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 TABLE OF CONTENTS
Serial no. Topic Page no.

1) Simplification 02 – 05

2) Approximation 05 – 08

3) Missing number series 08 – 11

4) Wrong number series 11 – 14

5) Quadratic Equation 15 – 16

6) Mains Speed Maths 17 – 28

7) Solution 29 – 60

Page | 1
 SIMPLIFICATION
1) (25% 𝑜𝑓 800) ÷ 4 + 15 × 3 − √49 = ?
a) 66
b) 77
c) 88
d) 99
e) None of these

2) 5 × (8 + 12) ÷ 2 − √81 + 10% 𝑜𝑓 500 = ?

a) 91
b) 81
c) 77
d) 73
e) None of these

3) (18 ÷ 2) × 7 + √64 = (30% 𝑜𝑓 300)+ ?

a) -19
b) -13
c) -14
d) -18
e) None of these

4) √121 + 25% 𝑜𝑓 160 − (45 ÷ 5) × 3 = ?

a) 25
b) 22
c) 24
d) 26
e) None of these

5) 6 × (15 ÷ 3) + 10% 𝑜𝑓 400 − √36 = ?

a) 72
b) 76
Page | 2
 c) 64
d) 68
e) None of these

6) (40 ÷ 8) × (25% 𝑜𝑓 200) = ? +15 − √100

a) 225
b) 235
c) 245
d) 255
e) None of these

7) √144 ÷ 3 + 30% 𝑜𝑓 150 = ? + (20 ÷ 4) × 2

a) 29
b) 39
c) 49
d) 59
e) None of these

8) (50 ÷ 10) × √49 + 15% 𝑜𝑓 600 =? + 20

a) 105
b) 115
c) 125
d) 135
e) None of these

9) √81 + (45 ÷ 9) × (25% 𝑜𝑓 200) − 30 = ?

a) 219
b) 229
c) 239
d) 249
e) None of these

10) (30% 𝑜𝑓 90) ÷ 3 + 20 × √16 =? + 25

Page | 3
 a) 48
b) 56
c) 64
d) 72
e) None of these

1 2 3
11) 2 × (3 + 1 ) − √49 = ?
2 5 10
a) 3(1/2)
b) 4(3/4)
c) 2(1/4)
d) 1(1/2)
e) None of these

1 2 1
12) 4 ÷ (2 × 1 ) + 25% 𝑜𝑓 80 = ?
3 5 6
a) 18(23/42)
b) 20(25/42)
c) 19(31/42)
d) 25(29/42)
e) None of these

1 2 1
13) 3 × (1 ÷ 2 ) − √121= ?
5 3 10
a) -8(29/63)
b) -7(29/63)
c) 7(29/63)
d) 8(29/63)
e) None of these

14) √196 × (25% 𝑜𝑓 160) ÷ 4 =? + 12

a) 126
b) 127
c) 128
d) 129

Page | 4
 e) None of these

15) (15% 𝑜𝑓 200) × 2 + √81 ÷ 3 =? + 5

a) 52
b) 56
c) 58
d) 60
e) None of these

APPROXIMATION
16) (49.8% 𝑜𝑓 799.9) ÷ 4.1 + 15.2 × 3.9 − √48.6 = ?
a) 153
b) 149
c) 147
d) 154
e) 157

17) 4.9 × (8.3 + 11.7) ÷ 2.1 − √80.9 + 9.8% 𝑜𝑓 502 = ?

a) 91
b) 97
c) 85
d) 83
e) 93

18) (17.6 ÷ 2.4) × 6.9 + √63.9 − (29.5% 𝑜𝑓 300) = ?

a) -17
b) -19
c) 11
d) 17
e) 19

19) √120.9 + 24.8% 𝑜𝑓 159.9 − (44.9 ÷ 4.8) × 3.1 = ?

Page | 5
 a) 21
b) 24
c) 28
d) 32
e) 36

20) 5.8 × (14.7 ÷ 3.1) + 9.9% 𝑜𝑓 399.9 =? + √35.8

a) 56
b) 64
c) 72
d) 78
e) 96

21) (39.6 ÷ 7.8) × (24.8% 𝑜𝑓 199.7) + √99.9 − 15.2 =?

a) 245
b) 235
c) 229
d) 242
e) None of these

22) √143.8 ÷ 3.1 + 29.7% 𝑜𝑓 149.8 − (19.6 ÷ 3.9) × 2.1 = ?

a) 29
b) 39
c) 49
d) 59
e) 69

23) (49.6 ÷ 9.9) × √48.9 + 14.8% 𝑜𝑓 599.3 − 19.9 = ?

a) 105
b) 100
c) 95
d) 115
e) 125

Page | 6
 24) √80.5 + (44.9 ÷ 8.9) × (24.8% 𝑜𝑓 199.2) − 29.7 = ?
a) 219
b) 229
c) 239
d) 249
e) 259

25) (29.7% 𝑜𝑓 89.8) ÷ 3.1 = ? − 19.7 × √15.9 + 24.7

a) 72
b) 56
c) 64
d) 78
e) 84

26) 3.1 × (1.6 ÷ 2.1 + 3.9) + √119.7 =? + 18.2

a) 5
b) 4
c) 8
d) 7
e) 6

27) 2.9 × (4.8 ÷ 3.2 + 3.1) =? + √80.2 − 20.4

a) 23
b) 24
c) 28
d) 26
e) 30

28) ? = √49.7 × (24.9% 𝑜𝑓 100) ÷ 4.81 − 14.1

a) 21
b) 42
c) 31

Page | 7
 d) 29
e) 35

29) √195.9 × (24.8% 𝑜𝑓 160) ÷ 4.1 = ? + 11.9

a) 124
b) 128
c) 132
d) 136
e) 138

30) (14.9% 𝑜𝑓 199.7) × 1.9 + √80.1 ÷ 2.9 − 4.9 = ?

a) 52
b) 58
c) 56
d) 60
e) 62

MISSING NUMBER SERIES

31) 27 40 55 72 91 ?
a) 115
b) 122
c) 112
d) 116
e) None of these

32) 552 600 650 702 ? 812

a) 756
b) 780
c) 800
d) 754
e) None of these

Page | 8
 33) 242 200 162 128 98 ?
a) 80
b) 82
c) 76
d) 72
e) None of these

34) 12 24 41 72 133 ?
a) 225
b) 249
c) 219
d) 115
e) None of these

35) 12 14 17 27 42 ?
a) 65
b) 64
c) 60
d) 68
e) None of these

36) 31 30 58 171 ? 3395

a) 650
b) 684
c) 690
d) 680
e) None of these

37) 212 213 221 248 312 X

a) 417
b) 427
c) 437
d) 447
e) None of these
Page | 9
 38) 34 ? 68 207 824 4125
a) 32
b) 33
c) 34
d) 35
e) None of these

39) 235 360 396 ? 803 1532

a) 735
b) 732
c) 728
d) 743
e) None of these

40) 120 263 458 713 ? 1435

a) 1028
b) 1014
c) 1046
d) 1076
e) None of these

41) ? 40.5 41.5 85 343 2748

a) 81
b) 42
c) 50
d) 91
e) None of these

42) 114 240 492 996 ? 4020

a) 2004
b) 2010
c) 2020
d) 2030
Page | 10
 e) None of these

43) 140 ? 557 1170 2365 4766

a) 276
b) 290
c) 295
d) 280
e) None of these

44) 90 96 108 138 194 ?

a) 321
b) 326
c) 325
d) 323
e) None of these

45) 219 363 507 651 795 ?

a) 939
b) 937
c) 941
d) 943
e) None of these

WRONG NUMBER SERIES

46) 12 25 51 91 142 207
a) 25
b) 142
c) 12
d) 51
e) None of these

Page | 11
 47) 8 17 26 45 80 147
a) 45
b) 80
c) 147
d) 26
e) None of these

48) 1372 196 98 14 7 4

a) 14
b) 196
c) 4
d) 7
e) None of these

49) 42 43 47 56 75 97
a) 75
b) 56
c) 43
d) 97
e) None of these

50) 2 18 63 319 1600 8006

a) 2
b) 18
c) 63
d) 319
e) None of these

51) 26 68 98 118 130 140

a) 140
b) 130
c) 118
d) 98
e) None of these
Page | 12
 52) 512 128 64 48 56 60
a) 512
b) 56
c) 128
d) 48
e) None of these

53) 3 12 33 45 135 228

a) 135
b) 12
c) 228
d) 45
e) None of these

54) 1 3 8 40 305 2750

a) 3
b) 305
c) 2750
d) 40
e) None of these

55) 15 21 33 39 51 60
a) 33
b) 60
c) 39
d) 51
e) None of these

56) 1350 1747 2216 2763 3395 4115

a) 1747
b) 2216
c) 3395
d) 4115
Page | 13
 e) None of these

57) 2603 2813 3030 3257 3491 3733

a) 3733
b) 3030
c) 2603
d) 2813
e) None of these

58) 3457 2001 1000 433 129 17

a) 3457
b) 1000
c) 433
d) 17
e) None of these

59) 9 40 195 972 4845 24220

a) 40
b) 195
c) 24220
d) 972
e) None of these

60) 2 5 8 19 34 72
a) 72
b) 8
c) 19
d) 34
e) None of these

Page | 14
 QUADRATIC EQUATION
In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and answer the following questions.
इनमें से प्रत्येक प्रश्न में दो समीकरण (I) और (II) ददए गए हैं । आपको दोनोों
समीकरणोों को हल करना है और दनम्नदलखित प्रश्नोों के उत्तर दे ने हैं ।

a) x > y
b) x < y
c) x ≥ y
d) x ≤ y
e) x = y or cannot be determined

61) x² + 11x = - 28
y² + 19y – 92 = 0

62) x² + 31x + 58 = 0
y² - 13y +36 = 0

63) 5x² + 18x = 35

2y² + 21y + 55 = 0

64) 2x² + 31x - 51 = 0

y² - 40y + 144 = 0

65) 2x² - 6x – 80 = 0
3y² - 54y + 240 = 0

66) x² - 31x +198 =0

y² + 35y + 124 = 0

67) x² + 55x =114

y² - 4y – 165 = 0

Page | 15
 68) x² - 36x + 323 =0
y² - 6y – 91 = 0

69) x² + 48x – 153 = 0

y² - 23y +132 = 0

70) x² - 41x + 148 = 0

y² + 20y – 261 = 0

71) x² − 4x – 96 =0
y² + 7y – 60=0

72) x² + x – 56 = 0
y² − 17y + 70 = 0

73) x² − 19x + 78 = 0
y² − 25 = 0

74) x² + 9x − 22 = 0
y² − 11y + 24 = 0

75) 2x + 3y = 13
8x − 6y = 4

Page | 16
 MAINS SPEED MATHS
Find the value of x and y in the given series and answer the following
questions.
दी गई श्रोंिला में x और y का मान ज्ञात कीदिए और दनम्नदलखित प्रश्नोों के उत्तर
दीदिए।

5 5 3 1 7
76) x = ( ) + ( ) − ( ) + ( ) − ( )
8 6 4 3 10
5 11 9 1
y=( )− ( )+ ( )− ( )
12 14 15 12
a) x > y
b) x ≥ y
c) x > y
d) x ≤ y
e) x = y or No relation can be formed

1
(3) 2
77) (85184) − √961 ∗ 𝑥 + ( ) 𝑜𝑓 375 – 48 = 22
5
5
6 % 𝑜𝑓 9600 + (1425 ÷ 25 ÷ 3] = 127 + 𝑦
8
Find the value of (y - x³).
(y - x³) का मान ज्ञात कीदिए।
a) 424
b) 464
c) 444
d) 484
e) None of these

78) 55 % 𝑜𝑓 200 + 85% 𝑜𝑓 140 + 𝑥 = 160 % 𝑜𝑓 240

(y ÷ 133) * (√361 ÷ 357) = (12 ÷ y) * (1 / √289)
Find the value of √(2x – 3y - 15)
√(2x – 3y - 15) का मान ज्ञात कीदिए
a) 15
Page | 17
 b) 13
c) 11
d) 17
e) None of these

79) 88.88 % 𝑜𝑓 387 + 14.28 % 𝑜𝑓 280 = 𝑥 + 23 ∗ 8

60% 𝑜𝑓 740 + 98% 𝑜𝑓 1200 − √784 % 𝑜𝑓 800 = 𝑦
Find (2y - 7x)
(2y - 7x) ज्ञात करें
a) 1392
b) 1272
c) 1532
d) 1712
e) None of these

Find the approximate value of x and y in the given series and answer
the following questions.
दी गई श्रोंिला में x और y का अनुमादनत मान ज्ञात कीदिए और दनम्नदलखित प्रश्नोों
के उत्तर दीदिए।

80) 249.87*24.83 + x² * 119.81 + 16.11*14.13 = 14153.91

89.71% of 199.83 + 75.11% of 559.97 – 190.19 = y
Find the value of (y+30)/x
(y+30)/x का मान ज्ञात कीदिए
a) 45
b) 55
c) 65
d) 75
e) 85

81) 59.73% of 359.86 + 30.13% of 239.81 – 24.87% of 399.93 = x

(1234.83 ÷ 18.91) * (434.17 ÷ √960) = y * 12.98
Find the value of (x – y).

Page | 18
 (x – y) का मान ज्ञात कीदिए।
a) 118
b) 116
c) 114
d) 112
e) 110

82) 79.88% of 239.81 + 24.93% of 144.11 – 39.87% of 219.97 = x

15.91% of 349.81 + 27.99% of 124.83 – 455.93 ÷ 19.11 = y
Find the value of (x/2 – y).
(x/2 – y) का मान ज्ञात कीदिए।
a) 5
b) 3
c) 6
d) 7
e) 2

83) 61.89% of 300.11 + 130.97 = x % of 79.88 + 111.99

59.81% of 44.93% of 400.11 + (2/7) of 104.83 = y
Find the of (x – y)
(x – y) का मान ज्ञात कीदिए
a) 103
b) 107
c) 111
d) 113
e) 119

84) 44.98% of 239.81 – 23.86% of 549.87 = x - √1445

√170 * √63 - √730 * √145 = √3026 * 1.97 – y
Find the value of ((8x – y/6) – 12)2
((8x – y/6) – 12) 2 का मान ज्ञात कीदिए
a) 1600
b) 2025

Page | 19
 c) 1764
d) 1936
e) 2304

85) 14.182 × 6.81 of 29.87% of 839.98 ÷ 20.83 = x × 783.87

36.13% of 349.81 + (575.78 ÷ (479.93 ÷ 11.97)) * 4.83 = y
Find the value of (y - 14)/(x + 2)
(y - 14)/(x + 2) का मान ज्ञात कीदिए
a) 9
b) 8
c) 7
d) 6
e) 5

86) I. 5x + 2y + 3z = 128
II. 2x – 7y + 4z = - 35
III. 6x – 4y – 6z = - 48
a) x < y = z
b) x = y > z
c) x < y < z
d) x > y < z
e) x < y > z

87) I. ³√(27) x² - √(1156) x + (7*13) = 0

II. 2y² - 37y + (5³ + 18) = 0
Which of the following equations has its roots equal to the larger root
of equation I and equation II?
दनम्नदलखित में से दकस समीकरण के मूल समीकरण I और समीकरण II के बडे
मूल के बराबर हैं ?
a) p² - 20p + 91 = 0
b) 2p² - 91p - 20 = 0
c) p² + 20p – 91 = 0
d) 2p² + 20p – 91 = 0

Page | 20
 e) p² + 15p – 20 = 0

88) Below is a quadratic equation and find the roots of the equation. The
larger root is ‘a’ and the smaller root is ‘b’.
Quadratic equation: x² − 40x + 399 = 0
(i) Subtract 11 from ‘a’ and then substitute the resultant number as x
in the LHS of the equation to get the value of ‘m’
(ii) Add 1 to ‘b’ and then substitute the resultant number as x in the
LHS of the equation to get the value of ‘n’
What is the value of ‘m – n’?
88) नीचे एक दिघात समीकरण ददया गया है और समीकरण की िडें ज्ञात कीदिए।
बडी िड ‘a’ है और छोटी िड ‘b’ है ।
दिघात समीकरण: x² − 40x + 399 = 0
(i) ‘a’ से 11 घटाएँ और दिर पररणामी सोंख्या को समीकरण के बाएँ पक्ष में x के
रूप में प्रदतस्थादपत करें तादक ‘m’ का मान प्राप्त हो सके
(ii) ‘b’ में 1 िोडें और दिर पररणामी सोंख्या को समीकरण के बाएँ पक्ष में x के रूप
में प्रदतस्थादपत करें तादक ‘n’ का मान प्राप्त हो सके
‘m – n’ का मान क्या है ?
a) 112
b) 102
c) 120
d) 90
e) 100

89) Below is a quadratic equation, find the roots of this equation in which
the larger root is ‘a’ and the smaller root is ‘b’.
Quadratic equation: x² − x − 870 = 0
(i) Subtract 12 from ‘a’ and then substitute the resultant number as x
in the LHS of the equation to get the value of ‘m’
(ii) Add 4 to ‘b’ and then substitute the resultant number as x in the
LHS of the equation to get the value of ‘n’
What is the value of ‘m + n?

Page | 21
 89) नीचे एक दिघात समीकरण ददया गया है , इस समीकरण की िडें ज्ञात करें
दिसमें बडी िड ‘a’ है और छोटी िड ‘b’ है ।
दिघात समीकरण: x² − x − 870 = 0
(i) ‘a’ से 12 घटाएँ और दिर पररणामी सोंख्या को समीकरण के बाएँ पक्ष में x के
रूप में प्रदतस्थादपत करें तादक ‘m’ का मान प्राप्त हो सके
(ii) ‘b’ में 4 िोडें और दिर पररणामी सोंख्या को समीकरण के बाएँ पक्ष में x के रूप
में प्रदतस्थादपत करें तादक ‘n’ का मान प्राप्त हो सके
‘m + n’ का मान क्या है ?
a) -725
b) -645
c) -784
d) -894
e) -781

90) The table below contains columns I and II. Column I has rows A, B, and
C, and Column II has rows D, E, and F. Which parts of Column I match
correctly with Column II?
नीचे दी गई तादलका में स्तोंभ I और II हैं । स्तोंभ I में पोंखियाँ A, B और C हैं , और
स्तोंभ II में पोंखियाँ D, E और F हैं । स्तोंभ I का कौन सा भाग स्तोंभ II से सही ढों ग से
मेल िाता है ?
Equation Condition
D. Sum of the roots is the square of a
A. x² + 6x – 315 = 0
number
B. y² - 11y – 350 = 0 E. Difference between two roots is 6
F. One of the roots is the square of a
C. z² - 49z + 580 = 0
prime number
a) Only AE
b) Only BF
c) Only CD and AE
d) Only BF and CD
e) None of the above

Page | 22
 91) The table below contains columns I and II. Column I has rows A, B, and
C, and Column II has rows D, E, and F. Which parts of Column I match
correctly with Column II?
नीचे दी गई तादलका में स्तोंभ I और II हैं । स्तोंभ I में पोंखियाँ A, B और C हैं , और
स्तोंभ II में पोंखियाँ D, E और F हैं । स्तोंभ I का कौन सा भाग स्तोंभ II से सही ढों ग से
मेल िाता है ?
Equation Condition
A. 3x² + 7x – 20 = 0 D. One of the roots is a prime number
E. Difference between the square of
B. 2y² - 17y + 35 = 0
one of the roots and 35 is 46
F. Difference between the cube of one
C. z² - 5z – 36 = 0
of the roots and 27 is 35
a) Only CE
b) Only BD and AF
c) Only AF
d) Only BD, CE
e) Only BD, CE and CF

92) I. 3x² - 22x + 35 = 0

II. 2x² - 10x = 0
Note:
1. If 8 is added to the LHS of equation II, the square of the sum of the
newly formed roots is taken as ‘a’.
2. If equation I and equation II are equated, the difference of the
square of the newly formed roots is taken as ‘b’
Find which of the following condition is true
नोट:
1. यदद समीकरण II के बाएँ पक्ष में 8 िोडा िाता है , तो नवगदित मूलोों के योग का
वगग 'a' के रूप में दलया िाता है ।
2. यदद समीकरण I और समीकरण II को समान दकया िाता है , तो नवगदित मूलोों
के वगग का अोंतर 'b' के रूप में दलया िाता है । दनम्नदलखित में से कौन सी खस्थदत सत्य
है , यह पता लगाएँ
a) a > b
Page | 23
 b) a < b
c) a ≥ b
d) a ≤ b
e) a = b

93) I. x² - ax + (b – 3) = 0
II. y² - (a + 1) y + b = 0
III. z² - 10z + 21 = 0
Note:
i) The root values of I are p and 4
ii) The root values of II are p and 5
Find which of the following statement is/ are correct.
1. One of the roots of III is equal to the value of p
2. Product of the roots of II is less than the product of the roots of III
3. One of the roots of III is greater than (b – a)
नोट:
i) I के मूल मान p और 4 हैं
ii) II के मूल मान p और 5 हैं
दनम्नदलखित में से कौन सा कथन सही है /हैं , यह पता लगाएों ।
1. III की एक िड p के मान के बराबर है
2. II की िडोों का गुणनिल III की िडोों के गुणनिल से कम है
3. III की एक िड (b – a) से बडी है
a) Only 1
b) Both 1 and 2
c) Only 3
d) Both 1 and 3
e) All 1, 2 and 3

94) In the following questions, a series is given in which one term is wrong
with which another series is started. Find the 5th term of the new
series so formed. Both series follow the same pattern.

Page | 24
 दनम्नदलखित प्रश्नोों में एक श्रोंिला दी गई है दिसमें एक पद गलत है दिसके साथ दू सरी
श्रोंिला शुरू की गई है । इस प्रकार बनी नई श्रोंिला का 5वाँ पद ज्ञात कीदिए। दोनोों
श्रोंिलाएँ समान पैटनग का अनुसरण करती हैं ।
2 10 30 106 322 970
a) 2590
b) 2410
c) 2280
d) 2640
e) None of these

95) Analyze the pattern of the series given below and answer the
following questions. Series II follows the pattern same as Series I.
नीचे दी गई श्रोंिला के पैटनग का दवश्लेषण करें और दनम्नदलखित प्रश्नोों के उत्तर दें ।
श्रोंिला II, श्रोंिला I के समान पैटनग का अनुसरण करती है ।
Series I: 8, 10, 17, 31, x, 88
Series II: a, b, c, (x+3), d
Find the value of (d+a).
d+a का मान ज्ञात कीदिए।
a) 154
b) 184
c) 114
d) 94
e) None of these

96) There are two number series with missing terms and both series
follow different patterns. Read the question carefully and answer
accordingly.
दो सोंख्या श्रोंिलाएँ हैं दिनमें लुप्त पद हैं और दोनोों श्रोंिलाएँ अलग-अलग पैटनग का
अनुसरण करती हैं । प्रश्न को ध्यान से पढें और उसके अनुसार उत्तर दें ।
Series I: 25 32 71 220 x 4442
Series II: 20 102 411 1238 2483 y
Find x + [(y/2) + 13]/12.

Page | 25
 x + [(y/2) + 13]/12 ज्ञात कीदिए।
a) 992
b) 972
c) 994
d) 996
e) None of these

97) There are two number series with missing terms and both series
follow different patterns. Read the question carefully and answer
accordingly.
दो सोंख्या श्रोंिलाएँ हैं दिनमें लुप्त पद हैं और दोनोों श्रोंिलाएँ अलग-अलग पैटनग
का अनुसरण करती हैं । प्रश्न को ध्यान से पढें और उसके अनुसार उत्तर दें ।
Series I: x 19 34 93 356 1755
Series II: 10 15 30 75 225 y
Find (x² + 2y - 75) /4.
(x² + 2y - 75) /4 ज्ञात कीदिये।
a) 425
b) 475
c) 575
d) 525
e) 450

98) There are three series I, II & III are given, you have to find the wrong
number in these series which is represented by x, y and z respectively
and established the relationship between x, y and z.
तीन श्रोंिलाएँ I, II और III दी गई हैं , आपको इन श्रोंिलाओों में गलत सोंख्या ढू ों ढनी
है दिसे क्रमशः x, y और z िारा दशाग या गया है और x, y और z के बीच सोंबोंध
स्थादपत करना है ।
Series I: 243 81 54 60 70 120
Series II: 70 71 67 76 60 84
Series III: 80 40 45 60 120 300
a) x > y > z
b) x = y = z
Page | 26
 c) x > y < z
d) x < y > z
e) x < y < z

99) Two series I and II are given below with the missing term 'J' in series
I and the missing term 'W' in series II.
Series 1: 500, 379, 265, 164, 82, J, 13
Series II: W, 577, 773, 954, 1118, 1263
Which of the following statement/s is/are False?
(i) Both J and W are prime numbers.
(ii) One among J and W is a perfect square and the other is a perfect
cube.
(iii) Any one of J and W has a value of 368.
नीचे दो श्रोंिला I और II दी गई हैं , दिनमें श्रोंिला I में लुप्त पद 'J' और श्रोंिला II में
लुप्त पद 'W' है ।
श्रोंिला 1: 500, 379, 265, 164, 82, J, 13
श्रोंिला II: W, 577, 773, 954, 1118, 1263
दनम्नदलखित में से कौन सा कथन गलत है ?
(i) J और W दोनोों अभाज्य सोंख्याएँ हैं ।
(ii) J और W में से एक पूणग वगग है और दू सरा पूणग घन है ।
(iii) J और W में से दकसी एक का मान 368 है ।
a) Both I and III
b) Both I and II
c) Both II and III
d) All I, II and III
e) Only I

100) Two series I and series II are given. Which of the following is correct
about the relationship among the missing numbers in the following
series?
Series I: 128, 64, 96, 240,840, (T + 2756)
Series II: 329, (W + 114), 289, 458, 97, 938
(i) The LCM of these two terms T and W is 7168.
Page | 27
 (ii) The absolute difference between these two terms T and W is 700.
(iii) The Sum of these two terms T and W is divisible by 12.
दो श्रोंिला I और श्रोंिला II दी गई हैं । दनम्नदलखित श्रोंिला में लुप्त सोंख्याओों के बीच
सोंबोंध के बारे में दनम्नदलखित में से कौन सा सही है ?
श्रोंिला I: 128, 64, 96, 240,840, (T + 2756)
श्रोंिला II: 329, (W + 114), 289, 458, 97, 938
(i) इन दो पदोों T और W का LCM 7168 है ।
(ii) इन दो पदोों T और W के बीच का पूणग अोंतर 700 है ।
(iii) इन दो पदोों T और W का योग 12 से दवभाज्य है ।
a) Both I and III
b) Both I and II
c) Both II and III
d) All I, II and III
e) Only I

Page | 28
 SOLUTION
1) Answer
(25% of 800) ÷ 4 + 15 × 3 - √49
? = (200) ÷ 4 + 45 - 7
? = 50 + 45 - 7
? = 88

2) Answer
5 × (8 + 12) ÷ 2 - √81 + 10% of 500
= 5 × 20 ÷ 2 - 9 + 50
= 100 ÷ 2 - 9 + 50
= 50 - 9 + 50
= 91

3) Answer
(18 ÷ 2) × 7 + √64 - (30% of 300)
= 9 × 7 + 8 - 90
= 63 + 8 - 90
= -19

4) Answer
√121 + 25% of 160 - (45 ÷ 5) × 3
= 11 + 40 - 27
= 51 - 27
= 24

5) Answer
6 × (15 ÷ 3) + 10% of 400 - √36
= 6 × 5 + 40 - 6
= 30 + 40 - 6

Page | 29
 = 64

6) Answer
(40 ÷ 8) × (25% of 200) + √100 - 15
= 5 × 50 + 10 - 15
= 250 + 10 - 15
= 245

7) Answer
√144 ÷ 3 + 30% of 150 - (20 ÷ 4) × 2
= 12 ÷ 3 + 45 - 10
= 4 + 45 - 10
= 39

8) Answer
(50 ÷ 10) × √49 + 15% of 600 - 20
= 5 × 7 + 90 - 20
= 35 + 90 - 20
= 105

9) Answer
√81 + (45 ÷ 9) × (25% of 200) - 30
= 9 + 5 × 50 - 30
= 9 + 250 - 30
= 229

10) Answer
(30% of 90) ÷ 3 + 20 × √16 - 25
= 27 ÷ 3 + 20 × 4 - 25
= 9 + 80 - 25
= 64

Page | 30
 11) Answer
2 1/2 × (3 2/5 + 1 3/10) - √49
= 5/2 × (17/5 + 13/10) - 7
= 5/2 × 47/10 - 7
= 235/20 - 7
= 11 15/20 - 7
= 4 15/20 = 4 ¾

12) Answer
4 1/3 ÷ (2 2/5 × 1 1/6) + 25% of 80
= 13/3 ÷ (12/5 × 7/6) + 20
= 13/3 ÷ 14/5 + 20
= 13/3 × 5/14 + 20
= 65/42 + 20
= 20 25/42

13) Answer
3 1/5 × (1 2/3 ÷ 2 1/10) - √121
= 16/5 × (5/3 ÷ 21/10) - 11
= 16/5 × 50/63 - 11
= 800/315 - 11
= 2 170/315 - 11
= -8 145/315 = -8 29/63

14) Answer
√196 × (25% of 160) ÷ 4 - 12
= 14 × 40 ÷ 4 - 12
= 560 ÷ 4 - 12
= 140 - 12
= 128

15) Answer
Page | 31
 (15% of 200) × 2 + √81 ÷ 3 - 5
= 30 × 2 + 9 ÷ 3 - 5
= 60 + 3 - 5
= 58

16) Answer
(49.8% of 799.9) ÷ 4.1 + 15.2 × 3.9 - √48.6
≈ (50% of 800) ÷ 4 + 15 × 4 - √49
= 400 ÷ 4 + 60 - 7
= 100 + 60 - 7
= 153

17) Answer
4.9 × (8.3 + 11.7) ÷ 2.1 - √80.9 + 9.8% of 502
≈ 5 × (8 + 12) ÷ 2 - √81 + 10% of 500
= 5 × 20 ÷ 2 - 9 + 50
= 50 - 9 + 50
= 91

18) Answer
(17.6 ÷ 2.4) × 6.9 + √63.9 - (29.5% of 300)
≈ (18 ÷ 2) × 7 + √64 - (30% of 300)
= 9 × 7 + 8 - 90
= 63 + 8 - 90
= -19

19) Answer
√120.9 + 24.8% of 159.9 - (44.9 ÷ 4.8) × 3.1
≈ √121 + 25% of 160 - (45 ÷ 5) × 3
= 11 + 40 - 27
= 24

Page | 32
 20) Answer
5.8 × (14.7 ÷ 3.1) + 9.9% of 399.9 - √35.8
≈ 6 × (15 ÷ 3) + 10% of 400 - √36
= 6 × 5 + 40 - 6
= 30 + 40 - 6
= 64

21) Answer
(39.6 ÷ 7.8) × (24.8% of 199.7) + √99.9 - 15.2
≈ (40 ÷ 8) × (25% of 200) + √100 - 15
= 5 × 50 + 10 - 15
= 250 + 10 - 15
= 245

22) Answer
√143.8 ÷ 3.1 + 29.7% of 149.8 - (19.6 ÷ 3.9) × 2.1
≈ √144 ÷ 3 + 30% of 150 - (20 ÷ 4) × 2
= 12 ÷ 3 + 45 - 10
= 4 + 45 - 10
= 39

23) Answer
(49.6 ÷ 9.9) × √48.9 + 14.8% of 599.3 - 19.9
≈ (50 ÷ 10) × √49 + 15% of 600 - 20
= 5 × 7 + 90 - 20
= 35 + 90 - 20
= 105

24) Answer
√80.5 + (44.9 ÷ 8.9) × (24.8% of 199.2) - 29.7
≈ √81 + (45 ÷ 9) × (25% of 200) - 30
= 9 + 5 × 50 - 30
Page | 33
 = 9 + 250 - 30
= 229

25) Answer
(29.7% of 89.8) ÷ 3.1 + 19.7 × √15.9 - 24.7
≈ (30% of 90) ÷ 3 + 20 × √16 - 25
= 27 ÷ 3 + 80 - 25
= 9 + 80 - 25
= 64

26) Answer
3.1 × (1.6 ÷ 2.1 + 3.9) + √119.7 - 18.2
≈ 3 × (2 ÷ 2 + 4) + √121 - 18
= 3 × (1 + 4) + 11 - 18
= 3 × 5 + 11 - 18
= 15 + 11 - 18
=8

27) Answer
2.9 × (4.8 ÷ 3.2 + 3.1) - √80.2 + 20.4
≈ 3 × (5 ÷ 3 + 3) - √81 + 20
= 3 × (2 + 3) - 9 + 20
= 3 × 5 - 9 + 20
= 15 - 9 + 20
= 26

28) Answer
√49.7 × (24.9% of 100) ÷ 4.81 - 14.1
≈ √49 × (25% of 100) ÷ 5 - 14
= 7 × 25 ÷ 5 - 14
= 175 ÷ 5 - 14
= 35 - 14
Page | 34
 = 21

29) Answer
√195.9 × (24.8% of 160) ÷ 4.1 - 11.9
≈ √196 × (25% of 160) ÷ 4 - 12
= 14 × 40 ÷ 4 - 12
= 560 ÷ 4 - 12
= 140 - 12
= 128

30) Answer
(14.9% of 199.7) × 1.9 + √80.1 ÷ 2.9 - 4.9
≈ (15% of 200) × 2 + √81 ÷ 3 - 5
= 30 × 2 + 9 ÷ 3 - 5
= 60 + 3 - 5
= 58

31) Answer
5²+2=27
6²+4=40
7²+6=55
8²+8=72
9²+10=91
10²+12=112

32) Answer
23²+23=552
24²+24=600
25²+25=650
26²+26=702
27²+27=756
28²+28=812
Page | 35
 33) Answer
2*(11²) =242
2*(10²) =200
2*(9²) =162
2*(8²) =128
2*(7²) =98
2*(6²) =72

34) Answer
12 24 41 72 133 249
12 17 31 61 116
5 14 30 55
9 16 25

35) Answer
14-12=2 = (1²+1)
17-14=3=(2²-1)
27-17=10=(3²+1)
42-27=15=(4²-1)
68-42=26=(5²+1)

36) Answer
31 * 1 – 1 = 31 – 1 = 30
30 * 2 – 2 = 60 – 2 = 58
58 * 3 – 3 = 174 – 3 = 171
171 * 4 – 4 = 684 – 4 = 680
680 * 5 – 5 = 3400 – 5 = 3395

37) Answer
212 + 1³ = 212 + 1 = 213
213 + 2³ = 213 + 8 = 221
Page | 36
 221 + 3³ = 221 + 27 = 248
248 + 4³ = 248 + 64 = 312
312 + 5³ = 312 + 125 = 437

38) Answer
34 * 1 + 1 = 34 + 1 = 35
35 * 2 – 2 = 70 – 2 = 68
68 * 3 + 3 = 204 + 3 = 207
207 * 4 – 4 = 828 – 4 = 824
824 * 5 + 5 = 4120 + 5 = 4125

39) Answer
235 + 5³ = 235 + 125 = 360
360 + 6² = 360 + 36 = 396
396 + 7³ = 396 + 343 = 739
739 + 8² = 739 + 64 = 803
803 + 9³ = 803 + 729 = 1532

40) Answer
120 263 458 713 1036 1435
12²-1 14²-1 16²-1 18²-1 20²-1

41) Answer
81 * 0.5 + 0 = 40.5 + 0 = 40.5
40.5 * 1 + 1 = 40.5 + 1 = 41.5
41.5 * 2 + 2 = 83 + 2 = 85
85 * 4 + 3 = 340 + 3 = 343
343 * 8 + 4 = 2744 + 4 = 2748

42) Answer
(114 + 6) * 2 = 120 * 2 = 240
(240 + 6) * 2 = 246 * 2 = 492
Page | 37
 (492 + 6) * 2 = 498 * 2 = 996
(996 + 6) * 2 = 1002 * 2 = 2004
(2004 + 6) * 2 = 2010 * 2 = 4020

43) Answer
140 * 2 + 2² = 280 + 4 = 284
284 * 2 + 3² = 568 + 9 = 577
577 * 2 + 4² = 1154 + 16 = 1170
1170 * 2 + 5² = 2340 + 25 = 2365
2365 * 2 + 6² = 4730 + 36 = 4766

44) Answer
90 + 2²+ 2 = 90 + 4 + 2 = 96
96 + 3² + 3 = 96 + 9 + 3 = 108
108 + 5² + 5 = 108 + 25 + 5 = 138
138 + 7² + 7 = 138 + 49 + 7 = 194
194 + 11² + 11 = 194 + 121 + 11 = 326

45) Answer
219 + 144 = 363
363 + 144 = 507
507 + 144 = 651
651 + 144 = 795
795 + 144 = 939

46) Answer
12 25 51 90 142 207
+13 +26 +39 +52 +65

47) Answer
8 15 26 45 80 147
7 11 19 35 67
Page | 38
 4 8 16 32

48) Answer
1372 196 98 14 7 1
÷7 ÷2 ÷7 ÷2 ÷7

49) Answer
42 + 1² = 43
43 + 2² = 47
47 + 3² = 56
56 + 4² = 72
72 + 5² = 97

50) Answer
2 12 63 319 1600 8006
*5+2 *5+3 *5+4 *5+5 *5+6

51) Answer
26+6*7 = 68
68+5*6 = 98
98+4*5 = 118
118+3*4 = 130
130+2*3= 136

52) Answer
512 128 64 48 48 60
*1/4 *2/4 *3/4 *4/4 *5/4

53) Answer
(1³+2) = 3
(2³+4) = 12
Page | 39
 (3³+6) = 33
(4³+8) = 72
(5³+10) = 135
(6³+12) = 228

54) Answer
1 2 8 43 305 2750
(1*1)+1 (2*3)+2 (8*5)+3 (43*7)+4 (305*9)+5

55) Answer
5* 3 = 15
7 * 3 = 21
11* 3 = 33
13* 3 =39
17* 3 = 51
19* 3 = 57

56) Answer
11³ + 19 =1350
12³ + 19 = 1747
13³ + 19 = 2216
14³ + 19 = 2763
15³ + 19 = 3394
16³ + 19 = 4115

57) Answer
51² + 2 = 2601 + 2 = 2603
53² + 4 = 2809 + 4 = 2813
55² + 6 = 3025 + 6 = 3031
57² + 8 = 3249 + 8 = 3257
59² + 10 = 3481 + 10 = 3491
61² + 12 = 3721 + 12 = 3733
Page | 40
 58) Answer
12³ * 2 +1 = 1728 * 2 +1 = 3457
10³ * 2 + 1 = 1000 * 2 +1 = 2001
8³ * 2 + 1 = 512* 2 +1 = 1025
6³ * 2 + 1 = 216 * 2 +1 = 433
4³ * 2 + 1 = 64 * 2 +1 = 129
2³ * 2 + 1 = 8 * 2 +1 = 17

59) Answer
9 * 5 – 5 = 45 – 5 = 40
40 * 5 – 5 = 200 – 5 = 195
195 * 5 – 5 = 975 – 5 = 970
970 * 5 – 5 =4850 – 5 = 4845
4845 * 5 – 5 = 24225 – 5 = 24220

60) Answer
2*2+1=5
5*2–2=8
8 * 2 + 3 = 19
19 * 2 - 4 = 34
34* 2 + 5 = 73

61) Answer
From (I)
x² + 11x = - 28
x² + 7x + 4x + 28 = 0
(x + 7) (x + 4) = 0
x = -7, -4
From (II)
y² + 19y – 92 = 0
Page | 41
 y² + 23y – 4y - 92 = 0
(y + 23) (y - 4) = 0
y = -23, 4
Thus, x=y or no relationship can be established

62) Answer
From (I)
x² + 29x + 2x + 58 = 0
(x + 29) (x + 2) = 0
x = -29, -2
From (II)
y² - 9y – 4y + 36 = 0
(y - 9) (y - 4) = 0
y = 9, 4
Thus, x < y

63) Answer
From (I)
5x² + 18x = 35
5x² - 7x + 25x - 35 = 0
x (5x – 7) + 5(5x – 7) = 0
(5x – 7) (x + 5) = 0
x = + 7/5, - 5
From (II)
2y² + 21y + 55 = 0
2y² + 10y + 11y + 55 = 0
2y (y + 5) +11(y + 5) = 0
y = – 5, – 11/2
Thus, x ≥ y

64) Answer
From (I)
Page | 42
 2x² + 31x - 51 = 0
2x² + 34x – 3x – 51 = 0
2x(x + 17) – 3(x + 17) = 0
x = - 17, 3/2
From (II)
y² - 40y + 144 = 0
y² - 36y – 4y + 144 = 0
(y – 36) (y – 4) = 0
y = 36, 4
Thus, x<y

65) Answer
From (I)
2x² - 6x – 80 = 0
2x² - 16x + 10x - 80 = 0
2x(x - 8) + 10(x - 8) = 0
x = 8, - 5
From (II)
3y² - 54y + 240 = 0
3y² - 24y – 30y + 240 = 0
3y(y - 8) - 30(y - 8) = 0
(3y – 30) (y - 8) = 0
y = 8, 10
Thus, x≤y

66) Answer
From (I)
x² - 31x +198 =0
x² - 22x - 9x + 198 = 0
(x - 22) (x - 9) = 0
x = 22, 9
From (II)
Page | 43
 y² + 35y + 124 = 0
y² + 31y + 4y +124 = 0
(y + 31) (y + 4) = 0
y = -31, -4
Thus, x > y

67) Answer
From (I)
x² + 57x - 2x - 114 = 0
(x + 57) (x - 2) = 0
x = -57, 2
From (II)
y² - 15y + 11y - 165 = 0
(y - 15) ( y + 11) = 0
y = 15, -11
Thus, x=y or no relationship can be established

68) Answer
From (I)
x² - 19x - 17x + 323 = 0
(x - 19) (x - 17) = 0
x = 19, 17
From (II)
y² - 13y +7y - 91 = 0
(y - 13) (y + 7) = 0
y = 13, -7
Thus, x > y

69) Answer
From (I)
x² + 48x – 153 = 0
x² + 51x – 3x - 153 = 0
Page | 44
 (x + 51) (x - 3) = 0
x = -51, 3
From (II)
y² - 23y +132 = 0
y² - 11y – 12y + 28 = 0
(y - 11) (y - 12) = 0
y = 11, 12
Thus, x < y

70) Answer
From (I)
x² - 37x - 4x + 148 = 0
(x - 37) (x - 4) = 0
x = 37, 4
From (II)
y² + 29y - 9y - 261 = 0
(y + 29) (y - 9) = 0
y = -29, 9
Thus, x=y or no relationship can be established

71) Answer
From (I)
x² − 4x − 96 = 0
x² − 12x + 8x – 96 = 0
(x −12) (x + 8) = 0
x = 12, − 8
From (II)
y² + 7y – 60 = 0
y² +12y − 5y – 60 = 0
y(y + 12) − 5(y + 12) = 0
(y + 12) (y − 5) = 0
y = − 12, 5
Page | 45
 Thus, no relationship can be established

72) Answer
From (I)
x² + x − 56= 0
x² − 7x + 8x – 56 = 0
x(x − 7) + 8(x − 7) = 0
x = 7, − 8
From (II)
y² − 17y + 70 = 0
y² − 7y − 10y + 70 = 0
y(y − 7) − 10(y − 7) = 0
(y − 7) (y − 10) = 0
y = 7, 10
Thus, x ≤ y

73) Answer
From (I)
x² − 19x + 78 = 0
x² − 13x − 6x + 78 = 0
x(x − 13) − 6(x − 13) = 0
(x − 13) (x − 6) = 0
x = 13, 6
From (II)
y² − 25 = 0
y² = 25
y = ±5
Thus, x > y

74) Answer
From (I)
x² + 9x − 22 = 0
Page | 46
 x² + 11x − 2x – 22 = 0
x(x + 11) − 2(x + 11) = 0
(x + 11) (x − 2) = 0
x = − 11, 2
From (II)
y² − 11y + 24 = 0
y² − 3y − 8y + 24 = 0
y(y − 3)− 8(y − 3) = 0
(y − 3) (y − 8) = 0
y = 3, 8
Thus, x < y

75) Answer
(I) * 2 ----> 4x + 6y = 26
(II) --------> 8x − 6y = 4
12x = 30
x = 5/2
Substitute x = 5/2 in (I)
2(5/2) + 3y = 13
5 + 3y = 13
3y = 8
y = 8/3
Thus x < y

76) Answer
Quantity I:
(5/8) + (5/6) - (3/4) + (1/3) - (7/10)
(15*5 + 20*5 - 30*3 + 40 - 12*7)/120
= (75 + 100 – 90 + 40 - 84)/120 = 41/120
Quantity II:
(5/12) - (11/14) + (9/15) - (1/12)
(35*5 - 11*30 + 28*9 - 35)/420
Page | 47
 = (175 – 330 + 252 - 35)/420 = 62/420
Quantity I > Quantity II

77) Answer
44 - (31*x) + (2/5)*375 – 48 = 22
44 – (31*x) + 150 – 48 = 22
44 + 150 – 48 – 22 = (31*x)
124 = (31*x)
X = 124/31 = 4
(53/800)*9600 + ((1425/25)/3) = 127 + y
636 + 19 – 127 = y
y = 528
Now,
528 – 43 = 528 – 64 = 464

78) Answer
55 % of 200 + 85% of 140 + x = 160 % of 240
110 + 119 + x = 384
x = 155 (y ÷ 133) * (√361 ÷ 357) = (12 ÷ y) * (1 /√289)
y / 7 * (1/357) = (12/y) * (1/17)
y2 = 1764
y = 42
√(2x – 3y - 15)
√(155*2 – 3*42 – 15)
√169
13

79) Answer
88.88 % of 387 + 14.28 % of 280 = x + 23 * 8
8/9 * 387 + (1/7) * 280 = x + 184
344 + 40 = x + 184
x = 200 60% of 740 + 98% of 1200 - √784 % of 800 =y
Page | 48
 444 + 1176 – 224 =y
1396=y Now,
(2y - 7x)
2792 – 1400
1392

80) Answer
249.87*24.83 + x² * 119.81 + 16.11*14.13 = 14153.91
250*25 + x² * 120 + 16*14 = 14154
6250 + x²*120 + 224 = 14154
6474 + x²*120 = 14154
x² *120 = 7680
x² = 64
x=8
89.71% of 199.83 + 75.11% of 559.97 – 190.19 = y
90 % of 200 + 75 % of 560 – 190 = y
180 + 420 – 190 = y
410 = y Now,
(410+30)/8 = 55

81) Answer
59.73% of 359.86 + 30.13% of 239.81 – 24.87% of 399.93 = x
60% × 360 + 30% × 240 – 25% × 400 =x
(60/100) × 360 + (30/100) × 240 – (25/100) × 400 =x
216 + 72 – 100 =x
x = 188
(1234.83 ÷ 18.91) * (434.17 ÷ √960) = y * 12.98
(1235 ÷ 19) * (434 ÷ √961) = y * 13
65 * 14 = y * 13
y = 70
Now,
188 – 70 = 118
Page | 49
 82) Answer
79.88% of 239.81 + 24.93% of 144.11 – 39.87% of 219.97 = x
80 % of 240 + 25 % of 144 – 40 % of 220 = x
192 + 36 – 88 = x
x = 140
15.91% of 349.81 + 27.99% of 124.83 – 455.93 ÷ 19.11 = y
16% of 350 + 28% of 125 – 456 ÷ 19 = y
56 + 35 – 24 = y
y = 67
Now,
140/2 – 67 = 70 – 67 = 3

83) Answer
61.89% of 300.11 + 130.97 = x % of 79.88 + 111.99
62% of 300 + 131 = x % of 80 + 112
186 + 131 – 121 = x * 80/100
x = 245
59.81% of 44.93% of 400.11 + (2/7) of 104.83 = y
60% of 45% of 400 + (2/7) of 105 = y
108 + 30 = y
y = 138
Now,
(245 – 138) = 107

84) Answer
44.98% of 239.81 – 23.86% of 549.87 = x - √1445
45% of 240 – 24% of 550 = x - √1444
-24 + 38 = x
x = 14
√170 * √63 - √730 * √145 = √3026 * 1.97 – y
√169 * √64 - √729 * √144 = √3025 * 2 – y
Page | 50
 104 – 324 = 110 – y
y = 330
Now,
((8*14 – 330/6) – 12)2 = 45*45 = 2025

85) Answer
14.182 × 6.81 of 29.87% of 839.98 ÷ 20.83 = x × 783.87
142 × 7 of 30% of 840 ÷ 21 = x × 784
196 × 7 × 30/100 × 840/21 = x × 784
x = 21
36.13% of 349.81 + (575.78 ÷ (479.93 ÷ 11.97)) * 4.83 = y
36 % of 350 + (576 ÷ (480 ÷ 12)) * 5 = y
126 + (576 / 40) * 5 = y
126 + 72 = y
y = 198
Now,
(y - 14)/(x + 2)
(198 - 14)/(21 +2)
184/23 = 8

86) Answer
5x + 2y + 3z = 128 ---------- equation 1
2x – 7y + 4z = - 35 ---------- equation 2
6x – 4y – 6z = - 48 ---------- equation 3
Divided by 2 in Equation 3
3x – 2y – 3z = - 24 ---------- equation 4
After solving equations 1 and 4, we get
x = 13
Substitute x = 13 in equation 1 and equation 2,
We get,
2y + 3z = 63 ------------- equation 5
-7y + 4z = - 61 ------------- equation 6
Page | 51
 After solving equations 5 and 6
y = 15
Substitute y = 15 in equation 5, we get
z = 11
= 13 < 15 > 11
=x<y>z

87) Answer
³√27x² - √1156x + (7 * 13) = 0
3x² - 34x + 91 = 0
3x² - 13x – 21x + 91 = 0
x (3x – 13) – 7(3x – 13) = 0
(x – 7) (3x – 13) = 0
x = 7, 13/3
From(II)
2y² - 37y + (5³ + 18) = 0
2y² - 37y + (125 + 18) = 0
2y² - 37y + 143 = 0
2y² - 11y – 26y + 143 = 0
y (2y – 11) – 13(2y – 11) = 0
(y – 13) (2y – 11) = 0
y = 13, 11/2
The larger roots of equation I and II = 7, 13
Option a)
p² - 20p + 91 = 0
p² - 13p – 7p + 91 = 0
p (p – 13) – 7 (p – 13) = 0
(p – 7) (p – 13) = 0
p = 7,13

88) Answer
x² − 40x + 399 = 0
Page | 52
 x² − 21x – 19x + 399 = 0
x(x – 21) – 19(x – 21) = 0
(x – 21) (x – 19) = 0
The roots are 21 and 19
Larger root = a = 21
Smaller root = b = 19
(i) Subtract 11 from ‘a’ and then substitute the resultant number as x
in the LHS of the equation to get the value of ‘m’.
a – 11 = 21 – 11 = 10
LHS of equation ‘x² − 40x + 399 = 0’
10² − 40 * 10 + 399 = 99
So, m = 99
(ii) Add 1 to ‘b’ and then substitute the resultant number as x in the
LHS of the equation to get value of ‘n’.
b + 1 = 19 + 1 = 20
LHS of equation ‘x² − 40x + 399 = 0’
20² − 40 * 20 + 399 = -1
So, n = − 1
m – n = 99 – (− 1) = 100

89) Answer
x² − x − 870 = 0
x² − 30x + 29x − 870 = 0
x(x – 30) + 29(x – 30) = 0
(x – 30) (x + 29) = 0
The roots are 30 and − 29
Larger root = a = 30
Smaller root = b = − 29
(i) Subtract 12 from ‘a’ and put the resultant number in LHS of
equation to get value of ‘m’
a – 12 = 30 – 12 = 18
LHS of equation ‘x² − x − 870 = 0’
Page | 53
 18² − 18 − 870 = − 564
So, m = − 564
(ii) Add 4 to ‘b’ and put the resultant number in LHS of equation to get
value of ‘n’
b + 4 = − 29 + 4 = − 25
LHS of equation ‘x² − x − 870 = 0’
25² − (−25) − 870 = − 220
So, n = − 220
Let
m + n = − 564 – 220 = − 784

90) Answer
A. x² + 6x – 315 = 0
x² - 15x + 21x - 315 = 0
x (x – 15) + 21 (x – 15) = 0
(x + 21) (x – 15) = 0
x = -21 (or) x = 15
So, none of the options - follows
B. y² - 11y – 350 = 0
y² + 14y – 25y – 350 = 0
y (y + 14) – 25(y + 14) = 0
(y – 25) (y + 14) = 0
y = 25 (or) y = -14
So, (F) One of the roots is the square of a prime number - follows
C. z² - 49z + 580 = 0
z² - 29z – 20z + 580 = 0
z (z – 29) – 20 (z – 29) = 0
(z – 20) (z – 29) = 0
z = 20 (or) z = 29
So, (D) Sum of the roots is the square of a number - follows

91) Answer
Page | 54
 A. 3x² + 7x – 20 = 0
3x² + 12x – 5x – 20 = 0
3x (x + 4) – 5(x + 4) = 0
(3x – 5) (x + 4) = 0
x = 5/3 (or) x = - 4
So, none of the options follows
B. 2y² - 17y + 35 = 0
2y² - 10y – 7y + 35 = 0
2y (y – 5) – 7(y – 5) = 0
(2y – 7) (y – 5) = 0
y = 7/2 (or) y = 5
So, (D) one of the roots is a prime number - follows
C. z² - 5z – 36 = 0
z² - 9z + 4z – 36 = 0
z (z – 9) + 4 (z – 9) = 0
(z + 4) (z – 9) = 0
z = -4 (or) z = 9
So, (E) Difference between the square of one of the roots and 35 is 46
– follows

92) Answer
To find ‘a’:
2x² - 10x + 8 = 0
2x² - 8x – 2x + 8 = 0
2x (x – 4) – 2 (x – 4) = 0
(2x – 2) (x – 4) = 0
x = 1 (or) x = 4
a = (1 + 4)² = 5²
a = 25
To find ‘b’:
3x² - 22x + 35 = 2x² - 10x
x² - 12x + 35 = 0
Page | 55
 x² - 7x – 5x + 35 = 0
x (x – 7) – 5 (x – 7) = 0
(x – 5) (x – 7) = 0
x = 5 (or) x = 7
b = 7² - 5² = 49 – 25
b = 24
So, a > b

93) Answer
From I
x² - ax + (b – 3) = 0
Substituting one of the root values of 4 in place of x
4² - 4a + b – 3 = 0
4a – b = 13 ---------- (1)
From II
y² - (a + 1) y + b = 0
Substituting one of the root values 5 in place of y
5² - (a + 1) * 5 + b = 0
25 – 5a – 5 + b = 0
5a – b = 20 ------------ (2)
Solving equations (1) and (2), we get
a = 7, b = 15
Substituting the values of a and b in I
x² - ax + (b – 3) = 0
x² - 7x + (15 – 3) = 0
x² - 7x + 12 = 0
x² - 3x – 4x + 12 = 0
x (x – 3) – 4 (x – 3) = 0
(x – 3) (x – 4) = 0
x = 3 (or) x = 4
So, the value of p = 3
From III
Page | 56
 z² - 10z + 21 = 0
z² - 7z – 3z + 21 = 0
z (z – 7) – 3 (z – 7) = 0
(z – 3) (z – 7) = 0
z = 3 (or) z = 7
By checking Statement 1
One of the roots of III is equal to the value of p
Roots of III = 3, 7
Value of p = 3
So, the statement I follows
By checking Statement II
The product of the roots of II is less than the product of the roots of III
Roots of II = 5, 3
Product of the roots of II = 15
Roots of III = 3, 7
Product of the roots of III = 21
So, Statement II follows
Option 3
One of the roots of III is greater than (b – a)
Roots of III = 3, 7
(b – a) = 15 – 7 = 8
So, statement 3 does not follows
Hence, Statement 1 and 2 follows

94) Answer
2 10 34 106 322 970
*3+4 *3+4 *3+4 *3+4 *3+4
Wrong = 30
30 94 286 862 2590
*3+4 *3+4 *3+4 *3+4

Page | 57
 95) Answer
8 10 17 31 54 88
1²+1 2²+3 3²+5 4²+7 5²+9
X = 54
34 36 43 (57) 80
1²+1 2²+3 3²+5 4²+7
a = 34, d = 80
a+d = 34 + 80 = 114

96) Answer
From Series I
(25 * 1) + 7 = 32
(32 * 2) + 7 = 71
(71 * 3) + 7 = 220
(220 * 4) + 7 = 887
(887 * 5) + 7 = 4442
Thus x = 887
From Series II
(20 * 5) + 2 = 102
(102 * 4) + 3 = 411
(411 *3) + 5 = 1238
(1238 * 2) + 7 = 2483
(2483 * 1) + 11 = 2494
Thus y = 2494
Required value = 887 + [(2494 / 2) + 13]/12 = 887 +105 = 992

97) Answer
From Series I
(20 - 1) * 1 = 19
(19 - 2) * 2 = 17 * 2 = 34
(34 - 3) * 3 = 31 * 3 = 93
(93 - 4) * 4 = 89 * 4 = 356
Page | 58
 (356 - 5) * 5 = 351 * 5 = 1755
Thus, x = 20
From Series II
10 * 1.5 = 15
15 * 2 = 30
30 * 2.5 = 75
75 * 3 = 225
225 * 3.5 = 787.5
Thus, y = 787.5
Required value = {(20)² + (2 * 787.5) - 75} / 4 = (400 + 1575 - 75) /
4 = 1900 / 4 = 475

98) Answer
243 81 54 54 72 120
*1/3 *2/3 *3/3 *4/3 *5/3
70 71 67 76 60 85
+1² -2² +3² -4² +5²
80 40 40 60 120 300
*0.5 *1 *1.5 *2 *2.5
x = 70
y = 85
z = 45
x<y>z

99) Answer
Series I:
500 379 265 164 82 29 13
121 114 101 82 53 16
7 13 19 29 37
Thus, the missing term is 29
Series II:
368 577 773 954 1118 1263
Page | 59
 209 196 181 164 145
13 15 17 19
Thus, the missing term is 368
(i) J is a prime number but W is not a prime number.
(ii) Any one of J and W is neither a perfect square nor a perfect cube.
(iii) the value of W is 368
So, the (i) and (ii) options are false.

100) Answer
Series I:
128 64 96 240 840 3780
*0.5 *1.5 *2.5 *3.5 *4.5
T + 2756 = 3780
T = 1024
329 + 3² = 338
338 - 7² = 289
289 + 13² = 458
458 - 19² = 97
97 + 29² = 938
W + 114 = 338
W = 224
i) the LCM of 1024 and 224 is 7168 is correct.
ii) difference of these two terms = 1024-224 = 800 so it is wrong
iii) sum of these two terms 1024+224 = 1248 is divisible by 12 is
correct.
Both 1 and 3 is correct.

Page | 60
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