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Solutions
S1. Ans.(c)
Sol.
? ≃ 1.8 × 25500 +50
100× 29000 ≃ 60,400
S2. Ans.(a)
Sol.
? ≃ 172 × 15 ÷ 25
≃ 103
S3. Ans.(b)
Sol.
? ≃ 175 × 28 + 275 × 28
≃ 12,600
S4. Ans.(c)
Sol.
? ≃ 325 × 16 ÷ 4 + 37
≃ 1337 ≃ 1340
S5. Ans.(c)
Sol.
? ≃ 1164 × 128 ÷ 8 + 969
≃ 19593
S6. Ans.(c)
Sol.
? ≃ 25 + 27
≃ 52
S7. Ans.(a)
Sol.
? ≃69
100× 700 +
33
100× 400
≃ 483 +132
≃ 615
S8. Ans.(d)
Sol.
? ≃(9320 + 5400 + 1000)
(500 + 930 + 660)≃ 7.5
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S9. Ans.(d)
Sol.
64
100× 8924 +
?
100× 5324 ≃ 6828
⇒ ? ≃ 21
S10. Ans.(a)
Sol.
? ≈67×800
100− 231 +
23×790
100
≈ 536 − 231 + 181.7
≈ 490
S11. Ans.(c)
Sol.
? ≈ 500 + 50 × 50
≈ 3000
S12. Ans.(c)
Sol.
? ≈74×1300
100+
10×1900
100
≈ 960 + 190
≈1150
S13. Ans.(a)
Sol.
? ≈67×800
100− 231 +
23×790
100
≈ 536 − 231 + 181.7
≈ 490
S14. Ans.(b)
Sol. 129 − 224 = −95
S15. Ans.(b)
Sol. ? ≈ 1956 + 8.25 + 7.28 ≈ 1970
S16. Ans.(c)
Sol.
? ≃68
100× 1400 −
14
100× 1300
≃ 770
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S17. Ans.(d)
Sol.
? ≃ 5467 – 3245 + 1123 – 2310
≃ 1035
S18. Ans.(d)
Sol.
? ≃6000
10+ 671 − 140
≃ 1131
≃ 1130
S19. Ans.(e)
Sol.
? ≃ 900 – 81 – 125
≃ 694
S20. Ans.(b)
Sol.
? ≃56 × 24 × 8
16
≃ 672
≃ 670
S21. Ans.(b)
Sol.
? ≈ 12 × 15 − 9 × 7
≈ 180 − 63 = 117
S22. Ans.(e)
Sol.
? ≈8400 × 105
100− 5600 ×
3
700+ 10
≈ 8820 − 24 + 10 = 8806
S23. Ans.(e)
Sol.
≈ 30² – 20² – ? = 22²
⇒ 900 – 400 – ? = 484
⇒ 500 – ? = 484
⇒ ? = 500 – 484 = 16
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S24. Ans.(c)
Sol.
? ≈ (5)2 + (21)3 + √1089
≈ 25 + 9261 + 33 ≈ 9319
S25. Ans.(b)
Sol.
? = √653
× 23.93 − 31.04
≈ √643
× 24 − 31
≈ 4 × 24 − 31 ≈ 96 − 31 ≈ 65
S26. Ans.(a)
Sol. 56
100× 958 +
67
100× 1008 = ? × 20
⇒ ? = 60.592
S27. Ans.(c)
Sol.
(?)² = 77 + 92
= 169
⇒ ? = ± 13
S28. Ans.(c)
Sol.
? =47 × 588
28 × 120
= 8.225
S29. Ans.(d)
Sol.
? =5
8×
4
9×
3
5× 222
= 37
S30. Ans.(b)
Sol.
? = 4441
S31. Ans.(d)
Sol.
441 – 63 = ? × 8
? = 47.25
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S32. Ans.(e)
Sol.
23
16=? −
7
64
? =23
16+
7
64=
92+7
64
? =99
64= 1
35
64
S33. Ans.(d)
Sol.
5.76 × 10−7 ÷ (0.000048) = 0.012
S34. Ans.(c)
Sol.
(58
7× 1568) + 265.75 − 2455.6 =?
? = 13257.75 – 2455.6
? = 10802.15
S35. Ans.(e)
Sol. (1.1)2 − (4.24 × 0.04) =?
Or, ?=1.0404
S36. Ans.(d)
Sol.
(? )1
2 = 4 + 6
= 10
? = 100
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S37. Ans.(b)
Sol. ? = √169 + 7 − 27 + 107
= √256
= 16
S38. Ans.(b)
Sol. = (0.7)?+3 =(0.7)8×(0.7)12
(0.7)16
= (0.7)4
⇒ ? = 4 – 3
⇒ ? = 1
S39. Ans.(c)
Sol.
(? )2
25=
45
100× 45 × 100
⇒ ? = ± 225
S40. Ans.(a)
Sol. ? = 15.8
S41. Ans.(a)
Sol. ? =11
4×
4
15×
125
16× 256
=4400
3
= 14662
3
S42. Ans.(c)
Sol. ? = 101 × 73 + 251
= 7373 + 251
= 7624
S43. Ans.(e)
Sol.
? =(0.7 − 0.5)(0.7 + 0.5)(0.72 + 0.52)
(0.7 − 0.5)(0.72 + 0.7 × 0.5 + 0.52)
? =1.2 × 0.74
1.09
? =88.8
109
? =444
545
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S44. Ans.(d)
Sol.
? =36
100× 545 +
32
100× 215 −
47
100× 1300
= 196.2 + 68.8 − 611 = −346
S45. Ans.(d)
Sol. ? = 35 ÷ 7 × 342 = 1710
S46. Ans.(b)
Sol.
35 ÷ 7 × 342 = ? Or, ? = 1710
S47. Ans.(a)
Sol.
805 + 187 + 2? = 1000
Or, 2? = 8
Or, ? = 3
S48. Ans.(d)
Sol.
18? = 187.9 × 180.1 ÷ 184 Or, ? = 7.9 + 0.1 - 4 = 4
S49. Ans.(b)
Sol. 35
?=
22
7+
13
5+
36
5−
38
7−
18
35=
245
35
Or, ? =35×35
245= 5
S50. Ans.(e)
Sol.
88.2 − 4 = 10−? Or, ? = -74.2
S51. Ans.(a)
Sol.
I. 2𝑥2 + 4𝑥 + 7𝑥 + 14 = 0
2𝑥(𝑥 + 2) + 7(𝑥 + 2) = 0 𝑥 = −2, −3.5
II. (2𝑦 + 3)2 = 0
𝑦 = −1.5, −1.5
x < y
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S52. Ans.(b)
Sol.
I. 𝑥 = ±2
II. 𝑦2 + 3𝑦 + 3𝑦 + 9 = 0
𝑦 = −3, −3
x > y
S53. Ans.(d)
Sol.
I. 𝑥2 − 3𝑥 − 4𝑥 + 12 = 0
𝑥(𝑥 − 3) − 4(𝑥 − 3) = 0
𝑥 = 3, 4
II. 𝑦2 + 4𝑦 − 3𝑦 − 12 = 0
𝑦(𝑦 + 4) − 3(𝑦 + 4) = 0
𝑦 = 3, −4
x ≥ y
S54. Ans.(e)
Sol.
I. 𝑥 = ±27
II. 𝑦 = 23
∴ No relation
S55. Ans.(e)
Sol.
I. 𝑥4 = 398 + 227 = 625
𝑥 = ±5
II. 𝑦2 = 346 − 321
𝑦 = ±5
no relation
S56. Ans.(e)
Sol. 𝑥 =1
3,
−1
3
4𝑦2 + 12𝑦 − 𝑦 − 3 = 0
4𝑦(𝑦 + 3) − 1(𝑦 + 3) = 0
𝑦 =1
4, −3
So, no relation can be established
S57. Ans.(a)
Sol. 𝑥 = √5, −√5
4𝑦2 − 14𝑦 − 10𝑦 + 35 = 0
2𝑦(2𝑦 − 7) − 5(2𝑦 − 7) = 0
𝑦 =5
2,
7
2
𝑥 < 𝑦
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S58. Ans.(d)
Sol. 𝑥2 − 7𝑥 + 2𝑥 − 14 = 0
𝑥(𝑥 − 7) + 2(𝑥 − 7) = 0
𝑥 = 7, −2
𝑦2 + 5𝑦 + 2𝑦 + 10 = 0
𝑦 = −2, −5
𝑥 ≥ y
S59. Ans.(d)
Sol. Solving these equations.
𝑥 = −3, 𝑦 = −4
𝑥 ≥ 𝑦
S60. Ans.(d)
Sol. 2𝑥2 − 4𝑥 − √13𝑥 + 2√13 = 0
2𝑥(𝑥 − 2) − √13(𝑥 − 2) = 0
𝑥 =√13
2, 2
10𝑦2 − 18𝑦 − 5√13𝑦 + 9√13 = 0
2𝑦(5𝑦 − 9) − √13(5𝑦 − 9) = 0
𝑦 =√13
2,
9
5
𝑥 ≥ 𝑦
S61. Ans.(c)
Sol. I. 3x² + 10x + 8 = 0
⇒ 3x² + 6x + 4x + 8 = 0
⇒ (x + 2) (3x + 4) = 0
⇒ x = –2, –4/3
II. 3y² + 7y + 4 = 0
⇒ 3y² + 3y + 4y + 4 = 0
⇒ (y + 1) (3y + 4) = 0
⇒ y = –1, –4/3
y ≥ x
S62. Ans.(e)
Sol. I. 2x² + 21x + 10 = 0
⇒ 2x² + 20 + x + 10 = 0
⇒ (x + 10) (2x + 1) = 0
⇒ x = –10, –1/2
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II. 3y² + 13y + 14 = 0
⇒ 3y² + 6y + 7y + 14 = 0
⇒ (y + 2) (3y + 7) = 0
⇒ y = –2, –7/3
No relation
S63. Ans.(e)
Sol. I. x² + x – 12 = 0
⇒ x² + 4x – 3x – 12 = 0
⇒ (x + 4) (x – 3) = 0
⇒ x = 3, –4
II. y² + 2y – 8 = 0
⇒ y² + 4y – 2y – 8 = 0
⇒ (y + 4) (y – 2) = 0
⇒ y = – 4, 2
No relation
S64. Ans.(e)
Sol. I. 4x² – 13x + 9 = 0
⇒ 4x² – 4x – 9x + 9 = 0
⇒ (x – 1) (4x – 9) = 0
⇒ x = 1, 9/4
II. 3y² – 14y + 16 = 0
⇒ 3y² – 6y – 8y + 16 = 0
⇒ (y – 2) (3y – 8) = 0
⇒ y = 2, 8/3
No relation
S65. Ans.(b)
Sol. I. 8x² + 18x + 9 = 0
⇒ 8x² + 12x + 6x + 9 = 0
⇒ (2x + 3) (4x + 3) = 0
⇒ x = –3/2, –3/4
II. 4y² + 19y + 21 = 0
⇒ 4y² + 12y + 7y + 21 = 0
⇒ (y + 3) (4y + 7) = 0
⇒ x = –3, –7/4
x > y
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S66. Ans.(a)
Sol. I. 3x² + 16x + 21 = 0
⇒ 3x² + 9x + 7x + 21 = 0
⇒ (x + 3) (3x + 7) = 0
⇒ x = –3, –7/3
II. 6y² + 17y + 12 = 0
⇒ 6y² + 9y + 8y + 12 = 0
⇒ 3y (2y + 3) + 4 (2y + 3) = 0
⇒ y = – 3/2, –4/3
y > x
S67. Ans.(b)
Sol. I. 16x² + 20x + 6 = 0
⇒ 8x² + 10x + 3 = 0
⇒ 8x² + 4x + 6x + 3 = 0
⇒ (2x + 1) (4x + 3) = 0
⇒ x = –1/2, –3/4
II. 10y² + 38y + 24 = 0
⇒ 5y² + 19y + 12 = 0
⇒ 5y² + 15y + 4y + 12 = 0
⇒ (y + 3) (5y + 4) = 0
y = –3, –4/5
x > y
S68. Ans.(c)
Sol. I. 8x² + 6x – 5 = 0
⇒ 8x² + 10x – 4x – 5 = 0
⇒ (4x + 5) (2x – 1) = 0
⇒ x = ½, –5/4
II. 12y² – 22y + 8 = 0
⇒ 6y² – 11y + 4 = 0
⇒ 6y² – 3y – 8y + 4 = 0
⇒ (2y – 1) (3y – 4) = 0
⇒ y = 1/2, 4/3
y ≥ x
S69. Ans.(a)
Sol. I. 17x² + 48x – 9 = 0
⇒ 17x² + 51x – 3x – 9 = 0
⇒ (x + 3) (17x – 3) = 0
⇒ x = 3/17, – 3
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II. 13y² – 32y + 12 = 0
⇒ 13y² – 26y – 6y + 12 = 0
⇒ (y – 2) (13y – 6) = 0
⇒ y = 2, 6/13
y > x
S70. Ans.(d)
Sol. I. 8x² + 26x + 15 = 0
⇒ 8x² + 20x + 6x + 15 = 0
⇒ 4x (2x + 5) + 3(2x + 5) = 0
⇒ (2x + 5) (4x + 3) = 0
⇒ x = – 5/2, –3/4
II. 4y² + 24y + 35 = 0
⇒ 4y² + 10y + 14y + 35 = 0
⇒ 2y (2y + 5) + 7 (2y + 5) = 0
⇒ (2y + 5) (2y + 7) = 0
⇒ y = –5/2, –7/2
x ≥ y
S71. Ans.(a)
Sol. I. 6x² + 19x + 15 = 0
⇒ 6x² + 9x + 10x + 15 = 0
⇒ (2x + 3) (3x + 5) = 0
⇒ x = –3/2, –5/3
II. 24y² + 11y + 1 = 0
⇒ 24y² + 8y + 3y + 1= 0
⇒ (3y + 1) (8y + 1) = 0
⇒ y = –1/3, –1/8
y > x
S72. Ans.(e)
Sol. I. 2x² + 11x + 15 = 0
⇒ 2x² + 6x + 5x + 15 = 0
⇒ (x + 3) (2x + 5) = 0
⇒ x = – 3, –5/2
II. 4y² + 22y + 24 = 0
⇒ 2y² + 11y + 12 = 0
⇒ 2y² + 8y + 3y + 12 = 0
⇒ (y + 4) (2y + 3) = 0
⇒ y = –4, –3/2
No relation
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S73. Ans.(b)
Sol. I. 2x² + 9x + 9 = 0
⇒ 2x² + 6x + 3x + 9 = 0
⇒ (x + 3) (2x + 3) = 0
⇒ x = –3, –3/2
II. 2y² + 17y + 36 = 0
⇒ 2y² + 8y + 9y + 36 = 0
⇒ (y + 4) (2y + 9) = 0
y = – 4, –9/2
x > y
S74. Ans.(a)
Sol.
I. 5x² + 29 + 20 = 0
⇒ 5x² + 25x + 4x + 20 = 0
⇒ (x + 5) (5x + 4) = 0
⇒ x = –5, –4/5
II. 25y² + 25y + 6 = 0
⇒ 25y² + 15y + 10y + 6 = 0
⇒ (5y + 3) (5y + 2) = 0
⇒ y = – 3/5, –2/5
y > x
S75. Ans.(a)
Sol.
I. 3x² – 16x + 21 = 0
⇒ 3x² – 9x – 7x + 21 = 0
⇒ (x – 3) (3x – 7) = 0
⇒ x = 3, 7/3
II. 3y² – 28y + 65 = 0
⇒ 3y² – 15y – 13y + 65 = 0
⇒ (y – 5) (3y – 13) = 0
⇒ y = 5, 13/3
y > x
S76. Ans.(b)
Sol. Series is × 1.5, × 2, × 2.5, × 3, × 3.5
∴ ? = 135 × 3.5 = 472.5
S77. Ans.(d)
Sol. Series is ÷ 2 + 2, × 2+ 2, ÷ 2 + 2, × 2 + 2, ÷ 2 + 2
∴ ? = 78 ÷ 2 + 2 = 41
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S78. Ans.(c) Sol. Series is + 22, + 33, + 42, +53, + 62 ∴ ? = 201 + 62 = 237 S79. Ans.(e) Sol. Series is + 1.52, + 2.52, + 3.52, 4.52, + 5.52 ∴ ? = 46 + (5.5)2 = 76.25 S80. Ans.(d) Sol. Series is × 2 – 7, × 2 – 6, × 2 – 5, × 2 – 4, × 2 – 3 ∴ ? = 2114 × 2 – 3 = 4225 S81. Ans.(c) Sol. Pattern is +2², +3², +4², +5², +6² ∴ ? = 177 + 25 = 202 S82. Ans.(d) Sol. Pattern is +16, –32, +48, –64, +80 ∴ ? = 307 + 80 = 387 S83. Ans.(d) Sol. Pattern is × 3 – 1, × 3 – 2, × 3 –3, × 3 – 4, × 3 – 5, ∴ ? = 347 × 3 – 5 = 1036
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S84. Ans.(d)
Sol. Patter is ×2, ×4, ×6, ×8, ×10
∴ ? = 576 × 8 = 4608
S85. Ans.(b)
Sol. Patter is +312, +312, +312, +312, ….
∴ ? = 780 + 312 = 1092
S86. Ans. (c)
Sol. Pattern is (÷ 2), (÷ 2), (÷ 2) ………………
∴ 474 ÷ 2 = 237
S87. Ans. (a)
Sol. Pattern is (−19 × 1), (−19 × 2), (−19 × 3) ……………
∴ 317 − 19 × 3 = 260
S88. Ans. (d)
Sol. Pattern is (× 1 − 2), (× 4 − 3), (× 9 − 4), (× 16 − 5), (× 25 − 6)
∴ 3353 × 16 − 5 = 53643
S89. Ans. (b)
Sol. Pattern is 14, 24, 34, 44, 54
54 = 625
S90. Ans. (e)
Sol. Pattern is (÷ 2 + 0.5), (÷ 2 + 0.5)……….
∴ 18.5 ÷ 2 + 0.5 = 9.75
S91. Ans.(b)
Sol. Pattern is × 2 + 1, × 4 + 3, × 6 + 5, × 8 + 7, × 10 + 9
∴ ? = 1151 × 10 + 9
= 11519
S92. Ans.(c)
Sol. Pattern is × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4, × 5 + 5, ….
∴ ? = 63 × 4 + 4
= 256
S93. Ans.(a)
Sol. Series is
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S94. Ans.(b)
Sol. Pattern is × 0.5 + 2, × 1 + 2, × 1.5 + 2, × 2 + 2, × 2.5 + 2
∴ ? = 27 × 2.5 + 2
= 69.5
S95. Ans.(d)
Sol. Series is
S96. Ans.(d)
Sol. Series is
S97. Ans.(b)
Sol. Pattern is ÷8, ÷6, ÷4, ÷2
∴ ? = 12.5 ÷ 4
= 3.125
S98. Ans.(a)
Sol. Series is
S99. Ans.(d)
Sol. Pattern is + 14 × 1, + 14 × 3, + 14 × 9, + 14 × 27
∴ ? = 564 + 14 × 81
= 1698
S100. Ans.(b)
Sol. Pattern is × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4, × 5 + 5
∴ ? = 352 × 5 + 5
= 1765
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