Ssc Tier II Math Solution Paper 1

7/24/2019 Ssc Tier II Math Solution Paper 1

1/12

1. (C)1 3 5 997

2 2 2 .......... 2 3 5 7 999

=5 7 9 1001

..3 5 7 999

=1001

32. (A) 3600 = 4 9 100

= 2 2 3 2 5 2 2 2= 2 4 3 2 5 2

3240 = 810 4= 3 2 3 2 2 5 2 2= 3 4 2 3 5

T = 2 2 3 5 7 23. (*) NOTE : READ (0.021) 2 (0 .21) 2

2 2 2

2 2 2100 (0.003) (0.21) (0.0065)

10 (0.003) (0.21) (0.0065)

4. (B) P( ) = 2 3 2 ( ) ( 2+ )Q( ) = 2 3 3 2 ( ) ( 2 2 2 )R( ) = 2 2 3 ( )3H.C.F. = 6 ( )

5. (A) A 10 = B + 10 A B = 20 .... ( )

A + 20 = 2(B 20) A 2B = 60 .... ( )

F E . ( ) ( ), A = 100, B = 806. (C)A 8

8, . . 58N 8.H , N = 4A 11

0 11,. ., (M + 9 + 4 + 4 + 8) (3 + 0 + 8 + 5 + N)= M + 25 (16 + N) = M N + 9

(M N) + 9 11.

( 584 8. N = 4)

. . M N = 2

M = 2 + 4 = 6 M = 6, N = 47. (D) H = 15 .

S = 5 /S = 3 /

D 11 . = 5 6 3 5 = 15 .

= 11 .8. (A) T 5, 7, 11, 13

5 7 11 = 3857 11 13 = 1001

H , 5.9. (B) L .

T , = 20 ... .. ( )

( 5) = 5( 5) ..... ( )F E . ( ) ( )

20 + 5 = 5 25 = 10 = 30

10. (A) L . 2 , 5 , 13 .

N . = 20 ,

T = 15 2 +7.5 5 +2.5 13 = (30 + 37.5 + 32.5)

(100.0) 100

= 100 /20 = 5

11. (D) L ' 1 , 2 3 .

T ,

3321 =

10020

226 3

3321 =

1026 3 ... ( )

A , M + 1 = 39 ... ( )F E . ( ) ( ),

2 .12. (D) L

150 .ATQ,95% (150 + ) = 135 + 150 95 + 95 = 5

5750

=

= 150 13. (D) G , + + = 23 .... ( )

+ + + = 15 .... ( ) + + + = 18 .... ( )

+ + + + + + = 50 .... ( )S E . ( ), ( ),. ( ) ( )

= 3, = 6, = 6, = 9 = 514. (C) L .

I = 30 N = 33 N

=

32.1

33=25

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2/12

15. (B)

R = 120 (40 + 6 + 30)= 44

16.(*) L = F ,

I = 2 =

L 4 , 2 , 3 , 4 ,

= + 2 + 3 + 4 = 10 ( )

, , 2 + (2 )2 + (3 )2+ (4 )2 = 140000

30 2

= 140000

2

30 140000100

( )

2 140000 100

30K 2 = 4.7 ( .)

I = 4.7 L17. (A) L

3 .

T ,6163

=12

3 16 = 2 + 12 = 28

T = 3 +

= 4 28= 112

18. (B) (17 + 19) = 36% = 162

C =36

162 100

= 45019. (A) O 250 .

= 250 50 = 12500P

= 12500 10080

10085

10095

= 807520.(D) SP = 17,940, D = 8%

MP =92.0

17940 = 19500

G = 19.6% ( )

CP =196.1

17940= 15000

N SP = 19500G = (19500 15000) = 4500

G =15000

4500 100 = 30%

21. (B) S. I. = 100

=S. I. 100 620 100

2000 5

= 6.2%

= 6.2 + 3 = 9.2%

, S. I. = 92 5

2000100 10 100

= 920

A = 2000 + 920 = 292022. (B) G

P = 3000 = 10% . . = 3

L = A N ,

A P 1

100

A

1 2 1 1

100 100

= 30003

101

100

1000

2 110 10

1 1100 100

= 3993 1210 1100 = 1683

23. (A) A

1 = 4000

1005.7

1 1500 = 2800

2 = 2800

1005.7

1 1500 = 1510

3 = 1510 1005.71 1500 = 123.25

24. (B) L . T ,

1 =8

+

16)1(

+242

1211

=16

12

3 1 =12

1116

= 9

47

= 5

25. (A) A ' 1 =101

M ' 1 =100125

101

=81

S ' 1 =100160

81

=51

T =101

+81

+51

=4017

T =17

40 = 2

17

6



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3/12

26. (C) I 600 , A : B

600 : 54010 : 9

I 500 , B : C

500 : 47520 : 19

A : B : C= (10 20) : (9 20) : (19 9)= 200 : 180 : 171

S , A 200 C 171

A 1 C 200171

A 400 C 200

40071

= 342A C 400 342 = 58

27. (B) L / .

T , = 0.8 / .

T =

500 +

21

+ 8.0

500

23 =

1125 +

21

= 1125 452

= 50 /

S = 40 /

28. (D)

=3433 =

129 :

=

4443 =

1612

A : B : C = 9 : 12 : 16

A' =379

370 = 90

29. (B) ' = (700 3)

+

375

700 +

53

200500 6

= 7320' = 600 12 = 7200 '

= )72007320(7320

726 = 36630.(C) L D , = 60 1 (M ) , = 80 ( 1 2) (R )

60 1 = 80 1 160 , 20 1 = 160 , 1 = 8

R = 60 1 = 60 8 = 480

31. (A) L ,

2

.

A .

S , +2

= (48 + 42)

185

12

23

= 300 = 200

N ,

+ = 48 185

45 = 600

= 600 200 = 400 32. (D) L / .

T , = (48 + ) /

& S = (48 ) /

ATQ,

)48(200

)48(200

= 10

40 = (48) 2 2

2 + 40 2304 = 0 ( + 72)( 32) = 0 = 32 /

33. (C) L ' '

' '. AP.

S = 2

2 + ( 1)

,

3600 =2

40 2 + (40 1)

= 20(2 + 39 ) 180 = 2 + 39 ... ( )

A , 2400=2

302 + (30 1)

160 = 2 + 29 ... ( )S E . ( ) ( ),

20 = 10 = 2

T ,180 = 2 + 39 2

2 = 102 = 51

8 = 51 + (8 1) 2= 51 + 14 = R . 65

34. (C) L .

T , 250= 123

)1(722

250 = 41

41

142

250 = 7 +8

2

8

= 25



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4/12

35. (C) L . T ,C (2200 )ATQ,

100

95 + (2200 )

100

106 = 2200

95 + 233200 106 = 220000 11 = 13200 = 1200

2200 = 100036. (A) L P M P M

. : P + = 4(M )

P 4M = 5 ... ( ) : (P ) = 3(M + )

P 3M = 4 ... ( )S E . ( ) ( ),

M = 9 P = 31 P = 1, P = 31

37. (A) T

30203020

= 12

O 4 .N ,

(12 4) = 48S ,

32

12484812

= 1032

S ,

= 4 + 1032

= 1432

.

38. (C) 4

= 4

101

151

=32

.

.

=51

101

151

=30

1

=30

1 1

32

3302

= 20

39. (A) R =40

5.3305.410

=40

10545

=40

150=

415

40.(A) L .ATQ,

P I = 8000

10025

10080

= 80000

=2580

10010080000

= 400000 41. (D) L .

T ,

1000 +100

5.2 ( 4000) =100

5 + 600

2.5 = 30000 = 12000

42.(A) Q 1

=102

1 =51

A .

S , =31

51

=151

43. (C) L .

P 2 .ATQ,

23

(4 2 + ) = 2 + 4

12 +23

= 2 + 4

12 +23

= 2 + 4

2 = 8

= 16

R =164 =

41

44.(B) G , C. P. = 840

C.P. 1/4 =1

8404

= 210

& C. P. = 840 210 = 630L %

. , ,

80 (100 ) 120210 630 840

100 100 100

63168 (100 ) 100810

=1

333

%

45. (A) L CD . ( 1) 6 = 114

1 = 19 = 20

46. (*) R A, B, C & D

=321

:201

:301

:241

= 15 : 24 : 16 : 20



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5/12

C' =9940

25

= 10.1047. (C) L = N

T 6 = 30

1 = 5 3 = 15

S , 15 N = 80 N = 5.33 6

48. (A) L ' ' T ' ' /

( ) =

..... ( )

21

=4

..... ( )

+31

=4

..... ( )

S E . ( ), ( ) ( ), = 60 , = 20 / = 3

49. (B) L ' ' .

T , S = 2

2 + ( 1)

S 2 = 22

2 + (2 1)

S 3 = 23 2 + (3 1)

G S 2 = 3S

22

2 + (2 1) =32

2 + ( 1)

4 + (4 2) = 6 + (3 3) (4 2 3 + 3) = 2

=1

2

S = 12 2

S 3 = 112 2

3=

112 2

2121

=

61

3

= 6

50. (C) = 3, = 3 T 10 = + (10 1)

T 10

= 3 + 9 3 = 24

51. (A)

I OAP:

=OA

OA = I OBP:

=OB

OB = N :

I OAB:OB 2 = OA 2 + AB 2

AB 2 = OB 2 OA 2

AB2 = 2 2 2 2

AB2 = 2 2 2

AB2 = 2 ( 2 1) ( 2 1= 2 2 2

AB2 = 2 2222

= 22AB

52. (B) + = P( + )2 = P 2 ( )

21

= P 2

2

2

1)1(

= P2

11

= P 2

A C & D :

)1(111

=11

2

2

22

=11

2

2

=11

2

2



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6/12

53. (A)

I OAP:

=OA

OA = .... ( )I OBP:

= OB OB = .... ( )

S OAB . AB 2 = OA 2 + OB 2

2 = 2 2 + 2 2

= 22

54. (A) + = 2

= ( 2 1)

= 121 =

1212 = 12

55. (B) 31

31

31

= 0

31

31

= 31

3

31

31

=

3

31

3

131

31

31

.3 =

+ + = 31

31

31

..3 ( + + )3 = 27

56. (B) = 3 2 27= 3( 2 9)= 3( 3)( + 3)

3, ( 3), ( + 3) A .

57(C) 2 1 P( ) = 4 + 3 + 2 + +

P( 1) = 0 P(1) = 0 ( 1) 4 + ( 1) 3 + ( 1) 2 + ( 1) + = 0, + + = 0 + + = + A .

58. (B) 217 + 131 = 313 ...... ( )

131 + 217 = 827 ...... ( )A ( ) ( ):

348 + 348 = 1740 + = 5 ...... (A)

S ( ) ( ):86 86 = 86 = 1 ...... (B)

N : (A) (B):

2 = 6 = 3

, + = 5 = 2

59. (A) POB QOA

)()(

= 22

)(150

= 22

75

)( =25

49150 = 294 2

60. (B) PQ BC & P AC. Q AB.

N ,PB 2 = PQ 2 + QB 2

=2

BC21

+2

AB21

BC

21

PQ

=41

BC2 + AB 2

=41

AC 2

PB =21

AC A .

61. (B)

BEOD & BEAE OD AE, 'O' AB.

OD = 21

AE

8 =21

AE

AE = 16 I AED,

AD2 = AE 2 + DE 2= 16 2 + 105= 256 + 105= 361

AD = 19



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7/12

62. (C) DE BC

( ADE ABC)

AE =8

6.53= 2.1

63. (D) 1 & 2 & .

21 22 = 44

14)(2 21 = 14222744

=21

1 2 = 21

.... ( )A

222

1 = 99

14)(7

22 22

21 = 99

22

21 = 1422

799 =

49

( 1 + 2) ( 1 2) =94

1 + 2 = 49

21

= 25

.... ( )O ( ) & ( )

1 = 2.5 , 2 = 2

64. (A)

G :

H = 21 B = 40

N :

H = 22 2120

= 441400

= 841 = 29 S S A P

= 4 A

= 4 294021

= 4 20 29 = 2320 2 .

65. (A)

A1A2 = 1000 = 1 A2A1B 1 = 30

TA 2B 2 = 60I A1A2Q

30 =21

2

AAQA

A2Q = 21

1 =21

= B 2B 1 ......( )

30 = 1

1 2

A1Q = 23

1 =23

......( )

I TB 1B 2 :

45 =

1

1 1=

1 1

......( )

I TA 2B 2 :

60 =

2

2 2 =

1

121

=

111

121

3 =

23

21

F ( ), ( ) ( )

= 1.366 66. (A)

= 0.075 0.055 18 30 60 3= 133.65 3

N : = A

, 133.65 = 10.3 3.75

=75.38.10

65.133 = 3.3

67. (A) L : + = K ..... ( )

T :2 2 = 1

K( ) = 1

=K1

..... ( )

A ( ) ( ):

2 = K +K1

2

4

1

= K + K

1



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8/12

,

21

2 = K +K1

K = 2

K1

= 2

1

+ = K = 2 2

1

68. (A) + 2 + 3 = 1 + 3 = 1 2

1 + 2 = 2

2 1 + 2 2 = 4

(1 2 ) 1 + (1 2 ) 2 = 4

(1 2 ) 2 2 2 = 4

(1 2 ) 4 4 2 + 4 = 4

4 4 2 + 4 4 2 + 4 4 6

= 4

6 + 4 4 8 2 + 4 = 0 6 4 4 + 8 2 = 4

69. (A) 3 = 2 + (3 )= (2 + )

, 3 =

2

12

, 3 . 2 + 3 . = 2 . 1 2 . 3 . 2 3 . = 1

70. (A) =

1 =

1 2 =

2

=

= . =

1 =

2

=

= .

32

232

2

32

2).).(.( +

32

2 )..().(

32

2 )..( + 32

2 )..(

32

2.. +32

2..

32

332

3 2 + 2 = 1

71. (A)

A = (4, 3)B = ( , 5)O (2, 3)

N :OA 2 = OB 2

, (2 )2 + (3 3) 2 = (2 4) 2 + (3 3) 2, 4 + 2 2 + 4 = 4, (2 )2 = 0 = 2

72. (B)

= = 3

N :

A AOB =21

=21 6 3

= 9 . .73. (A) F

=105

=21

= 60N , AOB = 360 120 = 240N ,

=180

= 1802405

=3

20

74. (A)R AOC = 360 40 = 320

R =360

32021 360

32022

=360320

722 2

22

1

=360320

722

714 22

= 410.67 2

.



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9/12

75. (A) :

=26

3

3 = 26 2.45 = 2.75

=32

= 2.75 0.816

= 2.245 76. (B) = 3

=

2

2 =3

4

=

2

231

= 312

R R = 3 :4

3 :12

3

= 1 :4

:12

= 12 : 3 : A .77. (D) B :

2 = 28

27

22 = 28

=222

728

= 4.4545

N , . = 22

= 22 )4545.4(14

= 8429.19196 = 1570.176= 13.12 ( .)

78. (D) L = A :

41

+ 2 + 15 =

R 2 :

41

2 + 2 + 15 = 2

, 2 41

2 2 15 = 0

, 3 2 8 60 = 0

=32

603488 2

=67848

= 6,3

10

N : 2

= (6) 2 = 36 N . = 36

79. (D)

+

= 1

,

22= 1

, 2 + 2 = , ( 2 + 2 + ) = 0

N :( 3 3) = ( ) ( 2 + 2 + )

= ( ) 0 = 0= 0

80. (D) M 53

5

3

3

15 = 5

5

3

51

3 = 3S :

9 2 + 2251

+ 2 3 51

= 9

9 2 + 2251

= 9 56

=5

645 =

539

81.(D) AOB COD

ODOB

=OCOA

OB OC = OA OD( 3)( 5) = (3 19) 3

2 8 + 15 = 9 57 2 17 + 72 = 0

( 9) ( 8) = 0 = 9, 8

82. (D) G ,

A PQRS = PA PQ T = RA PSQ = T

N , =21

A

PQRS.A = (

)H , ( ), ( ) ( ) .



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10/12

83. (C) L O .

OQ . (OQ) 2 = (50) 2 + (120) 2

= 2500 + 14400= 16900

OQ = 130 84. (B) L 1 , 2 3 ,

1 + 2 = 2.2 ...... ( )2 + 3 = 3.2 ...... ( )1 + 3 = 4.0 ...... ( )

A E . ( ), ( ) ( )2( 1 + 2 + 3) = 9.6 1 + 2 + 3 = 4.8

3 = (4.8 2.2) = 2.61 = (4.8 3.4) = 1.42 = (4.8 4.0) = 0.8

T 2 1.4 = 2.8,2 0.8 = 1.6 2 2.6 = 5.2

85. (A) + + = 19 = 11

N :222 = 11

2 + 2 + 2 = 121 2A

= 2 + + = ( + + )2 2 + 2 + 2 = 19 2 121= 361 121= 240 2

86. (A) T .

A = 2244

=4

40 22 40)25(4 = 300 2

H =A

=300

2400 = 8

87. (A) T = 4 = 130

=4

130= 32.5

O , 1 = 33

N :

22 =

212

2

22

=22

)5.16()5.32( 2 = 56

N :

A =2

21 =2

5633= 924 2

N : = A

= 924 2.6= 2402.40 3

88. (D) T .

H , ( ) .

89. (D) G , AC = 2

BD =2

CD =

T ,AB = AC BC

= 2 (BD + CD)

=2

2

=21

( )

90. (C) =2120

=11

D :

11

11

=2120

=P

= 22 2021 = 400441= 29

= =2921



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11/12

12120

219

12120

219

=212029212029

=7030

=73

91. (D) C .

92. (D) C .93. (B)

O 50% .

94. (C)95. (B) I + A

50%.96. (A) 20%.97. (B) I 1998,

= 100 T G 1999

= 100 10015 = 15

I 1996 = 10% 1998

= 15 10090

= 13.5

98. (A) M 2001

= 150 10026

= 39

25%

= 39 10025

= 9.75

T = 9.75 1000 20 = 1.95

99. (C) 12% 2003,

= 175 100112

= 196

P

= 196 10026

= 50.96

100. (C) T 1998= 100

G 1998

= 100 10014

= 14

H =2

14

= 7

P =7

1000004.1

= 20000



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12/12

1. C2. A3. *4. B5. A6. C7. D8. A9. B10. A11. D12. D13. D

14. C15. B16. *17. A18. B19. A20. D

21. B22. B23. A24. B25. A26. C27. B28. D29. B30. C31. A32. D33. C

34. C35. C36. A37. A38. C39. A40. A

41. D42. A43. C44. B45. A46. *47. C48. A49. B50. C51. A52. B53. A

54. A55. B56. B57. C58. B59. A60. B

61. B62. C63. D64. A65. A66. A67. A68. A69. A70. A71. A72. B73. A

74. A75. A76. B77. D78. D79. D80. D

81. D82. D83. C84. B85. A86. A87. A88. D89. D90. C91. C92. D93. B

94. C95. B96. A97. B98. A99. C100. C


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Ssc Tier II Math Solution Paper 1

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