theheight (in metres) of the shorter post is

(A) 22

x(B)

4

x

(C) 2x (D) 2

x

59. If � is a positive acute angle and tan 2�

tan 3� = 1, then the value of ��

���

��1

2

5²cos2�

is

(A) 2

1� (B) 1

(C) 0 (D) 2

1

60. If y

xº17sin , then the value of

º73sinº17sec � is

(A) 22

2

xyx

y

�(B) 22

2

xyy

x

�

(C) 22

2

yxy

x

�(D) 22

2

yxx

y

�

61. In a right-angled triangle XYZ, right-angled

at Y, if XY = 62 and XZ - YZ = 2, then

XX tansec � is

(A) 6

1(B) 6

(C) 62 (D) 2

6

8

48. a b

aba ��� 232)1( )( ba �

(A) -5 (B) 3

(C) -3 (D) 5

49. 2443 � yx

X- Y-

A B OAB OA

OB P(2, 0) Q ��

���

�

2

3,0

O AB = 10

PQ =

(A) 20 (B) 2.5

(C) 40 (D) 5

50. 9x - 12y = 108

(A) 15 (B) 9

(C) 12 (D) 18

51. 31

2

��

���

��

xx x206 + x200 + x90 + x84 + x18

+ x12 + x6 + 1

(A) 0 (B) 1

(C) 84 (D) 206

52.76167616

7

���

(A) 2

1(B) 2

(C) 4

1(D)

2

3

53.12

12

�

�x 1xy

²23²2

²23²2

yxyx

yxyx

��

��

(A) 7

72(B)

65

71

(C) 71

65(D)

72

7

54. )(4

baba

abx �

�

bx

bx

ax

ax

2

2

2

2

�

��

�

�

(A) 1 (B) 4

(C) 1/2 (D) 2

55. ��

���

���

�

���

��

���� cot

1

cos

1

cot

1

cos

1

(A) 0 (B) –1(C) +1 (D) 2

56.�

�� 2

22 tan1

5cos4

cosec

9

���

(A) 4 (B) 5

57. P

Q 'a' 'b'

(A) ab (B) b

a

ab a²b²

58. x

(A) 22

x(B)

4

x

(C) 2x (D) 2

x

59. � tan 2� tan 3� = 1

��

���

��1

2

5²cos2�

(A) 2

1� (B) 1

(C) 0 (D) 2

1

60.y

xº17sin , º73sinº17sec �

(A) 22

2

xyx

y

�(B) 22

2

xyy

x

�

(C) 22

2

yxy

x

�(D) 22

2

yxx

y

�

61. XYZ º90 Y

XY = 62 XZ - YZ = 2 XX tansec �

(A) 6

1(B) 6

(C) 62 (D) 2

6

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9

62. The angles of a triangle are in ArithmeticProgression. The ratio of the least angle indegrees to the number of radians in the

greatest angle is �:60 . The angles in

degrees are(A) 30º, 60º, 90º (B) 35º, 55º, 90º(C) 40º, 50º, 90º (D) 40º, 55º, 85º

63. A balloon leaves the earth at point A andrises at a uniform velocity. At the end of

2

11 min. an observer situated at a distance

of 200 m from A, finds the angular elevationof the balloon to be 60º. Find the speed ofthe balloon(A) 3.87 m/sec. (B) 7.74 m/sec.(C) 3.78 m/sec. (D) 7.56 m/sec.

64. The height of a house subtends a right angleat an opposite window and the line throughthe window to the top of the house makes

an angle of º� with the vertical. If the

breadth of the street be 'd' metre. Find theheight of the bouse.

(A) �� cossind (B) �� secsind

(C) �� cosecsecd (D) �� coseccosd

65. If the ratio of sines of angles of a triangle

is 1 : 1 : 2 , then the ratio of squares of the

greatest side to sum of the squares of othertwo sides is(A) 3 : 4 (B) 2 : 1(C) 1 : 1 (D) 1 : 2

66. Suppose ABC be a right-angled triangle

where º90 A and BCAD � . If

40ABC cm², 10ACD cm² and AC =9

cm, then the length of BC is(A) 12 cm (B) 18 cm(C) 4 cm (D) 6 cm

67. The length of the common chord of twointersecting circles is 24 cm. If thediameters of the circles are 30 cm and 26cm, then the distance between the centresin cm is(A) 13 (B) 14(C) 15 (D) 16

68. In ABC , D and E are pionts on AB and AC

respectively such that DE||BC and DE

divieds the ABC into two parts of equal

areas. Then ratio of AD and BD is

(A) 1 : 1 (B) 12:1 �

(C) 2:1 (D) 12:1 �

69. X and Y are centres of circles of radii 9 cmand 2 cm respectively, XY = 17 cm. Z is thecentre of a circle of radius r cm whichtouches the above circles externally. Given

that XZY = 90º, the value of r is

(A) 13 cm (B) 6 cm(C) 9 cm (D) 8 cm

70. If the radii of two circles be 6 cm and 3 cm

and the length of the transverse common

tangent be 8 cm, then the distance be

tween the two centres is

(A) 145 cm (B) 140 cm

(C) 150 cm (D) 135 cm

71. In the given figure, AB is the diameter of

the circle. Find the value of ACD :

(A) 30º (B) 60º

(C) 45º (D) 25º

72. In the given figure, ABCD is a cyclic

quadrilateral and diagonals bisect each

other at P. If º60 DBC and º30 BAC ,

then BCD is:

(A) 90º (B) 60º

(C) 80º (D) none of these

73. The diagram below represents three

circular garbage cans, each of diameter 2

m. The three cans are touching as shown.

Find, in metres, the perimeter of the rope

encompassing the three cans.

(A) 62 �� (B) 43 ��

(C) 64 �� (D) 66 ��74. In the adjoining figure, ABCD is a trapezium

in which AB||DC and AB = 3 DC. Determine

the ratio of the areas of ( AOB and COD ).

(A) 9 : 1 (B) 1 : 9

(C) 3 :1 (D) 1 : 3

10

62.

�:60

(A) 30º, 60º, 90º (B) 35º, 55º, 90º

63. A

2

11

A 200

60º

(A) 3.87 / (B) 7.74 /

(C) 3.78 / (D) 7.56 /

64. 90º

º�

'd'

(A) �� cossind (B) �� secsind

(C) �� cosecsecd (D) �� coseccosd

65. sines 1 : 1

: 2

(A) 3 : 4 (B) 2 : 1

66. ABC º90 A

BCAD � 40ABC

10ACD AC =9

BC

(A) 12 (B) 18

(C) 4 (D) 6

67.

24 30 26

(A) 13 (B) 14

68. ABC AB AC

D E DE||BC DE, ABC

AD

BD

(A) 1 : 1 (B) 12:1 �

(C) 2:1 (D) 12:1 �

69. X Y 9 2

XY = 17 Z, r

XYZ = 90º

r

(A) 13 (B) 6

(C) 9 (D) 8

70. 6

3

8

(A) 145 (B) 140

(C) 150 (D) 135

71. AB ACD

(A) 30º (B) 60º

(C) 45º (D) 25º

72. ABCD

P º60 DBC

º30 BAC BCD

(A) 90º (B) 60º

(C) 80º (D)

73.

(A) 62 �� (B) 43 ��

(C) 64 �� (D) 66 ��

74. ABCD

AB DC AB = 3DC � AOB � COD

(A) 9 : 1 (B) 1 : 9

(C) 3 :1 (D) 1 : 3

Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR �������� DILSHAD GARDEN�������� ROHINI �������� BADARPUR BORDER

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11

75. The sides of a right triangle are 9, 12 and

15 cm long. Find the sum of the squares of

the medians.

(A) 150 cm (B) 337.5 cm

(C) 225 cm (D) 222.5 cm

76. An equilateral triangle is drawn on the

diagonal of a square. The ratio of the area

of the triangle to that of the square is

(A) 2:3 (B) 3:2

(C) 3:2 (D) 2:1

77. The diameter of the moon is assumend to

be one fourth of the diameter of the earth.

Then the ratio of the volume of the earth to

that of the moon is

(A) 64 : 1 (B) 1 : 64

(C) 60 : 7 (D) 7 : 60

78. A rectangular circuit board is designed to

have width w cm, perimeter p cm and area

k sq. cm. Of the following, the equation

which must be true is

(A) 2w² – pw – 2k = 0

(B) 2w² – pw + 2k = 0

(C) w² – pw + 2k = 0

(D) 2w² + pw + 2k = 0

79. A cylindrical container of redius 6 cm and

height 15 cm is filled with ice-cream. The

whole ice-cream has to be disributed to 10

children in equal cones with hemispherical

tops. If the height of the conical portion is

four times the redius of its base, then the

radius of the base of the ice-cream cone is

(A) 4 cm (B) 4.5 cm

(C) 3 cm (D) 3.5 cm

80. Two circles with centres A and B and radius

2 units touch each other externally at 'C'.

A third circle with centre 'C' and radius '2'

units meets other two at D & E. Then the

area of the quadrilateral ABDE is

(A) 22 sq. unit (B) 33 sq. unit

(C) 23 sq. unit (D) 32 sq. unit

81. A playground is in the shape of a rectangle.

A sum of ` 1,000 was spent to make the

ground usable at the rate of 25 paise per sq.

m. The breadth of the ground is 50 m. If the

length of the ground is increased by 20 m,

what will be the expenditure in rupees at

the same rate per sq. m. ?

(A) 1,250 (B) 1,000

(C) 1,500 (D) 2,250

82. A cylindrical can whose base is horizontaland is of internal radius 3.5 cm containssufficient water so that when a solid sphereis placed inside, water just covers thesphere. The sphere fits in the can exactly.The depth of water in the can before thesphere was put is

(A) 3

35 cm (B)

3

17 cm

(C) 3

7 cm (D)

3

14 cm

83. The height of a circular cylinder is increasedsix times and the base area is decreased toone-ninth of its value. The factor by which thelateral surface of the cylinder increases is

(A) 2 (B) 2

1

(C) 3

2(D)

2

3

84. If the diagonals of a rhombus are 8 and 6,then the square of its side is(A) 25 (B) 55(C) 64 (D) 36

85. The volume of a solid hemisphere is 19404cm3. Its total surface area is(A) 4158 cm² (B) 2858 cm²(C) 1738 cm² (D) 2038 cm²

86. The area of the square inscribed in a circleof radius 8 cm is(A) 256 sq. cm (B) 250 sq. cm(C) 128 sq. cm (D) 125 sq. cm

87. Find the ratio of areas of inscribed squarein a semicircle and a circle while the radiiof circle and semicircle are equal.(A) 2 : 5 (B) 3 : 5(C) 1 : 2 (D) 1 : 3

88. A chord AB of a circle of radius 10 cm makesa right angle at the centre of the circle. Findthe difference between the areas of themajor and minor segments of the circle.(use � = 3.14)(A) 285.5 cm² (B) 385.5 cm²(C) 485.5 cm² (D) 185.5 cm²

89. There is a square field whose side is 44 m.A square flowerbed is prepared in its centre,leaving a gravel path of uniform width allaround the flowerbed. The total cost of layingthe flowerbed and gravelling the path at Rs.2 and Re. 1 per square metre respectivelyis Rs. 3536. Find the width of the gravelledpath.(A) 1 metre (B) 1.5 metre(C) 2 metre (D) 2.5 metre

90. Find the area of a trapezium whose parallelsides are 77 cm, 60 cm and the other sidesare 25 cm and 26 cm.(A) 1640 sq. cm. (B) 1644 sq. cm.(C) 1740 sq. cm. (D) 1744 sq. cm.

12

75.

(A) 150 (B) 337.5

(C) 225 (D) 222.5

76.

(A) 2:3 (B) 3:2

(C) 3:2 (D) 2:1

77.4

1

(A) 64 : 1 (B) 1 : 64

(C) 60 : 7 (D) 7 : 60

78. w , p

k

(A) 2w² – pw – 2k = 0

(B) 2w² – pw + 2k = 0

(C) w² – pw + 2k = 0

(D) 2w² + pw + 2k = 0

79. 6

15

10

(A) 4 (B) 4.5

(C) 3 (D) 3.5

80. A B 2

'C' 'C'

'2' D

E ABDE

(A) 22 (B) 33

(C) 23 (D) 32

81.

`

(A) 1,250 (B) 1,000

(C) 1,500 (D) 2,250

82.

(A) 3

35(B)

3

17

(C) 3

7(D)

3

14

83.

1

9

(A) 2 (B) 2

1

(C) 3

2(D)

2

3

84.

(A) 25 (B) 55

85.

(A) 4158 (B) 2858

(C) 1738 (D) 2038

86.

(A) 256 (B) 250

(C) 128 (D) 125

87.

(A) 2 : 5 (B) 3 : 5

88. AB 90º

( � = 3.14)

(A) 285.5 (B) 385.5

(C) 485.5 (D) 185.5

89.

` `

`

(A) 1 (B) 1.5

(C) 2 (D) 2.5

90.

(A) 1640 (B) 1644

(C) 1740 (D) 1744

Centres at: ���� MUKHERJEE NAGAR �������� MUNIRKA ��������UTTAM NAGAR �������� DILSHAD GARDEN�������� ROHINI �������� BADARPUR BORDER

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13

Directions (91-95): Study the following

histogram and answer the following questions.

91. The total number of persons in the age group

of 15 years to 45 years is:

(A) 450 (B) 800

(C) 1000 (D) 500

92. The number of persons in the age group 20-

30 years is:

(A) 475 (B) 400

(C) 300 (D) 700

93. The ratio of the number of persons between

the age group of 20-25 and 30-35 is :

(A) 1 : 3 (B) 2 : 1

(C) 10 : 3 (D) 6 : 1

94. The ratio of maximum population in an age

group to the total number of persons under

study is :

(A) 4 : 5 (B) 9 : 10

(C) 9 : 20 (D) 2 : 5

95. The percentage of population under study

which is in the age group os 40-45 is:

(A) 2.5 (B) 3.5

(C) 1.5 (D) 5

Directions: (96-100): For the question numbers

96 to 100, a pie graph is given. Study the graph

carefully and answer the following questions

by choosing the best answer from the five

alternatives given below the question.

The following pie-chart gives the monthly

expenditure of Apurva

96. If the salary of Apurva is ̀ 25,000, what would

be his expenditure on clothing and

miscellaneous?

(A) ` 7,500 (B) ̀ 10,000

(C) ` 11,500 (D) ̀ 12,500

97. How much should be the total expenditure

of Apurva if his expenditure on house rent

and travelling is ` 15,000 ?

(A) ` 35,000 (B) ̀ 45,000

(C) ` 50,000 (D) ̀ 55000

98. Each expenditure in the pie chart subtends

certain angle at the centre. Which of the

following shows a difference in an angle of

54º ?

(A) Entertainment and food

(B) Miscellaneous and house rent

(C) Miscellaneous and clothing

(D) Miscellaneous and food

99. The expenses on house rent is less than

food by

(A) 5% (B) 33.33%

(C) 20% (D) 25%

100. Which two expenditures together form a

central angle of 90º ?

(A) Travelling and clothing

(B) Entertainment and house rent

(C) Miscellaneous and house rent

(D) Travelling and entertainment

14

91.

(A) 450 (B) 800

(C) 1000 (D) 500

92.

(A) 475 (B) 400

(C) 300 (D) 700

93.

(A) 1 : 3 (B) 2 : 1

(C) 10 : 3 (D) 6 : 1

94.

(A) 4 : 5 (B) 9 : 10

(C) 9 : 20 (D) 2 : 5

95.

(A) 2.5 (B) 3.5

(C) 1.5 (D) 5

96. `

(A) ` 7,500 (B) ̀ 10,000

(C) ` 11,500 (D) ̀ 12,500

97. `

(A) ` 35,000 (B) ` 45,000

(C) ` 50,000 (D) ` 55000

98.

54º

(A)

(B)

(C)

(D)

99.

(A) 5% (B) 33.33%

(C) 20% (D) 25%

100. 90º

(A)

(B)

(C)

(D)