281 EQUATION - 197notesbag.com/wp-content/uploads/2018/01/Quadractic...33. I. 6x + 7y = 52 II. 14x +...
Transcript of 281 EQUATION - 197notesbag.com/wp-content/uploads/2018/01/Quadractic...33. I. 6x + 7y = 52 II. 14x +...
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EQUATION - 197Directions (Q. 1-5): Two equations (I) and (II) are given in each question. On the basis of these
equations you have to decide the relation between ‘x’ and ‘y’ and give answer.(1) if x > y (2) if x < y (3) if x y(4) if x y (5) if x = y or no relation can be established between ‘x’ and ‘y’.
1. I. 6x2 - 19x + 15 = 0 II. 10y2 - 29y + 21 = 02. I. 12x2 + 11x - 56 = 0 II. 4y2 - 15y + 14 = 03. I. 3x2 + 13x + 12 = 0 II. y2 + 9y + 20 = 04. I. 8x2 - 15x + 7 = 0 II. 2y2 - 7y + 6 = 05. I. 7x - 3y = 13 II. 5x + 4y = 40
Directions (Q. 6-10): In the following questions, two equations numbered I and II are given.You have to solve both the equations and give answer
(1) if x > y (2) if x < y (3) if x y(4) if x y (5) if x = y or no relation can be established between x and
6. I. 2x2 - 11x + 15 = 0 II. 21y2 - 23y + 6 = 07. I. 5x2 - 16x + 11= 0 II. 5y2 - 3y - 2 = 08. I. x2 + 11x + 28 = 0 II. 2y2 + 13y + 20 = 09. I. 6x2 + 29x + 35 = 0 II. 3y2 + 19y + 30 = 010. I. 2x + 5y = 6 II. 5x + 11y = 9
Directions (Q. Nos. 11-15) In the following questions two equations numbered I and II aregiven. You have to solve both the equations and—
Give answer(1) if x > y (2) if x > y (3) if x < y(4) if x < y (5) if x = y or the relationship cannot be established
11. I. 1225x 4900 0 II. (81)1/4 y + (343)1/3 = 0
12. I. 2 2 218 6 12 8
xx x x II. y3 + 9.68 + 5.64 = 16.95
13. I.5 3
3(2) (11) x6
II. 4y3 = - (589 4) + 5y3
14. I. 12x2 + llx + 12 = 10x2+22x II. 13y2 - 18y + 3 = 9y2 - 10y15. I. (x7/5 9) = 169 y3/5 II. y1/4 y1/4 7 = 273 y1/2
Directions (Q. 16 - 20): Two equations (I) and (II) are given in each question. On the basis ofthese equations you have to decide the relation between x and y and give answer
(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y, or no relation can be established between x and y.
16. I. x = 4 2401 II. 2y2 - 9y - 56 = 0
17. I. 5x2 + 3x - 14 = 0 II. 2y2 - 9y + 10 = 018. I. 8x2 + 31x + 21 = 0 II. 5y2 + 11y - 36 = 0
19. I. 3x - y = 12 II. y = 108920. I. 15x2 + 68x + 77 = 0 II. 3y2 + 29y + 68 = 0
Directions (Q. 21-25): Two equations (I) and (II) are given in each question. On the basis ofthese equations, you have to decide the relation between x and y and give answer
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(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y, or no relation can be established between x and y.
21. I. 2x2 + x - 1 = 0 II. 6y2 - 13y + 5 = 022. I. 21x2 - 122x + 165 = 0 II. 3y2 - 2y - 33 = 023. I. 5x2 - 29x + 36 = 0 II. 10y2 - 3y - 27 = 024. I. 7x + 4y = 3 II. 5x + 3y = 325. I. 7x2 - 54x + 99 = 0 II. 4y2 - 16y + 15 = 0
Directions (Q. 26-30): Two equations (I) and (II) are given in each question. On the basis ofthese equations, you have to decide the relation between x and y and give answer
(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y, or no relation can be established between x and y.
26. I. 5x2 - 87x + 378 = 0 II. 3y2 - 49y + 200 = 027. I. 10x2 - x - 24 = 0 II. y2 - 2y = 028. I. x2 - 5x + 6 = 0 II. 2y2 - 15y + 27 = 029. I. 3x + 2y = 301 II. 7x - 5y = 7430. I. 14x2 - 37x + 24 = 0 II. 28y2 - 53y + 24 = 0
Directions (Q. 31-35): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or relationship between x and y cannot be established
31. I. 11x + 5y = 117 II. 7x + 13y = 15332. I. 6x2 + 51x + 105 = 0 II. 2y2 + 25y + 78 = 033. I. 6x + 7y = 52 II. 14x + 4y = 3534. I. x2 + 11x + 30 = 0 II. y2 + 12y + 36 = 035. I. 2x2 + x - 1 = 0 II. 2y2 - 3y + l = 0
Directions (Q.36-40) In the following questions three equations numbered I, II and III aregiven. You have to solve all the equations either together or separately, or two together and oneseparately, or by any other method and give answer If
(1) x < y = z (2) x < y < z (3) x < y > z (4) x = y > z(5) x = y = z or if none of the above relationship is established
36. I. 7x + 6y + 4z = 122 II. 4x + 5y + 3z = 88 III. 9x + 2y + z = 7837. I. 7x + 6y =110 II. 4x + 3y = 59 III. x + z = 15
38. I. x = 1/2 1/4(36) (1296) II. 2y + 3z = 33 III. 6y + 5z = 71
39. I. 8x + 7y= 135 II. 5x + 6y = 99 III. 9y + 8z = 12140. I. (x + y) 3= 1331 II. x - y + z = 0 III. xy = 28
Directions (Q. 41-45): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or relationship between x and y cannot be established
41. I. 7x2 - 9x + 2 = 0 II. y2 - 4y + 3 = 042. I. x2 = 64 II. 2y2 + 25y + 72 = 043. I. x2 + x - 20 = 0 II. 2y2 - 19y + 45 = 044. I. 7x + 3y = 26 II. 2x + 17y = -4145. I. 3x2 - 20x + 33 = 0 II. 2y2 - 11y + 15 = 0
Directions (Q. 46-50): In each of these questions, two equations (I) and (II) are given. You
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have to solve both the equations and give answer(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or relationship between x and y cannot be established.
46. I. 4x2 - 43x + 105 = 0 II. 7y2 - 29y + 30 = 047. I. x2 + 13x + 40 = 0 II. y2 + 7y + 10 = 0
48. I. 3x 2197 II. 2y2 - 54y + 364 = 0
49. I. 5x2 - 27x + 36 = 0 II. y2 - 2y + 2 = 050. I. 13x - 8y + 81 = 0 II. 15x + 5y + 65 = 0
Directions (Q. 51-55): Two equations (I) and (II) are given in each question. On the basis ofthese equations, you have to decide the relation between x and y and give answer
(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y, or no relation can be established between x and y.
51. I. 15x2 - 19x + 6 = 0 II. 6y2 - 5y + 1 = 0
52. I. x 172 II. y2 - 29y + 210 = 053. I. 3x2 - 20x + 32 = 0 II. 2y2 - 19y + 44 = 054. I. 3x + 8y = -2 II. 4x + 18y = l55. I. 2x2 - 15x + 28 = 0 II. 10y2 - y - 119 = 0
Directions (Q. 56-70): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or relationship between x and y cannot be established.
56. I. 676x2 - l = 0 II. 3
1y13824
57. I. 8x + 13y = 62 II 13x - 17y + 128 = 058. I. 7x2 + 2x = 120 II. y2 + 11y + 30 = 059. I. x2 = 7x II. (y + 7)2 = 060. I. 2x2 + 5x - 33 = 0 II. y2 - y - 6 = 0
Directions (Q. 61-65): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or the relationship between x and y cannot be established.
61. I. x2 + 12x + 36 = 0 II. y2 + 15y + 56 = 062. I. x2 = 35 II. y2 + 13y + 42 = 063. I. 2x2 - 3x - 35 = 0 II. y2 - 7y + 6 = 064. I. 6x2 - 29x + 35 = 0 II. 2y2 - 19y + 35 = 065. I. 12x2 - 47x + 40 = 0 II. 4y2 + 3y - 10 = 0
Directions (Q. 66-70): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between ‘x’ and ‘y’.
66. I. x2 + 3x - 28 = 0 II. y2 - 11y + 28 = 067. I. 6x2 - 17x + 12 = 0 II. 6y2 - 7y + 2 = 0
68. I.256x576
II. 3y2 + y-2 = 0
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69. I. x2 = 64 II. y2 = 9y70. I. x2 + 6x - 7 = 0 II. 41y + 17 = 140
Directions (Q. 71-75): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or a relationship between x and y cannot be established.
71. I. x2 + 3x = 28 II. y2 + 16y + 63 = 0
72. I. x = 3 2197 II. y2 = 169
73. I. 8x2 - 49x + 45 = 0 II. 8y2 - y - 9 = 074. I. 42x - 17y = -67 II. 7x + 12y = -2675. I. x2 - 8x + 15 = 0 II. 2y2 - 21y + 55 = 0
Directions (Q. 76-80): In each of these questions two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if p > q (2) if p q (3) if p < q (4) if p q(5) if p = q or no relation can be established between p and q.
76. I. 2.3p - 20.01 = 0 II. 2.9q - p = 0
77. I. p = 1764 II. q2 = 1764
78. I. p2 - 26p + 168 = 0 II. q2 - 25q + 156 = 079. I. p2 - 13p + 42 = 0 II. q2 + q - 42 = 080. I. 6p - 5q = -47 II. 5p + 3q = 11
Directions(Q. 81-85): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between ‘x’ and ‘y’.
81. I. 2x2 + 13x - 7 = 0 II. 2y2 - 5y + 3 = 082. I. 2x2-15x + 28 = 0 II. 4y2 - 16y + 15 = 083. I. x2 + 8x + 16 = 0 II. y2 = 1684. I. x2 - 2x - 24 = 0 II. y2 + 8y = 0
85. I. x2 + 4x = 0 II. y2 + 10y + 25 = 0
Directions (Q. 86-90): In each of these questions two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y
86. I. 2x2 + x – 1 = 0 II. 2y2 + 13y + 15 = 087. I. x2 + 12x + 32 = 0 II. 2y2 + 15y + 27 = 088. I. 6x2 – 17x + 12 = 0 II. 7y2 – 13y + 6 = 089. I. x2 – 82x + 781 = 0 II. y2 = 504190. I. 6x2 – 47x + 80 = 0 II. 2y2 – 9y + 10 = 0
Directions (Q. 91-95): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation between ‘x’ and ‘y’ can be established.
91. I. 3x2 – 7x – 20 = 0 II. y2 – 8y + 16 = 092. I. x2 – 72 = 0 II. y2 – 9y + 8 = 093. I. 9x2 – 114x + 361 = 0 II. y2 = 3694. I. 13x + 17y = 107 II. x – 11y = – 41
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95. I. 9x2 + 18x + 9 = 0 II. y2 – 3y + 2 = 0Directions (Q. 96-100) : In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and give answer .(l) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between ‘x’ and y.
96. I. 4x + 7y = 42 II. 3x - 11y = – l97. I. 9x2 – 29x + 22 = 0 II. y2 – 7y + 12 = 098. I. 3x2 – 4x – 32 = 0 II. 2y2 – 17y + 36 = 099. I. 3x2 – 19x – 14 = 0 II. 2y2 + 5y + 3 = 0100. I. x2 + 14x + 49 = 0 II. y2 + 9y = 0
Directions (Q. 101-105): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer ,
(1) if x < y (2) if x y(3) if x = y, or no relation can be established between x and y(4) if x > y (5) if x y
101. I. 9x2 = 1 II. 4y2 + 11y - 3 = 0102. I. 3x2 + 5x - 2 = 0 II. 2y2 - 7y + 5 = 0103. I. 6x2 + 13x + 5 = 0 II. 3y2 + 11y + 10 = 0104. I. 7x - 4y = 29 II. 5x + 3y - 50 = 0105. I. x2 - 5 = 0 II. 4y2 - 24y + 35 = 0
Directions (Q. 106-110) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y
106. I. 35x2 - 53x + 20 = 0 II. 56y2-97y + 42 = 0107. I. x = 3 4913 II. 13y + 3x = 246108. I. x2 - 5x - 14 = 0 II. y2 + 7y + 10 = 0109. I. x2 - 3481 = 0 II. 3y2 = 3 216000110. I. 5x2 + 2x - 3 = 0 II. 2y2 + 7y + 6 = 0
Directions (Q. 111-115) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relationship can be established.
111. I. 20x2 - 67x + 56 = 0 II. 56y2 - 67y + 20 = 0112. I. x4 = 65536 II. y = 3 4096113. I. 2x2 + 11x - 40 = 0 II. 4y2 - 27y + 44 = 0114. I. 7x = 4y + 85 II. y = 3 17576
115. I. x2 = 14641 II. y = 14641Directions (Q. 116-120): In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and give answer(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or if there is no relation between ‘x’ and ‘y’.
116. I. x2 + 42 = 13x II. 4y 1296
117. I. x2 + x - 2 = 0 II. y2 + 7y + 12 = 0118. I. 3x2 - 23x + 40 = 0 II. 2y2 - 23y + 66 = 0119. I. 15x2 - 46x + 35 = 0 II. 4y2 - 15y + 14 = 0120. I. x2 + 5x - 6 = 0 II. 2y2 - 11y + 15 = 0
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Directions (Q. 121-125) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or If there is no relation between ‘x’ and ‘y’.
121. I. 2x2 – 21x + 54 = 0 II. y2 – 14y + 49 = 0122. I. x2 – 19x + 70 = 0 II.2y2 – 17y + 35 = 0123. I. 3x2 + 5x – 8 = 0 II. y2 – 4y + 3=0124. I. 12x2 – 16x + 5 = 0 II. 18y2 – 45y + 25 = 0125. I. 3x2 + 11x + 8 = 0 II. 3y2 + 20y + 32 = 0
Directions (Q. 126-130) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(l) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relationship can be established between ‘x’ and ‘y’.
126. I. x = 3 357911 II. y = 5041127. I. 5x + 7y = -43 II. 9x – 17y = 41128. I. x2 + 11x + 30 = 0 II. y2 + 9y + 20 = 0129. I. 4x2 + 3x – l = 0 II. 6y2 – 5y + l = 0130. I. 3x2 + 15x + 18 = 0 II. 2y2 + 15y + 27 = 0
Directions (Q. 131-135) : In the following questions, two equations numbered I and H aregiven. You have to solve both the equations and give answer—
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or relationship cannot be established
131. I. 4x + 3y = (1600)1/2 II. 6x – 5y = (484)1/2
132. I. 22x (4 13)x 2 13 0 II. 210y (18 5 13)y 9 13 0
133. I. (6x2 + l7) – (3x2 + 20) = 0 II. (5y2 – 12) – (9y2 – 16) = 0
134. I. 1/2(169) x 289 134 II. 1/2 2(361) y 270 1269
135. I. 82lx2 – 757x2 = 256 II. 3 3196 y 12y 16
Directions (Q. 136-140) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(l) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y.
136. I. 5x - 7y = -24 II. 13x + 3y = 86137. I. x2 - 13x + 40 = 0 II. y2 + 3y - 40 = 0138. I. 8x2 - 26x+15 = 0 II. 2y2 - 17y + 30 = 0139. I. x2 = 484 II. y2 - 45y + 506 = 0
140. I. 13x - 21=200 - 4x II. y = 3 2197Directions (Q. 141-145) : In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and give answer(1) if p > q (2) if p q (3) if p < q (4) if p q(5) if p = q or there is no relation between ‘p’ and ‘q’.
141. I. (p + q) 2 = 3136 II. q + 2513 = 2569142. I. 4p2 - 16p +15 = 0 II. 2q2 + 5q - 7 = 0143. I. p2 = 49 II. q2 +15q + 56 = 0144. I. 2p2 + 5p - 12 = 0 II. 2q2 - q - 1 = 0145. I. p2 - 12p + 35 = 0 II. q2 - 25 = 0
Directions (Q. 146–150) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y or there is no relation between ‘x’ and ‘y’.
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146. I. 3x2 + 7x + 2 = 0 II. 2y2 + 9y + 10 = 0147. I. x2 + x – 2 = 0 II. y2 – 3y + 2 = 0148. I. 20x2 – 51x + 27 = 0 II. 15y2 – 16y + 4 = 0149. I. 7x2 + 16x – 15 = 0 II. y2 – 6y – 7 = 0150. I. x2 = 729 II. y2 + 58y + 840 = 0
Directions (Q. 151-155) : In the following questions two equations numbered I and II aregiven. You have to solve both the equations and give answer if
(l) x > y (2) x y (3) x < y (4) x y(5) x = y or the relationship between ‘x’ and ‘y’ cannot be established.
151. I.1215 9 (x)
x x II. y10 - (36)5 = 0
152. I. 5x + 2y = 96 II. 3(7x + 5y) = 489
153. I.1
2 22(441) x 111 (15) II. 2 3121y (6) 260
154. I. 17x = (13)2 + 196 + (5) 2 + 4x II. 9y - 345 = 4y - 260155. I. 3x2 - 13x + 14 = 0 II. y2 - 7y + 12 = 0
Directions (Q. 156-160) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y.
156. I. 2x2 – 15x + 28 = 0 II. 2y2 + 3y-35 = 0157. I. 7x – 5y = 24 II. 4x + 3y = 43
158. I. x = 3 2744 II. y = 487159. I. x2 – 9x + 8 = 0 II. 2y2 – 11y + 5 = 0160. I. 2x2 + 3x + 1 = 0 II. 6y2 + 17y + 12 = 0
Directions (Q. 161-165) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y.
161. I. 3x2 – 29x + 56 = 0 II. 3y2 – 5y – 8 = 0162. I. 5x2 + 26x – 24 = 0 II. 5y2 – 34y + 24 = 0163. I. x2 – 7x = 0 II. 2y2 + 5y + 3 = 0164. I. 7x – 4y = 40 II. 8x + 8y = 8165. I. 15x2 – 41x + 14 = 0 II. 2y2 – 13y + 20 = 0
Directions (Q. 166-170) : In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer “>
(1) if x > y (2) if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y.
166. I. 2x 8 3x 45 0 II. 2y 2y 24 0
167. I. x 7 2x 24 0 II. y 5 2y 12 0
168. I. 12x2 - 17x + 6 = 0 II. 20y2 - 31y + 12 = 0169. I. 3x2 - 8x + 4 = 0 II. 4y2 - 15y + 9 = 0170. I. x2 -16x + 63 = 0 II. y2 - 2y - 35 = 0
Directions (Q. 171-175): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x > y (2)if x y (3) if x < y (4) if x y(5) if x = y or no relation can be established between x and y.
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171. I. 63x 94 x 35 II. 32y 52 y 21 0
172. I. 2x 7 3x 35 15 5 5x II. 2y 5 5y 30 0173. I. 14x2 + 11x - 15 = 0 II. 20y2 - 31y + 12 = 0
174. I. 25x 16y 41 II. 16x 25y 40
175. I.
152
2
(18)x 0x
II.
92(19)y 0
y
Directions (Q. 176-180) : In each of these questions, two equations (I) and (II) are given.Solve both the equations and give answer
(1) if x > y (2) if x < y (3) if x y (4) if x y(5) if x = y or no relation can be established between ‘x’ and ‘y’.
176. I. 63x 194 x 143 0 II. 99y 255 y 150 0
177. I. 16x2 – 40x – 39 = 0 II. 12y2 – 113y + 255 = 0
178. I. x 7 3x 36 0 II. y 12 2y 70 0
179. I. 2x 7 7x 84 0 II. 2y 5 5y 30 0
180. I. 10x – 6y = 13 II. 45x + 24y = 56Directions (Q. 181-185) : In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and give answer(1) if x > y (2) if x y (3) if x < y (4) I x y(5) if x = y or no relation can be established between x and y.
181. I. x2 - 2x -15 = 0 II. y2 + 5y + 6 = 0182. I. x2 - x - 12 = 0 II. y2 - 3y + 2 = 0
183. I. x - 169 = 0 II. y2 - 169 = 0
184. I. x2 - 32 = 112 II. y - 256 = 0
185. I. x2 - 25 = 0 II. y2 - 9y + 20 = 0Directions (Q. 186-190): In the following questions, three equations numbered I, II and III
are given. You have to solve all the equations either together or separately, or two together andone separately or by any other method and give answer
(1) if x = y > z (2) if x < y = z (3) if x < y > z(4) if x = y = z or if none of the above relationship can be established. (5) if x y < z
186. I. 3x + 5y = 69 II. 9x + 4y = 108 III. x + z = 12
187. I.1 13 4y (729) (6541) II. 2x + 5z = 54 III. 6x + 4z = 74
188. I. 2x + 3y + 4z = 66 II. 2x + y + 3z = 42 III. 3x + 2y + 4z = 63189. I. (x + z)3 = 1728 II. 2x + 3y = 35 III. x - z = 2190. I. 4x + 5y = 37 II. x + z = 8 III. 7x + 3y = 36
Directions (Q. 191-194): In each of these questions, two equations (I) and (II) are given. Youhave to solve both the equations and give answer
(1) if x < y (2) if x y(3) if x = y or no relation can be established (4) if x > y (5) if x y
191. I. 7x + 3y = 77 II. 2x + 5y = (2601)12
192. I. 23x (6 17)x 2 17 0 II. 210y (18 5 17)y 9 17 0
289
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193. I.12(289) x 324 203 II.
12(484) y 225 183
194. I. 679x2 - 168x2 = 3066 II. 3 3144y 9y 1536
Directions (Q. 195-197): In the following questions two equations numbered I and II aregiven. Solve both the equations and give answer
(1) if x < y (2) if x y (3) if x y (4) if x > y(5) if x = y or no relationship can be established
195. I. 3x + 4y = (1681)12 II. 3x + 2y = (961)
12
196. I. 23x (6 17)x 2 17 0 II. 210y (15 17) 3 17 0
197. I. x2 - 16x + 63 = 0 II. y2 - 2y - 35 = 0
290
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SHORT ANSWER1. (3) 2. (4) 3. (1) 4. (2) 5. (2) 6. (1) 7. (3) 8. (4)9. (1) 10. (2) 11. (1) 12. (5) 13. (1) 14. (2) 15. (4) 16. (5)17. (2) 18. (5) 19. (2) 20. (1) 21. (4) 22. (5) 23. (3) 24. (2)25. (1) 26. (1) 27. (5) 28. (4) 29. (2) 30. (3) 31. (3) 32. (1)33. (3) 34. (2) 35. (4) 36. (1) 37. (3) 38. (2) 39. (4) 40. (5)41. (4) 42. (5) 43. (3) 44. (1) 45. (2) 46. (1) 47. (4) 48. (4)49. (1) 50. (3) 51. (1) 52. (2) 53. (4) 54. (2) 55. (3) 56. (3)57. (3) 58. (1) 59. (1) 60. (5) 61. (1) 62. (1) 63. (5) 64. (4)65. (2) 66. (4) 67. (1) 68. (2) 69. (5) 70. (3) 71. (2) 72. (2)73. (2) 74. (3) 75. (4) 76. (1) 77. (2) 78. (5) 79. (2) 80. (3)81. (3) 82. (1) 83. (4) 84. (5) 85. (1) 86. (1) 87. (5) 88. (1)89. (5) 90. (2) 91. (4) 92. (5) 93. (1) 94. (3) 95. (3) 96. (1)97. (3) 98. (4) 99. (1) 100. (5) 101. (3) 102. (1) 103. (5) 104. (4)105. (1) 106. (3) 107. (1) 108. (2) 109. (5) 110. (1) 111. (1) 112. (4)113. (3) 114. (1) 115. (4) 116. (2) 117. (1) 118. (3) 119. (3) 120. (3)121. (3) 122. (2) 123. (4) 124. (4) 125. (2) 126. (5) 127. (1) 128. (4)129. (3) 130. (2) 131. (1) 132. (2) 133. (5) 134. (2) 135. (4) 136. (3)137. (2) 138. (4) 139. (4) 140. (5) 141. (3) 142. (1) 143. (2) 144. (5)145. (2) 146. (3) 147. (4) 148. (1) 149. (5) 150. (1) 151. (2) 152. (1)153. (1) 154. (3) 155. (3) 156. (2) 157. (1) 158. (3) 159. (5) 160. (1)161. (2) 162. (4) 163. (1) 164. (1) 165. (3) 166. (5) 167. (2) 168. (4)169. (5) 170. (1) 171. (5) 172. (1) 173. (3) 174. (1) 175. (3) 176. (5)177. (2) 178. (2) 179. (1) 180. (2) 181. (2) 182. (5) 183. (2) 184. (3)185. (5) 186. (3) 187. (3) 188. (2) 189. (1) 190. (2) 191. (4) 192. (3)193. (4) 194. (1) 195. (4) 196. (5) 197. (2)
291
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01. 3; I. 6x2 - 9x - 10x + 15 = 0or, 3x(2x - 3) - 5(2x - 3) = 0or, (3x - 5) (2x - 3) = 0
5 3x ,3 2
II. 10y2 - 15y - 14y + 21 = 0or, 5y(2y - 3) - 7(2y - 3) = 0or, (5y - 7) (2y - 3) = 0
7 3y ,5 2
x y2. 4; I. 12x2 + 32x - 21x - 56 = 0
or, 4x(3x + 8) - 7(3x + 8) = 0or, (4x - 7) (3x + 8) = 0
7 8x ,4 3
II. 4y2 - 8y - 7y + 14 = 0or, 4y(y - 2) - 7(y - 2) = 0or, (4y - 7) (y - 2) = 0
7y 2,4
x y3. 1; I. 3x2 + 9x + 4x + 12 = 0
or, 3x(x + 3) + 4(x + 3) = 0or, (3x + 4) (x + 3) = 0
4x , 33
II. y2 + 5y + 4y + 20 = 0or, y(y + 5) + 4(y + 5) = 0or, (y + 4) (y + 5) = 0y = - 4, - 5 x > y
4. 2; I. 8x2 - 8x - 7x + 7 = 0or, 8x(x - 1) -7(x - 1) = 0or, (8x - 7) (x - 1) = 0
7x ,18
II. 2y2 - 4y - 3y + 6 = 0or, 2y(y - 2) -3(y - 2) = 0or, (y - 2) (2y - 3) = 0
3y 2,2
5. 2; Eqn (I) × 4 + Eqn (II) × 328x - 12y = 5215x + 12y = 12043x = 172 x = 4 and y = 5
x < y6. 1; I. 2x2 - 6x - 5x + 15 = 0
or,2x(x - 3) - 5(x - 3) = 0or, (2x - 5) (x - 3) = 0
5x 3,2
II. 21y2 - 14y - 9y + 6 = 0or,7y(3y - 2) - 3 (3y - 2) = 0or,(7y - 3)(3y - 2) = 0
3 2y ,7 3
x > y
7. 3; I. 5x2 - 5x - 11x + 11 = 0or,5x(x - 1) - 11(x - 1) = 0or,(x - 1) (5x - 11) = 0
x = 1,115 x > y
II. 5y2 - 5y + 2y - 2 = 0or, 5y (y - 1) + 2(y - 1) = 0or, (5y + 2)(y - 1) = 0
y = 1, - 25 x > y
8. 4; I. x2 + 4x + 7x + 28 = 0or, x(x + 4) +7(x + 7) = 0or, (x + 4) (x + 7) = 0 x = - 4, - 7II. 2y2 + 8y + 5y + 20 = 0or, 2y(y + 4) + 5(y + 4) = 0or, (y + 4) (2y + 5) = 0
y = -4,52
x < y
9. 1; I. 6x2 + 15x + 14x + 35 = 0or, 3x(2x + 5) + 7(2x + 5) = 0or,(3x + 7) (2x + 5) = 0
7 5x ,3 2
II. 3y2 + 9y + 10y + 30 = 0or, 3y(y + 3) +10(y + 3) = 0or,(3y + 10) (y + 3) = 0
10y 3,3
x > y
10. 2; eqn (I) × 5 - eqn (II) × 210x + 25y = 3010x ± 22y = 18- - - . 3y = 12 y = 4 and x = -7 y > x
11. 1; I. 1225x 4900 0
DETAIL - EXPLANATIONS
292
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
or, 35x + 70 = 0 or, x =70 235
II. 3y + 7 = 0 or y = 73
:. x > y
12. 5; I. 2 2
18 6x 12 8x x
or, x = 13 = .333
II. y2 = 16.95 - 9.68 - 5.64 = 1.63:. y = ±1.277
13. 1; I. 3 32 1331 1363x6 6
II. 5y3 - 4y3 = 5894
or y3 =5894 :. x > y
14. 2; I. 2x2 - llx + 12 = 0
or, x = 4, 32
II. 4y2 - 8y + 3 = 0
3 1y ,2 2
:. x > y
15. 4; I. 7 35 5x 9 169 x
7 35 5or, x x 169 9
7 35or, x 1521
or, x2 = 1521
x = ± 39
II. 11 124 4 273y y y
7
or, 1 114 24y 39
or, y = 39x < y
16. 5; I. x = 4 2401 x = 7
II. 2y2 - 16y + 7y - 56 = 0 2y(y - 8) + 7(y - 8) = 0 (2y + 7) (y - 8) = 0
7y 8,2
Hence, no relation exists between x and y.17. 2; I. 5x2 + 10x - 7x - 14 = 0
or, 5x(x + 2) - 7(x + 2) = 0or, (x + 2) (5x - 7) = 0
x = - 2, 75
II. 2y2 - 4y - 5y + 10 = 0or, 2y(y - 2) - 5(y - 2) = 0
or, (2y - 5)(y - 2) = 0
or, y = 2, 52
x < y18. 5; I. 8x2 + 24x + 7x + 21 = 0
or, 8x(x + 3) + 7(x + 3) = 0or, (x + 3) (8x + 7) = 0
x = - 3, 78
II. 5y2 + 20y - 9y - 36 = 0or, 5y(y + 4) - 9(y + 4) = 0or, (y + 4) (5y - 9) = 0
y = -4, 95
Hence, no relation exists between x and y.
19. 2; I. y 1089or, y = 33
II. 12 y 12 33 45x 15
3 3 3
x < y20. 1; I. 15x2 + 68x + 77 = 0
or, 15x2 + 35x + 33x + 77 = 0or, 5x(3x + 7) + 11(3x + 7) = 0or, (5x + 11) (3x + 7) = 0
7 11x ,3 5
II. 3y2 + 29y + 68 = 0or, 3y2 + 12y + 17y + 68 = 0or, 3y(y + 4) + 17(y + 4) = 0or, (y + 4) (3y + 17) = 0
y = -4, 173
x > y
21. 4; I. 2x2 + 2x - x - 1 = 0or, 2x(x + 1) - 1(x + 1) = 0or, (x + 1) (2x - 1) = 0
x = - l, 12
II. 6y2 - 3y - 10y + 5 = 0or, 3y(2y - 1) - 5(2y - 1) = 0or, (3y - 5)(2y - 1) = 0
y = - 3, 113
x y22. 5; I. 21x2 - 45x - 77x + 165 = 0
or, 3x(7x - 15) - 11 (7x - 15) = 0or, (3x - 11) (7x - 15) = 0
293
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
11 15x ,3 7
II. 3y2 + 9y - 11y - 33 = 0or,3y(y + 3) - 11(y + 3) = 0or,(3y - 11) (y + 3) = 0
y = - 3, 113
Hence, no relation can be established between xand y.
23. 3; I. 5x2 - 20x - 9x + 36 = 0or, 5x(x - 4) - 9(x - 4) = 0or,(x - 4) (5x - 9) = 0
x = 4, 95
II. 10y2 + 15y - 18y - 27 = 0or, 5y(2y + 3) - 9(2y + 3) = 0or, (2y + 3) (5y - 9) = 0
y = 9 3,5 2
x y24. 2; eqn (I) × 3 - eqn (II) × 4
21x + 12y = 920x + 12y = 12- - - . x = - 3and y = 6 x < y
25. 1; I. 7x2 - 21x - 33x + 99 = 0or, 7x(x - 3) - 33(x - 3) = 0or, (x - 3) (7x - 33) = 0
x = 3, 337
II. 4y2 - 6y - 10y + 15 = 0or, 2y(2y - 3) - 5(2y - 3) = 0or, (2y - 3)(2y - 5) = 0
3 5 y= ,2 2
26. 1; I. 5x2 - 45x - 42x + 378 = 0or, 5x(x - 9) - 42(x - 9) = 0or, (5x - 42) (x - 9) = 0
x = 9, 425
II. 3y2 - 24y - 25y + 200 = 0or, 3y(y - 8) - 25(y - 8) = 0or, (y - 8) (3y - 25) = 0
25y 8,3
x > y27. 5; I. 10x2 - 16x + 15x - 24 = 0
or, 2x(5x - 8) + 3(5x - 8) = 0or, (2x + 3) (5x - 8) = 0
3 8x ,2 5
II. y2 - 2y = 0or, y(y - 2) = 0
y = 0, 2ie no relationship exists between x and y.
28. 4; I. x2 - 2x - 3x + 6 = 0or, x(x - 2) - 3(x - 2) = 0or, (x - 2) (x - 3) = 0
x = 2, 3II. 2y2 - 6y - 9y + 27 = 0or, 2y(y - 3) - 9(y - 3) = 0or, (y - 3) (2y - 9) = 0
y = 3, 92
x y29. 2; I. eqn (I) × 5 + eqn (II) × 2
15x + 10y = 150514x - 10y = 14829x = 1653
x = 1653
29 = 57
and y = 65 x < y30. 3; I. 14x2 - 37x + 24 = 0
or, 14x2 - 21x - 16x + 24 = 0or, 7x(2x - 3) - 8(2x - 3) = 0or, (2x - 3) (7x - 8) = 0
x =3 8,2 7
II. 28y2 - 53y + 24 = 0or, 28y2 - 21y - 32y + 24 = 0or, 7y(4y - 3) - 8(4y - 3) = 0or, (7y - 8) (4y - 3) = 0
8 3y ,7 4
x y31. 3; eqn (I) × 7
eqn (II) × 11 77x + 35y = 819 - 77x ± 143y = 1683 - 108y = - 864 y = 8, x = 7 ie x < y
32. 1; I. 6x2 + 21x + 30x + 105 = 0or, 3x(2x + 7) + 15(2x + 7) = 0or, (3x + 15) (2x + 7) = 0
x = -5, 72
II. 2y2 + 12y + 13y + 78 = 0or, 2y(y + 6) + 13(y + 6) = 0or, (2y + 13) (y + 6) = 0
294
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y = 13, 62
x < y33. 3; eqn (I) × 4
eqn (II) × 7 24x + 28y = 208- 98x ± 28y = 245 - 74x = - 37
x = 12 , y = 7
x < y34. 2; I. x2 + 5x + 6x + 30 = 0
or, x(x + 5) + 6(x + 5) = 0or, (x + 5) (x + 6) = 0 x = - 5, - 6II. y2 + 12y + 36 = 0or, (y + 6)2 = 0or, y + 6 = 0 y = - 6ie x y
35. 4; I. 2x2 + 2x - x - 1 = 0or, 2x(x + 1) - 1(x + 1) = 0or, (2x - 1) (x + 1) = 0
1x , 12
II. 2y2 - 2y - y + 1 = 0or, 2y(y - 1) - 1(y - 1) = 0or, (2y - 1)(y - 1) = 0
1y ,12
ie x y36. 1; 7x + 6y + 4z = 122 ... (i)
4x + 5y + 3z = 88 ... (ii)9x + 2y + z = 78 ... (iii)From (i) and (ii)
5x - 2y = 14... (iv)From (ii) and (iii)
23x + y = 146 ... (v)From (iv) and (v),
x = 6, y = 8Putting the value of x and y in eqn (i), we get
z = 8:. x < y = z
37. 3; 7x + 6y = 110 ... (i)4x + 3y = 59 ... (ii)x + z = 15 ... (iii)From eqn (i) and (ii), x = 8, y = 9Put the value of x in eqn (iii).Then, z = 7x < y > z
38. 2; 2 1/2 4 1/4(6 ) (6 )x
6 6 6 ... (i)
2y + 3z = 33 ... (ii)6y + 5z = 71 ... (iii)From eqn (ii) and (iii),
y = 6 and z = 7x = y , z
39. 4; 8x + 7y = 135 ... (i)5x + 6y = 99 ... (ii)9y + 8z = 121 ... (iii)From eqn (i) and (ii),
x = 9, and y = 9Putting the value of y in eqn (iii),
z = 5:. x = y > z
40. 5; (x + y)3 = 1331or, x + y = 11 ... (i)(x + y)2 = 121(x - y)2 + 4xy = 121x - y = 3... (ii)
[value of xy from eqn (iii)]From eqn (i) and (ii), x = 7, y = 4Put the value x and y in the eqn
x - y + z = 07 - y + z = 03 + z = 0z = -3
41. 4; I. 7x2 - 7x - 2x + 2 = 0or, 7x(x - 1) - 2(x - 1) = 0 (7x - 2) (x - 1) = 0
or, x = 2,17
II. y2 - y - 3y + 3 = 0or, y(y - 1) - 3(y - 1) = 0or, (y - 3) (y - 1) = 0 y = 1, 3 x y
42. 5; I. x2 = 64 x = ±8II. 2y2 + 9y + 16y + 72 = 0or, y(2y + 9) + 8(2y + 9) = 0or, (y + 8) (2y + 9) = 0
9y 8,2
ie, no relation between x and y.43. 3; I. x2 + x - 20 = 0
or, x2 + 5x - 4x - 20 = 0or, x(x + 5) - 4(x + 5) = 0or, (x - 4) (x + 5) = 0 x = 4, - 5II. 2y2 - 10y - 9y + 45 = 0or, 2y(y - 5) - 9(y - 5) = 0or, (y - 5) (2y - 9) = 0
9y 5,2
x < y
295
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
44. 1; Eqn (I) × 2Eqn (II) × 714x + 6y = 5214x + 119y = - 287 - - + . - 113y = 339 y = - 3 and x = 5, ie x > y
45. 2; I. 3x2 - 9x - 11x + 33 = 0or, 3x(x - 3) - 11(x - 3) = 0or, (3x - 11) (x - 3) = 0
x = 3, 113
II. 2y2 - 6y - 5y + 15 = 0or, 2y(y - 3) - 5(y - 3) = 0or, (y - 3) (2y - 5) = 0
5y 3,2
x y46. 1; I. 4x2 - 28x - 15x + 105 = 0
or, 4x(x - 7) - 15(x - 7) = 0or, (x - 7) (4x - 15) = 0
x = 7, 154
II. 7y2 - 14y - 15y + 30 = 0or, 7y(y - 2) - 15(y - 2) = 0or, (y - 2)(7y - 15) = 0
y = 2, 157
x > y47. 4; I. x2 + 8x + 5x + 40 = 0
or, x(x + 8) + 5(x + 8) = 0or, (x + 5) (x + 8) = 0 x = - 5, - 8II. y2 + 2y + 5y + 10 = 0or, y(y + 2) + 5(y + 2) = 0or, (y + 2)(y + 5) = 0 y = - 2, - 5 x y
48. 4; I. x = 3 2197 x = 13II. 2y2 - 28y - 26y + 364 = 0or, 2y(y - 14) - 26(y - 14) = 0or, (2y - 26) (y - 14) = 0 y = 14, 13 x y
49. 1; I. 5x2 - 15x - 12x + 36 = 0or, 5x(x - 3) - 12(x - 3) = 0or, (5x - 12) (x - 3) = 0
12x , 35
II. y2 - y - 2y + 2 = 0or, y(y - 1) - 2(y - 1) = 0or, (y - 1)(y - 2) = 0 y = 1, 2 x > y
50. 3; eqn (I) × 5 + eqn (II) × 8 65x - 40y + 405 = 0120x + 40y + 520 = 0185x + 0 + 925 = 0
925x 5185
13x 81y8
65 81 16 28 8
x < y51. 1; I. 15x2 - 10x - 9x + 6 = 0
or, 5x(3x - 2) -3(3x - 2) = 0or, (5x - 3) (3x - 2) = 0
3 2x ,5 3
II. 6y2 - 3y - 2y + 1 = 0or, 3y(2y - 1) -1(2y - 1) = 0or, (3y - 1)(2y - 1) = 0
1 1y ,3 2
x > y
52. 2; I. x 172
x = 13.11II. y2 - 14y - 15y + 210 = 0or, y(y - 14) - 15(y - 14) = 0or, (y - 14) (y - 15) = 0 y = 14, 15 x < y
53. 4; I. 3x2 -12x - 8x + 32 = 0or, 3x(x - 4) - 8(x - 4) = 0or, (x - 4) (3x - 8) = 0
x = 4, 83
II. 2y2 - 8y - 11y + 44 = 0or, 2y(y - 4) -11(y - 4) = 0or, (y - 4) (2y - 11) = 0
11y 4,2
x y54. 2; 4 × eqn (I) - 3 × eqn (II),
12x + 32y = -812x + 54y = 3
- - - .
296
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
-22y = -11
y = 12 and x = -2
x < y55. 3; I. 2x2 - 8x - 7x + 28 = 0
or, 2x(x - 4) - 7(x - 4) = 0or, (x - 4) (2x - 7) = 0
x = 4, 72
II. 10y2 - 35y + 34y - 119 = 0or, 5y(2y - 7) + 17(2y - 7) = 0or, (2y - 7)(5y + 17)
7 17y ,2 5
x y56. 3; I. 676x2 - 1 = 0
or x2 =1 1x
676 26
II. 3
1 1y y2413824
ie, x < y57. 3; On solving these two equations, we get
x = -2, y = 6ie, x < y
58. 1; I. 7x2 - 28x + 30x - 120 = 0or, 7x(x - 4) + 30(x - 4) = 0or, (x - 4) (7x + 30) = 0
x = 4, 307
II. y2 + 6y + 5y + 30 = 0or, y(y + 6) + 5(y + 6) = 0or, (y + 5) (y + 6) = 0y = -5, - 6ie, x > y
59. 1; I. x2 = 7xor, x2 - 7x = 0or, x(x - 7) = 0 x = 0, 7II. (y + 7)2 = 0or, (y + 7) = 0 y = -7ie, x > y
60. 5; I. 2x2 - 6x + 11x - 33 = 0or, 2x(x - 3) + 11(x - 3) = 0or, (2x + 11) (x - 3) = 0
x = 3, 112
II. y2 - 3y + 2y - 6 = 0or, y(y - 3) + 2(y - 3) = 0or, (y + 2)(y - 3) = 0 y = - 2, 3 i.e no relation exists between x and y
61. 1; I. x2 + 12x + 36 = 0
or, (x + 6)2 = 0or, x + 6 = 0or, x = - 6II. y2 + 15y + 56 = 0or, y2 + 7y + 8y + 56 = 0or, y(y + 7) + 8(y + 7) = 0or, (y + 7) (y + 8) = 0 y = -7, -8 x > y
62. 1; I. x2 = 35
x = ± 35II. y2 + 13y + 42 = 0or, y2 + 6y + 7y + 42 = 0or, y(y + 6) + 7(y + 6) = 0or, (y + 6) (y + 7) = 0 y = -6, - 7 x > y
63. 5; I. 2x2 - 3x - 35 = 0or, 2x2 - 10x + 7x - 35 = 0or, 2x(x - 5) + 7(x - 5) = 0or, (2x + 7) (x - 5) = 0
x =7 ,2
5
II. y2 - 7y + 6 = 0or, y2 - y - 6y + 6 = 0or, y(y - 1) - 6(y - 1)or, (y - 1)(y - 6) = 0 y = 1, 6No relation can be established between x and y.
64. 4; I. 6x2 - 29x + 35 = 0or, 6x2- 15x - 14x + 35 = 0or, 3x(2x - 5) -7(2x - 5) = 0or, (3x - 7) (2x - 5) = 0
7 5x ,3 2
II. 2y2 - 19y + 35 = 0or, 2y2 - 14y - 5y + 35 = 0or, 2y(y - 7) -5 (y - 7) = 0or, (2y - 5)(y - 7) = 0
y = 5 , 72
x y65. 2; I. 12x2 - 47x + 40 = 0
or, 12x2 - 32x - 15x + 40 = 0or, 4x(3x - 8) -5(3x - 8) = 0or, (4x - 5) (3x - 8) = 0
x = 5 8,4 3
II. 4y2 + 3y - 10 = 0
297
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or, 4y2 + 8y - 5y - 10 = 0or, 4y(y + 2) -5(y + 2) = 0or, (4y - 5) (y + 2) = 0
y = 5 , 24
x y66. 4; I. x2 + 7x - 4x - 28 = 0
or, x(x + 7) - 4 (x + 7) = 0or, (x - 4)(x + 7) = 0 x = 4, - 7II. y2 - 11y + 28 = 0or, y2 - 7y - 4y + 28 = 0or, y (y - 7) -4(y - 7) = 0or, (y - 4) (y - 7) = 0 y = 4, 7x y
67. 1; I. 6x2 - 17x + 12 = 0or, 6x2 - 9x - 8x + 12 = 0or, 3x (2x - 3) - 4 (2x - 3) = 0or, (3x - 4) (2x - 3) = 0
4 3x ,3 2
II. 6y2 - 3y - 4y + 2 = 0or, 3y (2y - 1) - 2 (2y - 1) =0or, (3y - 2) (2y - 1) = 0
2 1y ,3 2
x > y
68. 2; I. 256x576
16 2x24 3
II. 3y2 + y - 2 = 0or, 3y2 + 3y - 2y - 2 = 0or, 3y (y + 1) - 2(y + 1) = 0or, (3y - 2) (y + 1) = 0
y = 2 , 13
x y69. 5; I. x2 = 64
x = ± 8II. y2 = 9yor, y2 - 9y = 0or, y (y - 9) = 0 y = 0, 9 no relationship can be established between xand y.
70. 3; I. x2 + 6x - 7 = 0
or, x2 + 7x - x - 7 = 0or, x(x + 7) -1 (x + 7)= 0or, (x - 1) (x + 7) = 0 x = 1, -7II. 41y + 17 = 140or, 41y = 140 - 17 = 123
y = 123 341
x < y71. 2; I. x2 + 3x - 28 = 0
or, x2 + 7x - 4x - 28 = 0or, x (x + 7) - 4 (x + 7) = 0or, (x - 4) (x + 7) = 0or, x = 4, -7II. y2 + 9y + 7y + 63 = 0or, y(y + 9) + 7(y + 9) = 0or, (y + 7)(y + 9) = 0or, y = -7, -9 x y
72. 2; I. x = 3 2197 x = 13II. y2 = 169 y = ±13 x y
73. 2; I. 8x2 - 40x - 9x + 45 = 0or, 8x (x - 5) -9 (x - 5) = 0or, (8x - 9) (x - 5) = 0or, x = 5, 9/8II. 8y2 + 8y - 9y -9 = 0or, 8y (y + 1) -9 (y + 1) = 0or, (8y - 9) (y + 1) = 0
9y , 18
x y74. 3; 42x - 17y = -67
42x + 72y = -156 eqn (II) × 6 - - + .
-89y = 89
89y 1 and x 289
x < y75. 4; I. x2 - 8x + 15 = 0
or, x2 - 3x - 5x + 15 = 0or, x (x - 3) -5 (x - 3) = 0or, (x - 3) (x - 5) = 0or, x = 3, 5II. 2y2 - 10y + 55 = 0or, 2y (y - 5) -11 (y - 5) = 0or, (y - 5)(2y - 11) = 0
298
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or, y = 5, 112
x y76. 1; I. 2.3p - 20.01 = 0
20.01p 8.72.3
II. 2.9q - p = 0
or, p = 2.9q8.7
q 8.72.9
ie p > q
77. 2; I. p = 1764 p = 42II. q2 = 1764 q = + 42ie p > q
78. 5; I. p2 - 26p + 168 = 0 p2 - 12p - 14p + 168 = 0 p(p - 12) - 14(p - 12) = 0 (p - 12) (p - 14) = 0 p = 12, 14II. q2 - 25q + 156 = 0 q2 - 13q - 12q + 156 = 0q(q - 13) - 12(q - 13) = 0 (q - 12) (q - 13) = 0q = 12, 13Hence, no relation can be established between pand q
79. 2; I. p2 - l3q + 42 = 0p2 - 6p - 7p + 42 = 0p(p - 6) - 7(p - 6) = 0(p - 6) (p - 7) = 0 p = 6, 7II. q2 + q - 42 = 0q2 + 7q - 6p - 42 = 0q(q + 7) - 6(q + 7) = 0(q - 6)(q + 7) = 0 q = 6, - 7 ie p q
80. 3; eqn(I) × 3 18p - 15q = -141eqn (II) × 5 25p + 15q = 55
43p = -86
86p 243
5p + 3q = 113q = 11 - 5p 3q = 11 + 103q = 21 q = 7 ie p < q
81. 3; I. 2x2 + 13x - 7 = 0or 2x2 + 14x - x - 7 = 0or 2x (x + 7) - 1 (x + 7) = 0or (2x - 1) (x + 7) = 0
1x , 72
II. 2y2 - 5y + 3 = 0or 2y2 - 2y - 3y + 3 = 0
or 2y(y - 1) - 3(y - 1) = 0or (2y - 3) (y - 1) = 0
3y 1, 2
Hence x < y82. 1; I. 2x2 - 8x - 7x + 28 = 0
or 2x (x - 4) - 7(x - 4) = 0or (2x - 7) (x - 4) = 0
7x 4, 2
II. 4y2 - 16y + 15 = 0or 4y2 - 6y - 10y + 15 = 0or 2y (2y - 3) - 5(2y - 3) = 0or (2y - 5) (2y - 3) = 0
5 3y ,2 2
Hence x > y83. 4; I. x2 + 8x + 16 = 0
or (x + 4)2 = 0or x + 4 = 0 x = -4II. y2 = 16 y = ±4Hence, x y
84. 5; I. x2 - 2x - 24 = 0or x2 + 4x - 6x - 24 = 0or x(x + 4) - 6(x + 4) = 0or (x - 6) (x + 4) = 0 x = 6, - 4II. y2 + 8y = 0or y(y + 8) = 0 y = 0, - 8 ie No relation can be establishedbetween x and y.
85. 1; I. x2 + 4x = 0or x(x + 4) = 0 x = 0, - 4II. y2 + 10y + 25 = 0or (y + 5)2 = 0or y + 5 = 0 y = - 5 x > y
86. 1; I. 2x2 + 2x – x – 1 = 0or 2x(x + 1) – 1(x + 1) = 0or (2x – 1) (x + 1) = 0
1x 1,2
II. 2y2 + 3y + 10y + 15 = 0or y(2y + 3) + 5(2y + 3) = 0or (y + 5) (2y + 3) = 0
3y 5,2
x > y87. 5; I. x2 + 4x + 8x + 32 = 0
or x(x + 4) + 8(x + 4) = 0or (x + 4) (x + 8) = 0 x = – 4, – 8II. 2y2 + 6y + 9y + 27 = 0or 2y(y + 3) + 9(y + 3) = 0or (2y + 9) (y + 3) = 0
299
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9y , 32
No relation can be established between x and y.
88. 1; I. 6x2 – 9x – 8x + 12 = 0or 3x(2x – 3) – 4(2x – 3) = 0or (2x – 3) (3x – 4) = 0
3 4x ,2 3
II. 7y2 – 7y – 6y + 6 = 0or 7y(y – 1) – 6(y – 1) = 0or (7y – 6) (y – 1) = 0
6y 1,7
x > yNo relation between ‘x’ and ‘y’.
89. 5; I. x2 – 11x – 71x + 781 =0or x(x – 11) – 71(x – 11) = 0or(x – 11)(x – 71) = 0 x = 11, 71II. y2 = 5041 y = ± 71
90. 2; I. 6x2 – 15x – 32x + 80 = 0or 3x(2x – 5) – 16(2x – 5) = 0or (3x – 16) (2x – 5) = 0
16 5x ,3 2
II. 2y2 – 4y – 5y + 10 = 0or 2y(y – 2) – 5(y – 2) = 0or (y – 2) (2y – 5) = 0
5y 2,2
x y
91. 4; I. 3x2 - 12x + 5x - 20 = 0or 3x(x - 4) + 5(x - 4) = 0or (3x + 5) (x - 4) = 0
5x ,43
II. y2 - 8y + 16 = 0or (y - 4)2 = 0 (y - 4) = 0or y = 4 x y
92. 5; I. x2 - 72 = 0or x2 = 72 x = + 8.485II. y2 - y - 8y + 8 = 0or y(y - 1) - 8(y - 1) = 0or (y - 1) (y - 8) = 0y = 1, 8
93. 1; I. 9x2- l14x + 361 =0or (3x - 19)2 = 03x - 19 = 0
x = 193 = 6.33
II. y2 = 36 y = ±6 x > y
94. 3; I. 13x + 17y = 107 eqn (II) × 1313x ± 143y = ± 533 160y = 640
640y 4 and x=11y-41 160
x = 44 - 41 = 3 x < y
95. 3; I. 9x2 + 18x + 9 = 0or x2 + 2x + 1 = 0or (x + l)2 = 0 x + 1 = 0, or x = -1II. y2 - y - 2y + 2 = 0or y(y - 1) -2(y - 1) = 0or (y - 1) (y - 2) = 0
x < y
96. 1; eqn (I) ×3 - eqn (II) × 412x + 21y = 12612x - 44y = -4 - + + . 65y = 130 y = 2and x = 7
97. 3; I. 9x2 - 18x - 1 lx + 22 = 0or 9x(x - 2)- 11(x - 2) = 0or (x - 2)(9x - 11) = 0
11x 2,9
II. y2 - 3y - 4y + 12 - 0or y(y - 3) - 4(y - 3) = 0or (y - 3) (y - 4) = 0 y = 3, 4 x < y
98. 4; I. 3x2 - 4x - 32 = 0or 3x2 - 12x + 8x - 32 = 0or 3x(x - 4) + 8(x - 4) = 0or (3x + 8) (x - 4) = 0
8x 4,3
II. 2y2 - 8y - 9y + 36 = 0or 2y(y - 4) - 9(y - 4) = 0or (2y - 9) (y - 4) = 0or (2y - 9) (y - 4) = 0
9y 4,2
x y99. 1; I. 3x2 - 21x + 2x - 14 = 0
or 3x(x - 7) + 2(x - 7) = 0or (3x + 2) (x - 7) = 0
2x 7,3
II. 2y2 + 5y + 3 = 0or 2y2 + 2y + 3y + 3 = 0or 2y(y + 1) + 3(y + 1) = 0or (2y + 3) (y + 1) = 0
300
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
3y , 12
x > y100. 5; I. x2 + 14x + 49 = 0
or (x + 7)2 = 0 x + 7 = 0or, x = -7II. y2 + 9y = 0or y(y + 9) = 0 y = 0, -9 ie no relation between x and y.
101. 3; I. 9x2 = 1
2 1x9
1x3
II. 4y2 + 11y - 3 = 0or, 4y2 + 12y - y - 3 = 0or, 4y(y + 3) - 1(y + 3) = 0
1y , 34
Hence, there is no relation between x and y.102. 1; I. 3x2 + 5x - 2 = 0
or, 3x2 + 6x - x - 2 = 0or, 3x(x + 2) - 1(x + 2) = 0or, (3x - 1) (x + 2) = 0
1x 2,3
II. 2y2 - 2y - 5y + 5 = 0or, 2y(y - 1) - 5(y - 1) = 0
5y 1,2
Hence, x < y103. 5; I. 6x2 + 13x + 5 = 0
or, 6x2 + 3x + 10x + 5 = 0or, 3x(2x + 1) + 5(2x + 1) = 0or, (3x + 5) (2x + 1) = 0
5 1x ,3 2
II. 3y2 + 11y + 10 = 0or, 3y2 + 6y + 5y + 10 = 0or, 3y(y + 2) + 5(y + 2) = 0or, (3y + 5) (y + 2) = 0
5y , 23
Hence, x y104. 4; I. 7x - 4y = 29
II. 5x + 3y = 50(I) × 3 + (II) × 4
21x - 12y = 8720x + 12y = 200 41x = 287 x = 7Putting the value of x in (I), we gety = 5Hence, x > y
105. 1; I. x2 = 5
x 5 2.236
II. 4y2 - 24y + 35 = 0or, 4y2 - 14y - 10y + 35 = 0or, 2y(2y - 7) - 5(2y - 7) = 0or, (2y - 5) (2y - 7) = 0
5 7y , 2.5, 3.52 2
Hence, x < y106. 3; I. 35x2 - 28x - 25x + 20 = 0
or 7x(5x - 4) - 5(5x - 4) = 0or (7x - 5) (5x - 4) = 0
5 4x ,7 5
II. 56y2 - 48y - 49y + 42 = 0or 8y(7y - 6) - 7(7y - 6) = 0or (8y - 7) (7y - 6) = 0
7 6y ,8 7
x < y
107. l ; I. x = 3 4913 x = 17II. 13y = 246 - 3xor 13y = 246 - 51 = 195 y = 15 x > y
108. 2; I. x2 - 7x + 2x - 14 = 0or x(x - 7) + 2(x - 7) = 0(x + 2) (x - 7) = 0 x = -2, 7II. y2 + 5y + 2y + 10 = 0or y(y + 5) + 2(y + 5) = 0or (y + 2) (y + 5) = 0 y = -2, -5x y
109. 5; I. x2 = 3481 x = ± 59
II. 3y2 = 3 216000 3y2 = 60
y = ± 20No relation
110. 1; I. 5x2 + 5x - 3x - 3 = 0or 5x (x + 1) - 3(x + 1) = 0or (5x - 3) (x + 1) = 0
3x , 15
II. 2y2 + 4x + 3y + 6 = 0or 2y(y + 2) + 3(y + 2) = 0
301
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or (2y + 3) (y + 2) = 0
–3y , 22
ie x > y111. 1; I. 20x2 - 35x - 32x + 56 = 0
or 5x(4x - 7) - 8(4x - 7) = 0or (5x - 8) (4x - 7) = 0
x = 8 7,5 4
II. 56y2 - 32y - 35y + 20 = 0or 8y(7y - 4) - 5(7y - 4) = 0or (8y - 5) (7y - 4) = 0
5 4y ,8 7
x > y
112. 4; I. x4 = 65536 x = +16
II. y = 3 4096 y = 16 x y
113. 3; I. 2x2 + 16x - 5x - 40 = 0or 2x(x + 8) - 5(x + 8) = 0or (2x - 5) (x + 8) = 0
x = 5 , 82
II. 4y2 - 16y - 11y + 44 = 0or 4y(y - 4) - 11(y - 4) = 0or(4y - 11) (y - 4) = 0
y = 4, 114 x < y
114. 1; I. 7x = 4y + 85or 7x = 4 × 26 + 85 (Put y = 26)
x = 189
7 = 27
II. y = 3 17576 y = 26 x > y
115. 4; I. x2 = 14641 x = ±121
II. y = 14641 y = 121 x y
116. 2; I. x2 + 42 = 13xor x2 - 13x + 42 = 0or x2 - 7x - 6x + 42 = 0or x(x - 7) - 6(x - 7) = 0or (x - 6) (x - 7) = 0 x = 6, 7
II. 4y 1296
y = 6 x y
117. 1; I. x2 + x - 2 = 0or x2 + 2x - x - 2 = 0or x(x + 2) - 1(x + 2) = 0or (x - 1) (x + 2) = 0 x = 1, - 2II. y2 + 7y + 12 = 0or y2 + 3y + 4y + 12 = 0or y(y + 3) + 4(y + 3) = 0
or (y + 3) (y + 4) = 0y = -3, -4 x > y
118. 3; I. 3x2 - 23x + 40 = 0or 3x2 - 15x - 8x + 40 = 0or 3x(x - 5) - 8(x - 5) = 0or (3x - 8) (x - 5) = 0
8x 5, 3
II. 2y2 - 23y + 66 = 0or 2y2 - 12y - 11y + 66 = 0or 2y (y - 6) -11 (y - 6) = 0or (y - 6)(2y - 11) = 0
11y 6, 2
x < y119. 3; I. 15x2 - 25x - 21x + 35 = 0
or 5x(3x - 5) - 7(3x - 5) = 0or (5x - 7) (3x - 5) = 0
57x ,5 3
II. 4y2 - 8y - 7y + 14 = 0or 4y(y - 2) - 7(y - 2) = 0or (4y - 7) (y - 2) = 0
y = 2, 74
x < y120. 3; I. x2 - x + 6x -6 = 0
or x(x - 1) + 6(x - 1) = 0or (x - 1) (x + 6) = 0 x = 1, -6II. 2y2 - 6y - 5y + 15 = 0or 2y(y - 3) - 5(y - 3) = 0or (y - 3) (2y - 5) = 0
y = 3, 52
x < y121. 3; I. 2x2 - 21x + 54 = 0
or 2x2 - 12x - 9x + 54 = 0or 2x(x - 6) - 9(x - 6) = 0or (x - 6) (2x - 9) = 0
9x 6,2
II. y2 - 14y + 49 = 0or (y - 7)2 = 0or y - 7 = 0 y = 7 Hence x < y
122. 2; I. x2 - 19x + 70 = 0or x2 - 5x - 14x + 70 = 0or x(x - 5) - 14(x - 5) = 0or (x - 5) (x - 14) = 0 x = 5, 14II. 2y2 - 10y - 7y + 35 = 0or 2y(y - 5) - 7(y - 5) = 0or (y - 5) (2y - 7) = 0
y = 5, 72 Hence x y
123. 4; I. 3x2 + 5x - 8 = 0or 3x2 - 3x + 8x - 8 = 0or 3x(x - 1) + 8(x - 1) = 0
302
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or (x - 1) (3x + 8) = 0
8x 1,3
II. y2 - 4y + 3 = 0or y2 - y - 3y + 3 = 0or y(y - 1) - 3(y - 1) = 0or(y - l)(y - 3) = 0 y = 1, 3 Hence, x y
124. 4; I. 12x2 - 16x + 5 = 0or 12x2 - 6x - 10x + 5 = 0or 6x(2x - 1) - 5(2x - 1) = 0or (6x - 5) (2x - 1) = 0
1 5x ,2 6
II. 18y2 - 45y + 25 = 0or 18y2 - 30y - 15y + 25 = 0or 6y(3y - 5) - 5(3y - 5) = 0or (3y - 5) (6y - 5) = 0
5 5y , Hence, x y3 6
125. 2; I. 3x2 + 11x + 8 = 0or 3x2 + 3x + 8x + 8 = 0or 3x(x+ 1) + 8(x + 1) = 0or (x + 1) (3x + 8) = 0
8x 1,3
II. 3y2 + 20y + 32 = 0or 3y2 + 12y + 8y + 32 = 0or 3y(y + 4) + 8(y + 4) = 0or (3y + 8) (y + 4) = 0
8y 4,3
Hence, x y
126. 5; I. x = 3 357911 x = 71
II. y = 5041 y = 71 x = y
127. 1; Eqn(l) × 9 - Eqn (II) × 545x + 63y = -38745x - 85y = 205
- + - . 148y = -592 y = -4 and x = -3 x > y
128. 4; I. x2 + 11x + 30 = 0or x(x + 5) + 6(x + 5) = 0 or (x + 5) (x + 6) = 0 x = -5, -6II. y2 + 4y + 5y + 20 = 0or y(y + 4) + 5(y + 4) = 0or (y + 4) (y + 5) = 0 y = -4,-5 x y
129. 3; I. 4x2 + 4x - x - l = 0or 4x(x+ 1)- l(x + 1) = 0or (4x - 1) (x + 1) = 0
x = -l, 14
II. 6y2 - 3y - 2y + 1 = 0or 3y(2y - 1) - l(2y - 1) = 0
or (3y - 1) (2y - 1) = 0
1 1y ,2 3
x < y130. 2; I. 3x2 + 9x + 6x + 18 = 0
or 3x(x + 3) + 6(x + 3) = 0or (x + 3)(3x + 6) = 0 x = -3, -2II. 2y2 + 6y + 9y+ 27 = 0or 2y(y + 3) + 9(y + 3) = 0or (2y + 9)(y + 3) = 0
9y 3,2
x y131. 1; 4x + 3y = 40 .........(i) ×6
6x - 5y = 22 .........(ii) ×4 24x +18y = 240 24x - 20y = 88
- + - . 38y = 152
152y 438
Putting the value of y in equation (i), we have4x + 3 x 4 = 40or, 4x = 40 12 = 28 x = 7Hence, x > y.
132. 2; 22x 4x 13x 2 13 0 ...(i)
or, 2x x 2 13 x 2 0
or, x 2 2x 13 0
13x 2,2
210y 18y 5 13y 9 13 0 ...(ii)
or, 2y 5y 9 13(5y 9) 0
or, (2y 13)(5y 9) 0
9 13y ,5 2
Hence, x y.133. 5; 6x2 + 17 - 3x2 - 20 = 0 ... (i)
or, 3x2 = 3 x ± l5y2 - 12 - 9y2 + 16 = 0 .... (ii)or, 4y2 = 4 y ± 1
Hence x = y.134. 2; 13x + 17 = 134 .... (i) .
117x 9.13
(36l)1/2y2 - 270 = 1269or, 19y2 = 1629 + 270 = 1539
2 1539y 8119
y ± 9
303
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Hence, x y.135. 4; 64x2 = 256 .... (i)
or, x2 = 4 x = ± 214y3 - 12y3 = 16 .... (ii)or, 2y3 = 16 y3 = 8 y = 2Hence x y.
136. 3; 15x - 21y = -7291x + 21y = 602106x = 530
x = 5, y = 7 x < y
137. 2; I. x2 - 13x + 40 = 0or x2 - 5x - 8x + 40 = 0or x(x - 5) -8(x - 5) = 0or (x - 5)(x - 8) = 0 x = 5, 8II. y2 + 3y - 40 = 0or y2 - 5y + 8y - 40 = 0or y(y - 5) + 8(y - 5) = 0or (y - 5) (y + 8) = 0 y = 5, -8Hence, x y
138. 4; I. 8x2 -26x + 15 = 0or 8x2 - 20x - 6x + 15 = 0or 4x(2x - 5) - 3(2x - 5) = 0or (4x - 3) (2x - 5) = 0
x = 3 5,4 2
II. 2y2-17y + 30 = 0or 2y2 - 12y - 5y + 30 - 0or 2y(y - 6) - 5(y - 6) = 0or (2y - 5) (y - 6) = 0
y = 5 , 62
x y139. 4; I. x2 = 484
x = + 22II. y2 - 45y + 506 = 0or y2 - 22y - 23y + 506 = 0or y(y - 22) - 23(y - 22) = 0or (y - 22) (y - 23) = 0 y = 22, 23 x y
140. 5; I. 13x -21 = 200- 4xor 13x + 4x = 200 + 21
x 221 1317
II. y = 3 2197 y = 13 x = y
141. 3; I. (p + q)2 = 3136 p + q = +56II. q + 2513 = 2569or, q = 2569 - 2513 = 56Putting the value of q in (I) we have,p = 0. -112 p < q
142. 1; I. 4p2 - 16p + 15 = 0or, 4p2 - 10p - 6p + 15 = 0
or, 2p(2p - 5) - 3(2p - 5) = 0or, (2p - 3) (2p - 5) = 0
p = 3 5,2 2
II. 2q2 + 5q - 7 = 0or, 2q2 + 7q - 2q - 7 = 0or, q(2q + 7) - 1(2q + 7) = 0or, (q - 1) (2q + 7) = 0
q = 71,2
143. 2; I. p2 = 49 P = ±7II. q2 + 15q + 56 = 0or, q2 + 8q + 7q + 56 = 0or, q(q + 8) + 7(q + 8) = 0or, (q + 7) (q + 8) = 0 q = -7, -8 p q
144. 5; I. 2p2 + 5p - 12 = 0or, 2p2 + 8p - 3p - 12 = 0or, 2p(p + 4) - 3(p + 4) = 0or, (2p - 3) (p + 4) = 0
p = 3 , 42
II. 2q2 - q - 1 = 0or, 2q2 - 2q + q - 1 = 0or, 2q(q - 1) + 1(q - 1) = 0or, (2q + 1) (q - 1) = 0
q = 1, 12
No reation between ‘p’ and ‘q’.145. 2; I. p2 - 12p + 35 = 0
or p2 - 5p - 7p + 35 = 0or p(p - 5) - 7(p - 5) = 0or (p - 7) (p - 5) = 0 p = 5, 7II. q2 - 25 = 0or, q2 = 25 q = +5 p q
146. 3; I. 3x2 + 6x + x + 2 = 0or 3x(x + 2) + 1(x + 2) = 0or (x + 2) (3x + 1) = 0
x = –2,13
II. 2y2 + 4y + 5y + 10 = 0or 2y(y + 2) + 5(y + 2) = 0or (2y + 5) (y + 2) = 0
y = –2, 52
x y147. 4; I. x2 + 2x – x – 2 = 0
or x(x + 2)– 1(x + 2) = 0or (x – 1) (x + 2) = 0 x = 1, –2II. y2 – y – 2y + 2 = 0or y(y – 1) – 2(y – 1) = 0or (y – 1)(y – 2) y = l, 2x y
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LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
148. 1; I. 20x2 – 15x – 36x + 27 = 0or 5x(4x – 3) – 9(4x – 3) = 0or (5x – 9) (4x – 3) = 0
x = 9 3,5 4
II. 5y2 – 10y – 6y + 4 = 0or 5y(3y – 2) – 2(3y – 2) = 0or (5y – 2) (3y – 2)
2 2y ,5 3
x > y149. 5; I. 7x2 + 21x – 5x – 15 = 0
or 7x(x + 3) – 5(x + 3) = 0or (x + 3) (7x – 5) = 0
5x 3,7
II. y2 – 7y + y – 7 = 0or y(y – 7) + 1(y – 7) = 0or (y + 1) (y – 7) y =–1, 7 no relation between ‘x’ and ‘y’.
150. 1; I. x2 = 729 x = ±27II. y2 + 58y + 840 = 0or y2 + 28y + 30y + 840 = 0or y(y + 28) + 30(y + 28) = 0or (y + 30) (y + 28) = 0 y = –30, –28 x > y
151. 2; I. 1215 9 (x)
x x
1215 9or, x x
x
or, x = 4 x = 4II. y10 - (36)5 = 0or, y10 = (36)5
or y =15210(36) 36
y = 36 6 x y
152. 1; 5x + 2y = 96 ... (i)21x + 15y = 489 ... (ii)Now, eqn (i) × 15 and eqn (ii) × 2
75x + 30y = 144042x + 30y = 978- - - .33x = 462 x = 14
Putting the value of x in eqn (i), we get5 × 14 + 2y = 96 or, 2y = 96 - 70 = 26
or, y =262 = 13
x > y
153. 1; I. 1
2 22(441) x 111 (15)
or, 12 22(21) x 225 111 336
or, 21x2 = 336
x = 336 1621
II. 2 3121y 6 260 or, 11y2 + 63 = 260or, 11y2 = 260 - 216 = 44or, y2 = 4 y = +2 x > y
154. 3; I. 17x = 169+ 14 + 25 + 4xor, 13x = 208
x = 208 1613
II. 9y - 4y = 345 - 260 = 85or, 5y = 85 y = 17 x < y
155. 3; I. 3x2 - 13x + 14 = 0or, 3x2 - 7x - 6x + 14 = 0or,3x(x - 2) -7(x - 2) = 0or, (3x - 7) (x - 2) = 0
x = 7 ,23
II. y2 - 7y + 12 = 0or, y2 - 4y - 3y + 12 = 0or, y(y - 4) -3(y - 4) = 0or,(y -3)(y - 4) = 0 y = 4, 3 x < y
156. 2; I. 2x2 - 8x - 7x + 28 = 0or 2x(x - 4) - 7(x - 4) = 0or (2x - 7) (x - 4) = 0
7x 4,2
II. 2y2 + 10y - 7y - 35 = 0or 2y(y + 5) - 7(y + 5) = 0or (2y - 7)(y + 5) = 0
7y , 52
x y157. 1; 28x - 20y = 96
28x + 21y = 301- - - . -41y = -205 y = 5 and x = 7 x > y
158. 3; I. x = 3 2744 14
II. y = 487 = 22
484 32
x < y159. 5; I. x2 - x - 8x + 8 = 0
or x(x - 1) - 8(x - 1) = 0or (x - 1) (x - 8) = 0 x = 1, 8II. 2y2 - y - 10y + 5 = 0or y(2y - 1) - 5(2y - 1) = 0or (y - 5) (2y - 1) = 0
y = 5, 12
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LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
160. 1; I. 2x2 + 2x + x + 1 = 0or 2x(x + 1) + 1(x + 1) = 0or (x + 1)(2x + 1) = 0
1x 1, 0.52
II. 6y2 + 9y + 8y + 12 = 0or 3y(2y + 3) + 4(2y + 3) = 0or (3y + 4) (2y + 3) = 0
4 3y , 1.33, 1.53 2
x > y161. 2; I. 3x2 - 29x + 56 = 0
or 3x2 - 21x - 8x + 56 = 0or 3x(x - 7) - 8(x - 7) = 0or (3x - 8) (x - 7) = 0
x = 8 ,73
II. 3y2 - 5y - 8 = 0or 3y2 + 3y - 8y - 8 = 0or 3y(y + 1) - 8(y + 1) = 0or (3y - 8) (y + 1) = 0or (3y - 8) (y + 1) = 0
y = 81,3
x y162. 4; I. 5x2 + 26x - 24 = 0
or 5x2 + 30x - 4x - 24 = 0or 5x(x + 6) - 4(x + 6) = 0or (5x - 4) (x + 6) = 0
x = 4 , 65
II. 5y2 - 30y - 4y + 24 = 0or 5y(y - 6) - 4(y - 6) = 0or (5y - 4) (y - 6) = 0 4
y = 4 ,65
x y163. 1; I. x2 - 7x = 0
or x (x - 7) = 0 x = 0, 7II. 2y2 + 5y + 3 = 0or 2y2 + 2y + 3y + 3 = 0or 2y(y + 1) + 3(y + 1) = 0or (2y + 3) (y + 1) = 0
y = 31,2
x > y164. l ; 7x - 4y = 40 ...(i)
and 8x + 8y = 8or x + y = 1 ...(ii)Solving (i) and (ii), we have x = 4, y = -3 x > y
165. 3; I. 15x2 - 4!x + 14 = 0or 15x2 - 6x - 35x + 14 = 0or 3x(5x - 2) - 7(5x - 2) = 0or (3x - 7)(5x - 2) = 0
x = 7 2,3 5
II. 2y2 - 13y + 20 = 0or 2y2 - 8y - 5y + 20 = 0or 2y(y - 4) - 5(y - 4) = 0or (2y - 5) (y - 4) = 0
y = 54,2
x < y
166. 5; I. 2x 8 3x 45 0
2or, x 5 3x 3 3x 45 0
or,x(x 5 3) 3 3(x 5 3) 0
or,(x 3 3)(x 5 3) 0
x 3 3, 5 3
II. 2y 2y 24 0
2or y 4 2y 3 2y 24 0
or (y 4 2y)(y 3 2) 0
or (y 3 2)(y 4 2)
y 3 2,4 2 Hence relation cannot be established between xand y.
167. 2; I. x 7 2x 24 0
or x 4 2x 3 2x 24 0
or x( x 4 2) 3 2( x 4 2) 0
or ( x 3 2)( x 4 2) 0
Now, if x 3 2 0
then x 3 2
x = 9 × 2 = 18
If x 4 2 0
then x 4 2
x = 16 × 2 = 32
II. y 5 2y 12 0
or y 3 2y 2 2y 12 0
or y( y 3 2) 2 2( y 3 2) 0
or ( y 2 2)( y 3 2) 0
If ( y 2 2) 0
then y 2 2
y = 4 × 2 = 8
if y 3 2 0
then y 3 2
y = 9 × 2= 18 x y
168. 4; I. 12x2 - 17x + 6 = 0or 12x2 - 9x - 8x + 6 = 0or 3x(4x - 3) - 2(4x - 3) = 0or (3x - 2) (4x - 3) = 0
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LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
If 3x - 2 = 0then 3x = 2
2x3
If 4x - 3 = 0
then x = 34
II. 20y2 - 31y + 12 = 0or 20y2 - 16y - 15y + 12 = 0or 4y(5y - 4) - 3(5y - 4) = 0or (4y - 3) (5y - 4) = 0
3 4y ,4 5
Hence x y169. 5; I. 3x2 - 8x + 4 = 0
or 3x2 - 6x - 2x + 4 = 0or (3x - 2) (x - 2) = 0
2x 2,3
II. 4y2 - 15y + 9 = 0or 4y2 - 12y - 3y + 9 = 0or 4y(y - 3) - 3(y - 3) = 0or (4y - 3) (y - 3) = 0
3y , 34
Relation cannot be established between x and y.170. 1; I. x2 - 16x + 63 = 0
or x2 - 9x - 7x + 63 = 0or x(x - 9) - 7(x - 9) = 0or (x - 7) (x - 9) = 0 x = 7, 9II. y2 - 2y - 35 = 0or y2 - 17y + 5y - 35 = 0or y(y - 7) + 5(y - 7) = 0or (y + 5) (y - 7) = 0 y = -5, 7Hence, x y
171. 5; I. 63x 94 x 35 0
or, or,63x 49 x 45 x 35 0
or, (9 x 7)(7 x 5) 0
49 25x ,81 49
II. 32y 52 y 21 0
or, 32y 28 y – 24 y 21 0
or,(4 y 3).(8 y 7) 0
9 49y ,
16 64Therefore relation can’t be established between xand y.
172. 1; I. 2x 7 3x 35 15 5 5x
2or, x 5 5x 7 3x 35 15 0
or, (x 7 3)(x 5 5) 0
x 7 3, 5 5
II. 2y 5 5y 30 0
2or, y 3 5y 2 5y 30 0
or, (y 3 5), (y 2 5) 0
y 3 5, 2 5173. 3; I. 14x2 + 11x - 15 = 0
or (7x - 5) (2x + 3) = 0
5 3x ,7 2
II. 20y2 - 31y + 12 = 0or (4y - 3), (5y - 4) = 0
3 4y ,4 5
x < y174. 1; I. 5x + 4y = 41 ... (i)
II. 4x + 5y = 40 ... (ii)On solving both equations, we havex = 5 and y = 4 x > y
175. 3; I.
152
2
(18)x 0x
5 152 2or x (18)
x = (18)3
II.
92(19)y 0
y
3 92 2or y (19)
y = (19)3
x < y
176. 5; I. 63x 194 x 143 0
or63x 117 x 77 x 143 0
or (7 x 13)(9 x 11) 0
169 121x ,49 81
II. 99y 225 y 150 0
or 99y 90 y 165 y 150 0
or (11 y 10)(9 y 15) 0
100 225y ,121 81
Therefore relation cannot be established betweenx and y.
177. 2; I. 16x2 - 40x - 39 = 0or 16x2 - 52x + 12x - 39 = 0or (4x- 13) (4x + 3)
13 3x ,4 4
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LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
II. 12y2 - 113y + 255 = 0or 12y2 - 45y - 68y + 255 = 0or (4y - 15) (3y - 17) = 0
15 17y ,4 3
Therefore y > xor, x < y
178. 2; I. x 7 3x 36 0
or x 7 3. x 36 0
or x 3 3. x 4 3. x 36 0
or ( x 3 3)( x 4 3) 0
x = 27, 48
II. y 5 2y 7 2y 70 0
or y 5 2. y 7 2. y 70 0
or ( y 5 2)( y 7 2) 0
y = 50, 98 x < y
179. 1; I. 2x 7 7x 84 0
or (x 4 7)(x 3 7) 0
x 4 7,3 7
II. 2y 5 5y 30 0
or (y 2 5)(y 3 5) 0
y 2 5, 3 5
x > y180. 2; I. 10x + 6y = 13
II. 45x + 24y = 56
On solving both eqns, x =4 5, y5 6
x < y181. 2; I. x2 - 2x - 15 = 0
or,x2 - 5x + 3x - 15 = 0or, x(x - 5) + 3(x - 5) = 0or,(x - 5) (x + 3) = 0x = 5, -3II. y2 + 5y + 6 = 0or, y2 + 3y + 2y + 6 = 0or, y(y + 3) + 2(y + 3) = 0or,(y + 3)(y + 2) = 0y = -3, -2
x y
182. 5; I. x2 - x - 12 = 0or, x2 - 4x + 3x - 12 = 0or, x(x - 4) + 3(x - 4) = 0or, (x - 4) (x + 3) = 0 x = 4, -3II. y2-3y + 2 = 0or, y2 - 2y - y + 2 = 0
or, y(y - 2) - 1 (y - 2) = 0or, (y - 2)(y - 1) = 0 y = 2, lHence, no relation can be established.
183. 2; I. x 169 0
or,x 169
x 13
II. y2 - 169 = 0or, y2 = 169
or, y = 169
y = ±13
Hence, x y
184. 3; I. x2 - 32 = 112or, x2= 112 + 32 = 144
or, x = 144
x = ±12
II. y - 256 = 0
or, y = 256
y = 16Hence, x < y
185. 5; I. x2 - 25 = 0or, x2 = 25
or, x = 25
x = ±5II. y2 - 9y + 20 = 0or, y2 - 5y - 4y + 20 = 0or, y(y - 5) - 4(y - 5) = 0or, (y - 5) (y - 4) = 0 y = 5, 4Hence, no relation can be established.
186. 3; 3x + 5y = 69 ... (i)9x + 4y = 108 ... (ii)x + z = 12 ... (iii)Now, from (i) and (ii), we have3x + 5y = 69 ... (i) × 49x + 4y = 108 ... (ii) × 512x + 20y = 27645x + 20y = 540
- 33x = - 264On subtracting, we getor, 33x = 264
x = 26433
= 8
Putting the value of x in equation (i), we get 3 × 8+ 5y = 69or, 5y = 69 - 24 = 45
y = 455 = 9
Again, putting the value of x in equation (iii),we get
308
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
x + z = 12or, z = 12 - 8 = 4Hence, x < y > z
187. 3; I. 1 13 43 4y 9 9 9 9 9
...(I)
II. 2x + 5z = 54 .. (ii)III. 6x + 4z = 74or, 3x + 2z = 37 ... (iii)From equation (ii) × 2 - (iii) × 5, we get
4x + 10z = 10815x + 10z = 185
- - - . - 11x = - 77or, 11x = 77 x = 7Putting the value of x in equation (ii), we get2 × 7 + 5z = 54or, 5z = 40 z = 8Hence, x < y > z
188. 2; I. 2x + 3y + 4z = 66 ... (i)II. 2x + y + 3z = 42 ... (ii)III.3x + 2y + 4z = 63 ... (iii)From (iii) and (i),x - y = - 3 ...(iv)From equation (i) × 3 - equation (ii) × 46x + 9y + 12z = 1988x + 4y + 12z = 168- - - - .2x + 5y = 30 ... (v)Solving equation (iv) and (v), we get
x = 5, y = 8Now, on putting the value of x and y in equation(i),
10 + 24 + 4z = 66or, 4z = 32
32z 84
Hence, x < y = z189. 1; I. (x + z)3 = 1728 = 123
or, x + z = 12 ...(i)II. 2x + 3y = 35 ... (ii)III. x - z = 2 ...(iii)Now, equation (i) and (ii),x = 7, z = 5Putting the value x in question (ii) we have,2 × 7 + 3y = 35or, 3y = 35 - 14 = 21
or, y = 213
= 7
Hence, x = y > z190. 2; 4x + 5y = 37 ... (i)
x + z = 8 ... (ii)7x + 3y = 36 ... (iii)From equation (i) and (iii),
4x + 5y = 37 ... (i) × 37x + 3y = 36 ... (ii) × 5
or, 12x + 15y = 11135x + 15y = 180- - - .-23x = - 69 x = 3
Putting the value of x in equation (i)4 × 3 + 5y = 37
or, y =25 55
Now, putting the value of x in equation (ii)z = 5. Hence, x < y = z
191. 4; I. 7x + 3y = 77 ... (i)
II. 2x + 5y = (2601)12 = 51 ...(ii)
Now, 7x + 3y = 77 ... (i) × 52x + 5y = 51 ... (ii) × 3
or, 35x + 15y = 385 6x + 15y = 153- - - .29x = 232
232x 829
Putting the value of x in equation (i), we have7 × 8 + 3y = 77or, 3y = 77 - 56 = 21
or, y = 213
= 7
Hence, x > y
192. 3; I. 3x2 - 6x - 17x 2 17 = 0
or, 3x(x - 2) - 17 (x - 2) = 0
or, (3x 17)(x 2) 0
x = 2, 173
II. 10y2 - 18y - 5 17y 9 17y 0
or, 2y(5y - 9) - 17 (5y - 9) = 0
or, (2y - 17 ) (5y - 9) = 0
17 9or, y ,2 5
193. 4; I. 12(289) x 324 203
or, 17x - 18 = 203or, 17x = 221
x = 22117 = 13
II. 12(484) y 225 183
or, 22y - 15 = 183
309
LEARN MATHS FROM S.K. RAJU (9811549822, 9811649822)
or, 22y = 198
198y 922
Hence, x > y194. 1; I. 511x2 = 3066
2 3066or, x 6511
x 6 II. 12y3 - 9y3 = 1536or, 3y3 = 1536
or, y3 =1536
3 = 512 = 83
y = 8 Hence, x < y
195. 4, I. 3x + 4y = (4681)12 = 41
or, 3x + 4y = 41 ... (i)
II. 3x + 2y = (961)12
3x + 2y = 31 ...(ii)Solving (i) and (ii), we get
3x + 4y = 41 ...(i) × 23x + 2y = 31 ...(ii) × 46x + 8y = 8212x + 8y = 124- - - . - 6x = - 42
42x 76
Putting the value of x in equation (i), we get 3 × 7
+ 4y = 41or, 4y = 41 - 21 = 20
or, y = 204 = 5
Hence, x > y
196. 5; I. 3x2 - 6x - 17x 2 17 0 ...(i)
or, 3x(x - 2) - 17 (x - 2) = 0
or, (3x - 17 )(x - 2) = 0
or, x = 2, 173
II. 10y2 - 15y + 17y 3 17 0
or, 5y(y - 3) + 17 (y - 3) = 0
or, (5y + 17 ) (y - 3) = 0
17y 3,5
197. 2; I. x2 - 16x + 63 = 0or, x2 - 9x - 7x + 63 = 0or, x(x - 9) - 7(x - 9) = 0or, (x - 7) (x - 9) = 0 x = 7, 9II. y2 - 2y - 35 = 0or, y2 - 7y + 5y - 35 = 0or, y(y - 7) + 5(y - 7) = 0or, (y - 7) (y + 5) = 0 y = 7, - 5Hence, x y