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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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