ESTD 2005

P R MOUNT SSC CGL

COACHING Pre + MAINS

ALGEBRA (LEVEL-1&2) Maths by Ramdev Bhati

(A) 3 (B) 4
1 1
If x  = 2 then find the value of x  2 :
2
1. (C) 5 (D) 6
x x
1 1
(A) 2 (B) 3 10. If x  = 5 find the value of x  x
(C) 4 (D) 5 x
(A) 3 (B) 4
1 1
If x  = 4 then find the value of x  3 :
3
2. (C) 5 (D) 6
x x
(A) 50 (B) 52 11. If a * b = 2a - 3b +ab, than 3 * 5 + 5 * 3 is equal to :
(C) 56 (D) 76 (A) 22 (B) 24
1 1 (C) 26 (D) 28
If x  = 5 then find the value of x  4 :
4
3.
x x 2a  b ab
(A) 525 (B) 527 12. If a  4b = 3. then find the value of a  2b = ?
(C) 529 (D) 531
5 2
1 1 (A) (B)
If x  = 3 then find the value of x  5 :
5
4. 9 7
x x
(A) 117 (B) 119 10 10
(C) (D)
(C) 121 (D) 123 9 7
1 1 144 14.4
If x  = 47 then find the value of x  :
4
5. 13. If = , then the value of x is :
x4 x 0.144 x
(A) 2 (B) 3 (A) 144 (B) 14.4
(C) 4 (D) 5 (C) 1.44 (D) 0.0144
1 1
6. If x 
4
4 = 119 then find the value of
x : 14. If 1 < x < 2, then the value of ( x -1)2 +
x x
(A) 2 (B) 3 ( x -3)2 is :
(C) 4 (D) 5
(A) 1 (B) 2
1 (C) 3 (D) 2x - 4
1 x  2
4

7. If x  = 4 then find the value of x :

x x 2  3x  1
15. If a = 0.1039, then the value of 4a 2  4a  1  3a
is :
(A) 50 (B) 52
(A) 0.1039 (B) 0.2078
(C) 56 (D) 76
(C) 1.1039 (D) 2.1039
1 16. If a = 0.25, b = -0.05, c = 0.5, then the value of
1 x5 
8. If x  = 5 then find the value of x3 = ?
a 2  b2  c 2  2bc
x x  4x  1
2
is :
a 2  b 2  2ab  c2
(A) 525 (B) 527
(C) 529 (D) 531 7 14
(A) (B)
1 1 8 17
9. If x  = 29 then find the value of x  x = ?
x

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 25 ab
(C) 1 (D) (C)  ab (D) All of the above
16 2
17. If 3x+3 + 7 = 250, then x is equal to :
 1  1 2 1  2 1 
(A) 5 (B) 3 27.  x  x  x  x   x  2  1  x  2  1 is
(C) 2 (D) 1    x  x 
equal to :
1 2 3 4 5 31 1
18. If     .....   , the value of x
4 6 8 10 12 64 2 x 1 1
(A) x6 + 6 (B) x8 +
is : x x8
(A) 31 (B) 32
1 1
(C) 36 (D) 37 (C) x8 - 8 (D) x6 -
x x6
n /5 2 n 1
(243) .3 28. If x, y are two positive real numbers and x1/3 = y1/4,
19. The value of is :
9 n.3n –1 then which of the following relations is true ?
(A) 1 (B) 9 (A) x3 = y4 (B) x3 = y
(C) 3 (D) 3n (C) x = y4 (D) x20 = y15
20. If x = 0.5 and y = 0.2, then value of 0.6 × (3y)x is 29. If x is real then the minimum value of (x2 - x + 1) is :
equal to : 3
(A) (B) 2
(A) 1.0 (B) 0.5 4
(C) 0.6 (D) 1.1
1
3x  2 y (C) 1 (D)
4
21. If x : y = 3:4 then the value of x  y = ?

4 2 3 x  3 x
(A) (B) 30. If = 2 then x is equal :
9 3 3  x  3 x

17 3 5 12
(C) (D) (A) (B)
7 2 12 5
22. If a = 7, b = 5 and c = 3, then the value of a2 + b2 +
c2 - ab - bc - ca is : 5 7
(C) (D)
(A) 12 (B) -12 7 5
(C) 0 (D) 8
3
1 31. If a = 7  2 12 , and b = 7  2 12 , then (a +
x
23. If 7 = , then the value of x is : b3) is equal to :
343
(A) 3 (B) -3 (A) 40 (B) 44
(C) 48 (D) 52
1 1
(C) (D)
3 7 1 x  1 x
3
24. If 0.13  p2 = 13, then p is equal to : 32. If x = , then the value of is :
2 1 x  1 x
(A) 10 (B) 0.01
(C) 0.1 (D) 100 (A) - 3 (B) -1
1 (C) 1 (D) 3
25. For what value (s) fo a is x + x  a 2 a perfect
4 33. If x = 19 and y = 18 then the value of
square ?
x 2 + y 2 + xy
1 1 is :
(A)  (B)  x3 - y 3
18 8
(A) 1 (B) 37
1 1 (C) 324 (D) 361
(C)  (D)
5 4
x+4  x - 4
26. If a  b. then which of the following statements is 34. If = 2 then x is equal to :
true ? x+4  x - 4
(A) 2.4 (B) 3.2
ab ab
(A) = ab (B)  ab (C) 4 (D) 5
2 2

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 (C) 40 (D) 45
x3 3 45. If a3 - b3 - c3 - 3abc = 0 then :
35. If 1  = then x equals :
100 5 (A) a = b = c (B) a + b + c = 0
(A) 2 (B) 4 (C) a + c = b (D) a = b + c
(C) 16 (D) (136)1/3 46. If x = b + c + - 2a, y = c + a - 2b, z = a + b - 2c, then
the value of x2 + y2 - z2 + 2xy is :
(A) 0 (B) a + b + c
x 13
36. If 1  = , then the value of x is : (C) a - b + c (D) a + b + c
9 3 47. If (a - 1)2 + (b + 2)2 + (c + 1)2 = 0 then the value of
1439 (2a - 3b + 7c) is :
(A) (B) 160 (A) 12 (B) 3
9
(C) -11 (D) 1
1443 48. (y - z)3 + (z - x)3 + (x - y)3 is equal to :
(C) (D) 169 (A) 3 (y - z) (z - x) (y - x)
9
(B) (x - y) (y - z) ( x - z)
4 3 5 2 (C) 3 (y - z) (z - x) (x - y)
37. If = a + b 6 , then the values of a (D) (y - z) (z - x) (x - y)
48  18
49. If x2 + 2 = 2x, than the value of x4 - x3 + x2 + 2 is :
and b are respectively :
(A) 0 (B) 1
8 4 3 4 (C) -1 (D)
(A) , (B) , 2
15 15 11 33 50. If (3a + 1) + ( b - 1) + (2c - 3)2 = 0, then the
2 2

9 2 3 4 value of (3a + b + 2c) is equal to :

(C) , (D) , (A) 3 (B) -1
10 5 5 15
(C) 2 (D) 5
2 51. The value of the expression
38. If x+ = 10, then the value of x is :
4 (a  b)2 (b  c)2 (c-a) 2
3
7 + + is
5 (b  c)(c  a) (a  b)(c  a) (a-b ) (b -c)
6
:
1276 53 (A) 0 (B) 3
(A) (B)
135 6 1
(C) 4.35 (D) 9 (C) (D) 2
3
39. If 9 x = 12 + 147 , then x = ? 52. If (a - 3)2 + (b - 4)2 + (c - 9)2 = 0 then the value of
(A) 2 (B) 3 a  b  c is :
(C) 4 (D) 5 (A) -4 (B) 4
a (C)  4 (D)  2
40. If the sum of and its reciprocal is 1 and a  0, b 53. If a + b + c = 6, a2 + b2 + c2 = 14 and a3 + b3 + c3 =
b
= 0, then the value of a3 + b3 is : 36, then the value of abc is :
(A) 2 (B) -1 (A) 3 (B) 6
(C) 0 (D) 1 (C) 9 (D) 12
41. If a = 23 and b = -29 then the value of 25a2 + 40ab 54. If x - y = 2 and xy = 24, then the value of (x2 + y2)
+ 16b2 is : is :
(A) 1 (B) -1 (A) 25 (B) 36
(C) 0 (D) 2 (C) 63 (D) 52

2 1 1 x2 y2
42. If n + n + n + n = 97 then the value of n is : 55. If the expression 2 + tx + is a perfect
3 2 7 y 4
(A) 40 (B) 42 square, then the values of t is :
(C) 44 (D) 46 (A)  1 (B)  2
43. If x - y = 2 and x2 + y2 = 20 the value of (x + y)2 is : (C) 0 (D)  3
(A) 38 (B) 36
56. If a + b = 1 and a3 + b3 + 3ab = k, then the value of
(C) 16 (D) 12
k is :
44. If x = 2 - 21/3 + 22/3, then the value of x3 - 6x2 + 18x +
(A) 1 (B) 3
18 is :
(C) 5 (D) 7
(A) 22 (B) 33
57. If a = x + y, b = x - y, c = x + 2y then a2 + b2 + c2 - ab

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 - bc - ca is : 68. Out of the given reponses, one of the factors of
(A) 4y2 (B) 5y2 (a2 - b2)3 + (b2 - c2)3 + (c2 - a2)3 is :
(C) 6y2 (D) 7y2 (A) (a + b) (a - b)
58. If ax2 + bx + c = a ( x - p)2, then the relation among (B) (a + b) (a + b)
a, b, c would be : (C) (a - b) (c - b)
(A) abc = 1 (B) b2 = ac (D) (b - c) (b - c)
(C) b2 = 4ac (D) 2b = a + c
59. If a + b + c + d = 1, then the maximum value of b2
69. If a = then the value of a3 + b3 is :
(1 + a) (1 + b) (1 + c) (1 + d) is : ba
2 (A) 6 ab (B) 0
1
(A) 1 (B) 2 (C) 1 (D) 2
 
2 4 4 15 x + 20
3 5 70. If x = , the value of +
(C) 4 (D)   5 3 x - 20
  4

60. x varies inversely as square of y. Given that y = 2 for x + 12

is :
x = 1, the value of x for y = 6 will be equal to : x - 12
(A) 3 (B) 9 (A) 1 (B) 2
1 1 (C) 3 (D) 5
(C) (D)
3 9 71. If 6x - 5y = 13, 7x + 2y = 23 then 11x + 18y =?
61. If x = -1, then the value of (A) -15 (B) 51
(C) 33 (D) 15
1 1 1 1 1 1 1
+ + + + + + - 1 is : 72. The value of
99 98 97 96 95 94
x x x x x x x (xb + c)b - c (xc + a)c - a (xa + b)a - b (x  0 ) is :
(A) 1 (B) 0 (A) 1 (B) 2
(C) -2 (D) -1 (C) -1 (D) 0
62. If a2 + c2 + b2 = 2 (a - b - c) -3, then the value of 2a 73. If p = 99, then value of p(p2 + 3p + 3) is :
- b + c is : (A) 999 (B) 9999
(A) 3 (B) 4
(C) 99999 (D) 999999
(C) 0 (D) 2
63. If x2 - y2 = 80 and x - y = 8 then the average of x 74. If p = 124, 3
p(p 2  3p  3)  1 = ?
and y is :
(A) 2 (B) 3 (A) 5 (B) 7
(C) 4 (D) 5 (C) 123 (D) 125
75. The expression x4 - 2x2 + k will be a perfect square
1 when the value of k is :
64. If = a 3 4 + b 3 2 + c and a, b, c
4  3 2 1
3 (A) 2 (B) 1
are rational nuymbers theen a + b + c is equal to : (C) -1 (D) -2
76. If p - 2q = 4, then the value of p3 - 8q3 - 24pq - 64 is :
(A) 0 (B) 1 (A) 2 (B) 0
(C) 2 (D) 3 (C) 3 (D) -1
65. If x2 + 9y2 = 6xy then x : y is
(A) 1 : 3 (B) 3:2 1 3
77. If a2 - 4a -1 = 0, then value fo a2 +  3a 
(C) 3 : 1 (D) 2:3 a2 a
4x is :
66. If + 2P = 12 for what value iof P, x = 6 ? (A) 25 (B) 30
3
(C) 35 (D) 40
(A) 6 (B) 4
(C) 2 (D) 1 78. If a2 + 1 = a, than the value of a12 + a6 + 1 is :
(A) -1 (B) 1
x - a 2 x  b2 x  c2 (C) 2 (D) 3
67. If   = 4 ( a + b + c), then x is
bc ca ab
79. The minimun value of (x - 2) (x - 9) is :
equal to :
(A) (a + b + c)2 11 49
(A)  (B)
(B) a2 + b2 + c2 4 4
(C) ab + bc + ca 49
(D) a2 + b2 + c2 - ab - bc - ca (C) 0 (D) 
4

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80. One of the factors of the expression 4 3x2 + 5x - 1
89. If x2 - 4x - 1 = 0 then the value of x2 + is
x2
2 3 is :
(A) 4 (B) 10
(A) 4x + 3 (B) 4x + 3 (C) 12 (D) 18
(C) 4x - 3 (D) 4x - 3 1
90. If x = 3 + 8 , then x2 + is equal to
x2
81. If x = 3 - 5 , then the value of x2 - 16x +6 is : (A) 38 (B) 36
(A) -1 (B) -2 (C) 34 (D) 30
(C) 2 (D) 4 1
91. If x2 - 3x + 1 = 0 then the value of x + is
x
82. If x = 3 5 + 2, then the value of x3 - 6x2 + 12x - 13 is
(A) 0 (B) 1
(A) -1 (B) 1 (C) 2 (D) 3
(C) 2 (D) 0
 3 1 
 1 92. If x = 3 + 2 , then the value of  x  x3  is
83. If x = 7 - 4 3 , then the value of  x +  is :  
 x
(A) 6 3 (B) 12 3
(A) 3 3 (B) 8 3
(C) 18 3 (D) 24 3
(C) 14 + 8 3 (D) 14
93. If x + y = 7 , then the value of x3 + y3 + 21xy is
5 7 13 16
84. If p = , q = ,r= and s = then : (A) 243 (B) 143
8 12 16 29 (C) 343 (D) 443
(A) p < q <r < s (B) s < q <p <r
(C) p < r <q < r (D) s < r <p <q 94. If x1/3 + y1/3 = z 1/3 then {( x + y- z)3 + 27 xyz } equal
1 (A) -1 (B) 1
85. If x = 3 + 2 2 , then the value of x - is : (C) 0 (D) 27
x
(A) 1 (B) 2 2 1  1
95. If x - = 4 then  x   is equal to
(C) 2 (D) 3 3 x  x

3 1 3 1 (A) 5 2 (B) 2 5
86. If x = and y the value of x2 + y2 is
3 1 3 1 (C) 4 2 (D) 4 5
(A) 14 (B) 13
(C) 15 (D) 10  2 1 
96. If x = 3 + 8 , then the value of  x + 2  is
 x 
x 3 6 y-x (A) 34 (B) 24
87. If y = the value of + y + x is : (C) 38 (D) 36
4 7
2 1 1
(A) 1 (B) 97. If 4b2 + 2 = 2 , then the value of 8b3 + is
7 b b3
3 3 (A) 0 (B) 1
(C) (D) 1 (C) 2 (D) 5
7 7
1 1
5 1 5 1 98. It 2p + p = 4 the value of p3 + 3 is
8p
88. If a = and b = then the value of
5 1 5 1 (A) 4 (B) 5
2 2 (C) 8 (D) 15
a  ab  b
is ba
a 2  ab  b 2 99. If 1.5 a = 0.04 b then is
ba
3 4
(A) (B) 73 77
4 3
(A) (B)
3 5 77 33
(C) (D) 2 75
5 3
(C) (D)
75 2

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 to
 1 
100. If x = 5 + 2 6 , then the value of  x +  is (A) 1 (B) 2
 x (C) 3 (D) 4
(A) 2 2 (B) 3 2 a b
112. If + = 1, a  0, b 0, the value of a3 + b3 is
(C) 2 3 (D) 3 3 b a
(A) 0 (B) 1
 3 1  (C) -1 (D) 2
101. If x = ( 2 + 1)-1/3 the value of  x  3  is 113. If a2 + b2 + c2 + 3 = 2 (a + b + c) the value of (a + b +
 x 
c) is
(A) 0 (B) - 2 (A) 2 (B) 3
(C) -2 (D) 3 2 (C) 4 (D) 5
2
x  x 1 2  1 2p 1
102. If then the value of  x +  is
= 1
2
x  x 1 3  x 114. If 2 = , p  0, then the value of p + p is
p  2p  1 4
(A) 4 (B) 5
(C) 6 (D) 8 (A) 4 (B) 5
103. For a > b , if a + b = 5 and ab = 6, then the value of (a2 (C) 10 (D) 12
- b2) is 1 2 1
(A) 1 (B) 3 115. If x - = 5 , then x + 2 is :
x x
(C) 5 (D) 7
(A) 5 (B) 25
104. If a4 + b4 = a2b2 then (a6 + b6) equals
(C) 27 (D) 23
(A) 0 (B) 1
(C) a2 + b2 (D) a2b4 + a4b2
 1 
e 2a 2  3c 2  4e 2 116. If x = 3 + 2 2 then the value of  x  x  is :
a c  
105. If = = f = 3 then =?
b d 2b 2  3d 2  4 f 2 (A) 1 (B) 2
(A) 2 (B) 3 (C) 2 2 (D) 3 3
(C) 4 (D) 9
106. If a1/3 = 11, then the value of a2 - 331a is 117. If x, y and z are real numbers such that (x - 3)2 + (y -
(A) 1331331 (B) 1331000 4)2 + (z - 5)2 = 0 then (x + y + z) is equal to
(C) 1334331 (D) 13330030 (A) -12 (B) 0
(C) 8 (D) 12
1 1
107. If x2 + y2 + + = 4 , then the value of x2 + y2 is
x 2 y2 a b c abc
(A) 2 (B) 4 118. If = = , then is equal to
2 3 5 c
(C) 8 (D) 16 (A) 2 (B) 4
108. If x2 = y + z, y2 = z + x, z2 = x + y , then the value of (C) 5 (D) 6
1 1 1 1
+ y 1 + is 1 x3 +
x 1 z 1 119. If x + = 3 then the value of x is :
(A) -1 (B) 1 x x2  x  1
(C) 2 (D) 4
3 5
(A) (B)
1 2 2
109. If x +
x
= 3 then the value of x18 + x12 + x6 + 1 is
7 11
(C) (D)
(A) 0 (B) 1 2 2
(C) 2 (D) 3
110. If a2 + b2 = 2 and c2 + d2 = 1 then the value of 1
120. If a + + 1 = 0 (a  0) then the value of (a4 - a) is
a
(ad - bc)2 + (ac + bd)2 is (A) 0 (B) 1
4 1 (C) 2 (D) -1
(A) (B)
9 2
(C) 1 (D) 2  2 1 
121. If x = 3 + 2 then the value of  x + x 2  is
1 2 1
111. If x + = 2, x  0 then value of x + 3 is equal (A) 4 (B) 6
x x
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 (C) 9 (D) 10 (C) 2 (D) 4
ab
9  2 9  132. If a2 + b2 + 2b + 4a + 5 = 0, then the value of is
122. If x + = 6, then the value of  x + 2  is ab
x  x 
(A) 3 (B) -3
(A) 8 (B) 9
(C) 10 (D) 12 1 1
(C) (D) 
3 3
1 1
123. If x = a + and y = a - , then the value of x4 + y4 1 1
a a 1
2 2 133. If x + y = + y (x y  0, x y) then the value
- 2x y is x
(A) 24 (B) 18 3 3
of x - y is
(C) 16 (D) 12 (A) 0 (B) 1
1 1 (C) -1 (D) 2
124. If x + = 2. find the value of 8x3 + 3
2x x 134. If x = a (b - c), y = b (c - a) and z = c (a - b), then
(A) 48 (B) 88 3 3 3
(C) 40 (D) 44 x  y  z 
a  +b +c =
1      
125. If x + = 2 and x is real then the value of x17 +
x xyz
(A) (B) 3xyzabc
1 3abc
is
x19
3xyz xyz
(A) 1 (B) 0 (C) (D)
abc abc
(C) 2 (D) -2
1
126. If for two real constants a and b the expressiion ax3 135. If xy (x + y) = 1, then the value of - x3 - y3 is
+ 3x2 - 8x + b is exactly divisible by (x + 2) and (x - 2), x3 y 3
then :
(A) a = 2, b = 12 (B) a = 12, b = 12 (A) 0 (B) 1
(C) a = 2, b = -12 (D) a = -2, b = 12 (C) 3 (D) -2
127. If x2 +y2 + 2x + 1 = 0, then the value of x31 + y35 is x 1  1
(A) -1 (B) 0 136. If = value of  x  x  is
2
2x + 5x + 2 6  
(C) 1 (D) 2
a b 2a  3b 1
128. If = ,then value of is (A) 2 (B)
3 2 3a  2b 2

12 5 1
(A) (B) (C) - (C) -2
5 12 2
12 2x - y 1 3x - y
(C) 1 (D) 137. If x + 2y = then vlaue of 3x + y is :
7 2
1 3 1
129. If x + = , find the value of 8x3 + 3 . 1 3
4x 2 8x (A) (B)
5 5
(A) 18 (B) 36
(C) 24 (D) 16 4
(C) (D) 1
4ab x + 2a x + 2a 5
130. If x = (a b) the value of + is
ab x  2a x  2a 1 2x
(A) a (B) b 138. If x  = 5, then 2 is equal to
x 3x - 5x + 3
(C) 2 ab (D) 2
1
1 (A) 5 (B)
131. If m + = 4, find the value of (m - 2)2 + 5
m2
1
1 (C) 3 (D)
3
 m  2 2
1
(A) -2 (B) 0 139. If x4 +
= 119 and x > 1, then the value of
x4
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 1 (A) 2 2 (B) 2 3
x3  3 is
x (C) 2 (D) 3
(A) 54 (B) 18 149. If p + q = 10 and pq = 5, then teh numerical value
(C) 72 (D) 36 p q
x+ y of q + p will be
xy
140. If x - y = = the numberical value of xy
7 4 (A) 16 (B) 20
is (C) 22 (D) 18
4 3 1 1
(A) (B) 150. If a + = 3 then the value of a6 - + 2 will
3 4 a a6
be
1 1
(C) (D) (A) 1 (B) 2
4 3
(C) 30 3 (D) 5
x2 y2 z2
141. If x + y + z = 0, then + + =? 1
yz zx xy 151. If x3 + y3 = 35 and x + y = 5 , then the value of
x
(A) (xyz)2 (B) x2 + y2 + z2
(C) 9 (D) 3 1
+ y will be
1
142. If a + b + c = 0, then the value of (a  b) (b  c) +
1 5
(A) (B)
3 6
1 1
(a  c) (b  a) + (a  c) (c  b) is : 2
(C) 6 (D)
(A) 1 (B) 0 3
(C) -1 (D) -2 152. If x = 3 + 2 2 and xy = 1, then the value of
1 3 1
143. If 3 x  = 5, then the value of 8 x  is : x 2  3 xy  y 2
2x 27 x3 is
x 2  3 xy  y 2
1 10
(A) 118 (B) 30
2 27 30 37
(A) (B)
(C) 0 (D) 1 31 31
144. If x + y = z , then the expression x3 + y3 - z3 + 3xyz 35 34
will be equal to : (C) (D)
51 31
(A) 0 (B) 3xyz
(C) -3xyz (D) z3 153. If a3 - b3 = 56 and a - b = 2, then value of a2 + b2 will
be
2
 1 (A) 84 (B) 20
145. If  x   = 3 then the value of (x72 + x66 + x54 + (C) 22 (D) 5
 x
x36 + x24 + x6 +1) is a b
154. If (a2 + b2)3 = (a3 + b3)2, then + is
(A) 1 (B) 2 b a
(C) 3 (D) 4
1 2
a 2  b2  c2 (A) (B)
146. If a + b + c = 0, then the value of is 3 3
a 2  bc
1 2
(A) 0 (B) 1 (C)  (D) 
(C) 2 (D) 3 3 3
2 1
 1 155. If x  = 5 , then the value of
147. If  x   = 3 , then the value of x206 + x200 + x90 x
 x
+ x84 + x18 + x12 + x6 + 1 is x4  3x3  5x2  3x 1
(A) 0 (B) 1
x4  1
(C) 84 (D) 206
43 47
 1 (A) (B)
148. If x = 3 + 2 , then the value of  x 
x 
is 23 21

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 (C) 756 (D) 160
41 45
(C) (D) 2
23 21  1 3 1
156. If ax + by = 3, bx - ay = 4. and x + y2 =1, then the
2 166. If  a +  = 3 then a + 3 = ?
 a  a
value jof a2 + b2 is
(A) 17 (B) 16 (A) 2 3 (B) 2
(C) 25 (D) 28
(C) 3 3 (D) 0
1 3 1
157. If x is real, x +  0 and x + 3 = 0. then the x 1 1
x x 167. If = - , then the value of x - x2 is :
a a x
4
 1
1
value of  x +  is
 x (A) -a (B)
a
(A) 4 (B) 9
(C) 16 (D) 25 1
(C) - (D) a
a
1  5 1 
158. If x + = 3, then the value of  x + 5  is x 1 1
x  x  3
168. If 2 = , then the value of x + 3 is :
(A) 322 (B) 126 x  2x  1 3 x
(C) 123 (D) 113 (A) 81 (B) 110
(C) 125 (D) 27
1 3 1
159. If x - = 3, the value of x - 3 is
x x  1 4 1
169. If  x +  = 4, then the value of x + 4 is :
(A) 32 (B) 36  x  x
(C) 40 (D) 49 (A) 64 (B) 194
1 1 (C) 81 (D) 124
160. If m4 + 4 = 119, then m  =? 170. If x2 + y2 + z2 = 2(x - y - z) - 3, then then value of2x
m m
- 3y + 4z [Assume that x, y, z are reall numbers] :
(A) 3 (B) 4
(A) 9 (B) 1
(C) 2 (D)  1 (C) 3 (D) 0
161. If x + y + z = 6 , then the value of (x - 1)3 + (y - 2)3 171. If a + b + c = 0, then the value of
+ (z - 3)3 is ab bc ca 
(A) 3 (x - 1) (y + 2) (z - 3)  c  a  b 
 
(B) 3 (x + 1) (y - 2) (z - 3)
(C) 3 (x - 1) (y + 2) (z + 3)  a b c 
(D) 3 (x - 1) (y - 2) (z - 3)  b  c  c  a  a  b  is :
 
x z
162. If x + y = 2z then the value of + y - z is (A) 8 (B) -3
x-z (C) 9 (D) 0
(A) 1 (B) 3
1
1 172. If a + = 4 , then the value of (a - 2)2 +
(C) (D) 2 a 2
2
2
 1 
x4  2
1  a  2  is
 
163. If x2 + 1 = 2x , then the value of x
x 2  3x  1 (A) 0 (B) 2
(C) -2 (D) 4
(A) 0 (B) 1
(C) 2 (D) -2
173. If x + y + z = 6 and x2 + y2 + z2 = 20 then the value
3 1 of x3 + y3 + z3 - 3xyz is :
164. If x = 3 + 2 , then the value of x  is : (A) 64 (B) 70
x3
(C) 72 (D) 76
(A) 14 2 (B) 14 3
3
 1
2 , the value of  x  x  is
(C) 22 2 (D) 10 2 174. If x = 1-
 
1 3 1
165. If x > 1 and x2 + = 83, then x - is (A) -8 (B) 8
2
x x3
(C) 2 2 (D) 1
(A) 764 (B) 150
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 (A) 32 (B) 16
a b
175. If + - 1 = 0, then the value of a3 + b3 is (C) 23 (D) -23
b a
(A) 3 (B) 0 3 2 3 2
184. If x = and y = then the value
(C) 1 (D) -1 3 2 3 2
of x3 + y3 is
1 100 x (A) 950 (B) 730
176. If x + = 99 find the value of 2
x 2 x  102 x + 2 (C) 650 (D) 970
185. If (x - a) (x - b) = 1 and a - b + 5 = 0, then the value
1 1
(A) (B) 1
6 2
of ( x  a)3 - ( x - a)3 is
1 1
(C) (D) (A) -125 (B) 1
3 4
(C) 125 (D) 140
2 1 186. If a2 + b2 + c2 = 2 (a - b - c) - 3, then the value of
177. If x = 3 + 2 2 the value of x + is 4a - 3b + 5c is
x2
(A) 36 (B) 30 (A) 2 (B) 3
(C) 32 (D) 34 (C) 5 (D) 6
2 3 1
178. If (x - 3)2 + (y - 5)2 + (z - 4)2 = 0. then the value fo 187. If 2x + = 3, then the value of x  3  2 is
x x
x2 y2 z 2
  is 9 25
9 25 16 (A) - (B) -
8 8
(A) 12 (B) 9
(C) 3 (D) 1 7
(C) (D) 11
 2 3 8
1
179. If x  3 -  = , then the value of x  2 is
2
188. If xy + yz + zx = 0, then
 x x x
 1 1 1 
1 4  2 + 2 + 2  ( x, y, z  0) is
(A) 2 (B) 2
9 9  ( x - yz ) (y - zx) ( z - xy ) 
1 4 equal to
(C) 3 (D) 3 (A) 3 (B) 1
9 9
(C) x + y + z (D) 0
1 1 189. If a + b + c = 9 (where a, b, c, are real numbers),
180. If x2 - 3x + 1 = 0, then the value of x2 + x + + 2 then the minimum value of a2 + b2 + c2 is
x x
(A) 100 (B) 9
is
(C) 27 (D) 81
(A) 10 (B) 2
190. If a + b + c = 15 and a2 + b2 + c2 = 83 then the
(C) 6 (D) 8
value of a3 + b3 + c3 - 3abc
(A) 200 (B) 180
4x - 3 4y -3 4z - 3
181. If + y + = 0 then the value of (C) 190 (D) 201
x z
5 1
191. If x 2  3x  1  0 , then the value of x  is
1 1 1 x5
+ + is
x y z equal to
(A) 9 (B) 3 (A) 87 (B) 123
(C) 4 (D) 6 (C) 135 (D) 201

182. If x = a - b, y = b - c, z = c - a then the numerical 192. If a - b = 3 and a3 - b3 = 117 then a  b is equal to

value of the algebraic expressiion x3 + y3 + z3 -
(A) 3 (B) 5
3xyz will be
(C) 7 (D) 9
(A) a + b + c (B) 0
(C) 4 (a + b + c) (D) 3abc 1 5 1
193. If x  = 1, then (x  1)  equals
x 1 (x  1)5
 a 2 b2 
183. If a2 + b2 = 5 ab, then the value of  2  2  is : (A) 1 (B) 2
b a  (C) 4 (D) 8

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194. If a + b + c = 0, then a3 + b3 + c3 is equal to (A) 1 (B) p+q+r
(A) a + b + c (B) abc (C) pqr (D) 0
(C) 2 abc (D) 3 abc
1
204. If a+b+c = 0 then the value of +
xy xz yz xb  x  c  1
195. If x + y = a , = b and y + z = c whre a, b,
x+ z
1 1
c are all non zero numbers then x equals to a + a is
x  x 1
c
x  x b  1
2abc 2 abc (A) 0 (B) 1
(A) (B)
ab + ac - ab ab + ac - bc (C) 2 (D) -1
2abc 2abc 205. If ax = (x+y+z)y, ay = (x+y+z)z and az = (x+y+z)x then
(C) (D) which of the following is true?
ab + bc - ab ab + bc + ac
(A) x+y+z = 0 (B) x+y+z =1
196. If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x (C) x+y+z = a (D) x+y+z  a
+ y) is equal to
(A) 70 (B) 40 p q r a b c
(C) 50 (D) 60 206. If + + = 1 and + q + = 0 then the
a b c p r
3 1
197. If x = 3
2  3 then the value of x  is p2 q2 r2
x3 value of + + is
a2 b2 c2
(A) 8 (B) 9
(C) 6 (D) 4 (A) 0 (B) 1
(C) -1 (D) 2
198. If m= 5  5  5  ... and n 5  5  5  ... 207. If x = 5 + 2 6 and y = 5-2 6 then the value of
then among the followig the relation between m &
n holds is x 2  xy  y 2
is
(A) m + n-1 = 0 (B) m - n -1 = 0 x 2  xy  y 2
(C) m - n + 1 = 0 (D) m + n + 1 = 0
99 97
3  5x 3  5 y 3  5z (A) (B)
97 99
199. If + 2y + = 0, then the value of
2x 2z
97 95
(C) (D)
2 2 2 95 97
+ y + is :
x z 208. If x =3+ 2 2 andy =3-2 2 then the value of is :
(A) 5 (B) 15
x 2  3xy  y 2
(C) 20 (D) 10
x 2 – 3xy  y 2
a 6 +a 4 +a 2 +1
200. If a = 2 + 3 , then the value of is : 31 35
a3 (A) (B)
(A) 56 (B) 45 35 31
(C) 65 (D) 42 37 31
(C) (D)
201. If x = 5 + 3 and y = 5 - 3 then the value 31 37
of x4-y4 is : 209. If a = 5 -2 6 and b = 5+2 6 then the value of
(A) 32 15 (B) 64 15 a 3  b3  2ab
is :
(C) 16 (D) 544 a 3  b3 – 2ab
1 3 1 141 243
202. If P4 = 119- p 4 , then the value of P - p3 is : (A) (B)
242 242
(A) 18 (B) 24 242 242
(C) 32 (D) 36 (C) (D)
243 241
1 210. 232 - (2+1) (22+1) (24+1) (28+1) (216+1) = ?
203. If pqr = 1 then the value of 1  p  q 1 + (A) 0 (B) 1
(C) 2 (D) 4
1 1
1 +
1 q  r 1  r  p 1 is

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 ANSWERS (LEVEL -1 )

1. (a) 2. (b) 3. (b) 4. (d) 5. (b) 6. (b) 7. (b) 8. (b) 9. (c) 10. (a)

11. (a) 12. (c) 13. (d) 14. (b) 15. (c) 16. (a) 17. (c) 18. (c) 19. (b) 20. (c)

21. (c) 22. (a) 23. (b) 24. (c) 25. (b) 26. (c) 27. (d) 28. (d) 29. (a) 30. (b)

31. (d) 32. (d) 33. (a) 34. (d) 35. (b) 36. (b) 37. (d) 38. (a) 39. (b) 40. (c)

41. (a) 42. (b) 43. (b) 44. (c) 45. (d) 46. (a) 47. (d) 48. (c) 49. (a) 50. (a)

51. (b) 52. (c) 53. (b) 54. (d) 55. (a) 56. (a) 57. (d) 58. (c) 59. (d) 60. (d)

61. (c) 62. (d) 63. (d) 64. (a) 65. (c) 66. (c) 67. (a) 68. (a) 69. (b) 70. (b)
71. (b) 72. (a) 73. (d) 74. (d) 75. (b) 76. (b) 77. (b) 78. (d) 79. (d) 80. (d)

81. (c) 82. (d) 83. (d) 84. (b) 85. (c) 86. (a) 87. (a) 88. (b) 89. (d) 90. (c)

91. (d) 92. (c) 93. (c) 94. (c) 95. (b) 96. (a) 97. (a) 98. (b) 99. (a) 100. (c)
101. (c) 102. (b) 103. (c) 104. (a) 105. (d) 106. (b) 107. (a) 108. (b) 109. (a) 110. (d)
111. (b) 112. (a) 113. (b) 114. (c) 115. (c) 116. (b) 117. (d) 118. (a) 119. (c) 120. (a)
121. (d) 122. (c) 123. (c) 124. (c) 125. (c) 126. (c) 127. (a) 128. (a) 129. (a) 130. (d)
131. (c) 132. (c) 133. (a) 134. (c) 135. (c) 136. (b) 137. (b) 138. (b) 139. (d) 140. (a)
141. (d) 142. (b) 143. (b) 144. (a) 145. (a) 146. (c) 147. (a) 148. (b) 149. (d) 150. (b)
151. (b) 152. (b) 153. (b) 154. (b) 155. (a) 156. (c) 157. (b) 158. (c) 159. (b) 160. (a)
161. (d) 162. (a) 163. (d) 164. (c) 165. (c) 166. (d) 167. (d) 168. (b) 169. (b) 170. (b)
171. (c) 172. (b) 173. (c) 174. (b) 175. (b) 176. (c) 177. (d) 178. (c) 179. (b) 180. (a)
181. (c) 182. (b) 183. (c) 184. (d) 185. (d) 186. (a) 187. (c) 188. (d) 189. (c) 190. (b)
191. (b) 192. (c) 193. (b) 194. (d) 195. (c) 196. (c) 197. (d) 198. (b) 199. (d) 200. (a)
201. (b) 202. (d) 203. (a) 204. (b) 205. (c) 206. (b) 207. (a) 208. (c) 209. (b) 210. (b)

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 ALGEBRA (LEVEL-2)
1. 3
16  3 32  1 = ? a b c
11. If + + = 1 then find the value of
b+c c+a a+b
(A) 3
4 1 (B) 3
4 1
(C) 3
2 1 (D) 3
2 1 a2 b2 c2
 
bc ca ab
 3
4  3 16  1  (A) 0 (B) 1
(A) 3
4 1 (B) 3
4 1 (C) 2 (D) 4

(C) 3
2 1 (D) 3
2 1 ab bc ca
12. If x = , y= and z = . Find the
ab bc ca
 x - a) (x - 3a) (x - 6a) (x - 8a) + ka4 . a is perfect value of a.
squre number. Find the value of k :
(A) 16 (B) 25 2xyz 2xyz
(A) xy  yz  zx (B) xy  yz  zx
(C) 81 (D) 4
4. (x - 2a ) (x - 5a ) (x - 8a) (x - 11a) + ka4, is a perfect 2xyz 2xyz
square. Find the value of k. (C) xy  yz  zx (D)  xy  yz  zx
(A) 16 (B) 25
(C) 81 (D) 4 1
13. If (x-a)(x-b) = 1 and a-b+3 = 0 then (x-a)3-
5. (x - 4a ) (x - 6a ) (x - 8a) (x - 10a) + ka a is a perfect4 (x  a)3
square no. Find the value of k. =?
(A) 16 (B) 25 (A) 18 (B) 36
(C) 81 (D) 4 (C) 72 (D) 9
5 1 1
6. If x   2525 then find the value of x  14. (x-a)(x-b) = 1 and a-b+5 = 0 then the value of (x-a)3-
x5 x
(A) 3 (B) 4 1
is :
(C) 5 (D) 6 (x  a)3
3 (A) 110 (B) 140
7. =? (C) 125 (D) 25
3
16  4  1 3

a b bc ca
(A) 3
4 1 (B) 3
4 1 15. If   = 1 and a-b+c  0 then
c a b
(C) 3
2 1 (D) 3
2 1 which of the following is true?
1 1 1 1 1 1 1
8. =? (A)   (B)  
3
4  3 2 1 c b a b a c
(A) 3
4 1 (B) 3
4 1 1 1 1 1 1 1 1
(C)   (D)   
(C) 3
2 1 (D) 3
2 1 a b c abc a b c
16. If x = 1+ 2  3 then find the value of
1
9. If = a 3 4  b3 2  c . Find the value of 2x4-8x3-5x2+26x-28 .
4  3 2 1
3
(A) 6 (B) 3 6
a + b + c.
(A) 0 (B) 1 (C) 6 6 (D) 2 6
(C) 2 (D) 4
17. If x = 5  2 then find the value of x3–6x2+12x-6 .
3
4 (A) 0 (B) 5
10. =?
3
25  3 5  1 (C) 6 (D) 7
18. If a =97, b = 98 and c = 99 then find the value of
(A) 3
5 1 (B) 3
5 1
a2+b2+c2-ab-bc-ca .
(C) 3
25  1 (D) 3
25  1 (A) 0 (B) 1
(C) 2 (D) 3

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19. If a =995, b = 997 and c = 999
3abc 3xyz
a2+b2+c2-ab-bc-ca = ? (A) (B)
(A) 0 (B) 4 xyz abc
(C) 6 (D) 12 (C) 3 (D) 1
20. If a =333, b = 333 and c = 334 then find the value of 32. If a = 1.11, b =2.22 and c = - 3.33 then find the value
a2+b2+c2-ab-bc-ca . of a3+b3+c3-3abc.
(A) 0 (B) 1 (A) 0 (B) 1
(C) 2 (D) 3 (C) 2 (D) 3
21. If a =332, b = 334 and c = 336 then find the value of 33. If a+b+1 = 0 then find the value of a3+b3+1.
a2+b2+c2-ab-bc-ca. (A) 3 (B) 1
(A) 0 (B) 4 (C) 3ab (D) 0
(C) 6 (D) 12 34. If a-b = 3, b-c = 5 and c-a =7 then find the value of
22. If a =555, b = 555 and c = 557 then find the value of
a2+b2+c2-ab-bc-ca . a 3  b 3  c 3  3abc
.
(A) 0 (B) 4 abc
(C) 6 (D) 12
1 1
23. If a =997, b = 998 and c = 999 then find the value of (A) 22 (B) 24
a3+b3+c3-3abc . 3 3
(A) 8888 (B) 9999 1 1
(C) 5928 (D) 8982 (C) 25 (D) 41
3 2
24. If a =995, b = 997 and c = 999 then find the value of
35. If a-b = 4 , b-c = 6 and c-a = 8 then find the value of
a3+b3+c3-3abc .
(A) 35892 (B) 35829 a 3  b 3  c 3  3abc
(C) 34692 (D) 34629 .
abc
25. If a =333, b = 333 and c = 334 then find the value of
(A) 116 (B) 58
a3+b3+c3-3abc .
(C) 29 (D) 85
(A) 0 (B) 1
36. If a= 2, b = 3 and c= -6 then find the value of
(C) 1000 (D) 999
26. If a =332, b = 334 and c = 336 then find the value of a 3  b 3  c 3  3abc
a3+b3+c3-3abc . .
ab  bc  ca  a 2  b 2  c 2
(A) 12042 (B) 12024
(A) -1 (B) 0
(C) 12124 (D) 10024
(C) 1 (D) 3
27. If a =555, b = 555 and c = 557 then find the value of
a3+b3+c3-3abc.
37. If xy + yz + zx= 0 then find the value of
(A) 6668 (B) 6686
(C) 3338 (D) 3383 1 1 1
+ + .
2 2 3 2 2 3
(a  b )  ( b  c )  (c  a ) 2 2 3 x 2  yz y 2  xz z 2  xy
28. =? (A) -1 (B) 0
(a  b ) 3  ( b  c ) 3  ( c  a ) 3
(C) 1 (D) 3
(A) (a+b) (b+c) (c+a) 38. If ab + bc + ca = 0 then find the value of
(B) 3(a+b) (b+c) (c+a)
(C) 1 (D) 3 a2 b2 c2
+ . +
a 2  bc b 2  ca c 2  ab
(a  b) 2 (b  c) 2 (c  a ) 2
29.  + =? (A) -1 (B) 0
(b  c)(c  a ) (a  b)(c  a ) (a  b)(b  c)
(C) 1 (D) 3
(A) (a+b) (b+c) (c+a) 39. If x2 +2 =2x then find the value of x4 - x3 + x2 + 2.
(B) 3(a+b) (b+c) (c+a) (A) -1 (B) 0
(C) 1 (D) 3 (C) 1 (D) 3
a 2 b2 c2 x2  a2 x2  b2 x2  c2
30. If a+b+c = 0 then find the value of   . 40. If + + = 4(a+b+c) then
bc ca ab bc ac ab
(A) 0 (B) 1 the value of x .
(C) 2 (D) 3 (A) a+b+c (B) (a+b+c)2
31. If x = a(b-c), y = b(c-a) and z = c(a-b) then find the 1
3 3 3
(C) (a+b+c) 2 (D) ab+bc+ca
x  y z
value of         . a 2
b c2 2
a  b c 41. If = = = 2 then find the
(by  cz ) (ax  cz) (ax  by )

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 x y z
value of ( a  2 x ) + (b  2 y ) + (c  2 z ) . x2 2 x2 3
+ is.
(A) 1 (B) 0 x-2 2 x2 3
(A) 0 (B) 1
1
(C) 2 (D) (C) 2 (D) 3
2
50. If x2 + x + 1 = 0 then the value of x3 + 1 is :
a2 b2 c2 (A) 0 (B) 1
42. If = = = 1 then find the value
by  cz ax  cz ax  by (C) 2 (D) 3

a b c 51. If x2 - x + 1 = 0 then the value of 1 + x3 + x9 + x18

of + b y + .
ax cz is:.
(A) 1 (B) 0 (A) 0 (B) 1
(C) 2 (D) 3
1
(C) 2 (D) 1
2 52. If x2 + = 1 then the value of x206 + x200 + x106
x2
43. If a2 = by +cz, b2 = cz + ax and c2 = ax + by then + x100 + x6 +1 is.
a b c (A) 0 (B) 1
find the value of +b y + . (C) 2 (D) 3
ax cz
(A) 1 (B) 0 1 1
53. If x + = 3 then the value of x17 + is.
x x 17
1
(C) 2 (D) (A) 3 (B) 2 3
2
44. If a2 = b + c, b2 = c +a and c2 = a + b then find the (C)  3 (D) 2 3
1 1 1
value of + + .
1 a 1 b 1 c 54. If x = 15 then the value of x5 - 16x4 + 16x3 - 16x2 + 15x
(A) 1 (B) 0 + 15 is :
1 (A) 0 (B) 15
(C) 2 (D) (C) 30 (D) 1
2
55. If x = 15 then the value of x5 - 16x4 + 16x3 - 16x2 + 16x
45. If a2 + b2 + c2 = 16 and a + b + c = 4 3 . Find the ratio + 15 is:
of a, b and c. (A) 0 (B) 15
(A) 1:2:3 (B) 2:3:4 (C) 30 (D) 1
(C) 1:1:1 (D) 1:2:1 1
x6  2
46. If x = 56. If x = 3 + 2 2 then find the value of x is.
3 + 2 and y = 3 - 2 then the value
x4 1
1 1 1151 577
of 1  y + is. (A) (B)
1 x 34 17
(A) 0 (B) 1 1157 567
(C) 2 (D) 3 (C) (D)
34 17

47. If a = 7 + 6 and b = 7 - 6 then find the 57. If x = 7 + 4 3 then find the value of
value of (1 + a)-1 + ( 1 + b)-1 x6  x 4  x 2 1
(A) 0 (B) 1 .
(C) 2 (D) 3 x3
(A) 2744 (B) 2760
8ab x  4a x  4b (C) 2716 (D) 2728
48. If x = then the value of + is.
a b x - 4a x - 4b
(A) 0 (B) 1 60 x 5
58. If x = then find the value of +
(C) 2 (D) 3 3 5 x 5

96 x 3
49. If x = then the value of .
3 2 x 3
(A) 0 (B) 1
(C) 2 (D) 3
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 1 (A) 1 (B) 2 / 3
x4  2
1 x
59. If x + = 6 then find the value of 2 . (C) 2- 3 (D) 2
x x  5x  1
(A) 216 (B) 234 1 1 1
(C) 198 (D) 204 70. If a + = 1 and b + = 1 then c + is equal to
b c a
60. For real a, b, c if a2 + b2 + c2 = cb + ab + ca, then value
a c 1
(A) 0 (B)
of is 2
b
(C) 1 (D) 2
(A) 1 (B) 2
71. If a, b, c, are real and a2 + b2 + c2 = 2 (a - b - c) - 3, then
(C) 3 (D) 0
the value of 2a - 3b + 4c is :
61. If a3b = abc = 180, a, b, c are positive integers, then
(A) -1 (B) 0
the value of c is.
(C) 1 (D) 2
(A) 110 (B) 1
(C) 4 (D) 25 x y z
72. If = = , then
62. If a, b are rational numbers and (a - 1) 2 + 3 = b+ c c+a a+b
b 2 + a, the value of (a + b ) is. x- y y-z z-x
(A) = =
(A) -5 (B) 3 b-a c-b a-c
(C) -3 (D) 5 x y z
63. The value of (x + y + z)3 - (y + z - x)3 - (z - y + x)3 - ( (B) = =
a b c
x + y - z)3 is.
(A) 12 xyz (B) 24 xyz x- y y-z z-x
(C) = =
(C) 36 xyz (D) 0 c b c
(D) None of the above is true
x
64. If x = 5 - 21 , then the value of is
32  2 x  21 1 1
73. If a, b, c are non-zero. a + = 1 and b + = 1, then
b c
   
1 1
(A) 3 7 (B) 7 3 the value of abc is :
2 2
(A) -1 (B) 3

   
1 1 (C) -3 (D) 1
(C) 7 3 (D) 7– 5
2 2 74. If a + b + c = 2s, then

65. If p = 999, then the value of 3

p(p 2  3p  3)  1 is.  s  a 2  (s  b)2  (s  c)2  s2
is equal to
(A) 1000 (B) 999 a 2  b 2  c2
(C) 998 (D) 1002 (A) a 2  b 2  c2 (B) 0
(C) 1 (D) 2
66. If p = 101, then the value of 3
p(p 2  3p  3)  1 is 75. When xm is multiplied by xn, product is 1. The relation
between m and n is
(A) 100 (B) 101
(A) m = n (B) m = -n
(C) 102 (D) 1000
(C) mn = 1 (D) m + n = 1

5 1 76. If 2s = a + b + c , then the value of s (s-c) + (s-a) (s-

67. If x = , then the value of 5x2 - 5x - 1 is b) is :
5 1
(A) 0 (B) 3 a+b+c
(A) abc (B)
(C) 4 (D) 5 2
7 5 (C) ab (D) 0
68. If 47.2506 = 4A + + 2C + + 6E then the value
B D 1
of 5A + 3B + 6C + D + 3E is. 77. If 2x = a + , a > 0, then the value of
a
(A) 53.6003 (B) 53.603
(C) 153.6003 (D) 213.0003 x2 1
is :
x  x2  1
3 1 x 1 x
69. If x = then + is equal to (A) a-1 (B) a+1
2 1 1 x 1 1 x

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 (A) 1 (B) 23458
1 1
(C) (a+1) (D) (a-1) (C) 23456 (D) 23457
2 2
1234567  1234569  1
a+b-c b+c-a c+a-b 88. =?
78. If = = and a+b+c  0 then. 1234568
a+b b+c c+a
(A) 1 (B) 1234567
(A) a  b = c (B) a  b  c
(C) a = b = c (D) a = b  c (C) 1234568 (D) 1234569
22334466  22334468  1
b+c 89. = ?
79. If bc + ab + ca = abc then the value of bc (a-1) + 22334467  22334467
(A) 1 (B) 22334466
a+c a+b (C) 22334467 (D) 22334468
ac (b-1) + ab (c-1) is : 90. If (11557722×11557724+x) is a perfect square num-
(A) 1 (B) 0 ber then the value of x is :
(A) 1 (B) 11557722
1 3
(C) (D) (C) 11557724 (D) 11557723
2 2
91. If x 2 -4x + 1 = 0 then the value of
a 2 -bc b2 -ca c2 -ab
80. If 2 + 2 + 2 = 1 then the value of 2x4  3x3  4x2  3x  2
a +bc b +ca c +ab is :
x4 1
a2 b2 c2
+ + is 7 22
a 2 +bc b 2 +ac c 2 +ab (A) (B)
(A) 2 (B) 0 22 7
(C) 1 (D) -1
23 7
(C) (D)
3
m  1  m 1
3
7 23
81. If x  then the value of x3-3x2+3x -m
3
m  1  3 m 1 92. If x = 3 2 2 then the value of
is.
(A) 0 (B) 1 2 x 4  3 x3  4 x 2  3x  2
is :
1 1 x4  1
(C) m  (D) m 
m m 17 45
(A) (B)
45 17
82. 3
1 2 . 6
3  2 2 is equal to
47 17
(A) 2- 2 (B) 2 -1 (C) (D)
17 47
(C) 1 (D) 3-2 2
  +x  
1 1
3 3
If a = x  x  y x2  y3
2 3
x z 93. then the
83. If x+y = 2x then the value of x  z  y  z is :
value of a3+3ax is :
(A) 1 (B) 2 (A) x (B) 2x
(C) 3x (D) 4x
(C) 3 (D) 1 2
1 1
If x  13 then the value of x  x 3 is :
3
94. =
x
84.  3  38 7  4 3 =?
(A) 36 (B) 27
(A) 1 (B) 2 (C) 18 (D) 9
(C) 3 (D) 8
1 1
If x  then the value of x  2 is :
2
95. =
3 1 x 2 3 x
85. If x = then the value of 4x3 + 2x2-8x +7 is :
2
(A) 2 3 (B) 6 3
(A) 0 (B) 1
(C) 4 (D) 10 (C) 8 3 (D) 12 3
86. If x+y+ z =1,xy+ yz + zx =-1 and xyz = -1 then the
1 1
If x  29 then the value of x 
4
value of x3+y3+x3 is. 96. = is :
(A) 0 (B) 1 x x4
(C) -1 (D) 2 (A) 27 29 (B) 13 29
2
87. If 23456 × 23458+1 = (x) then the value of x is.
(C) 135 29 (D) 140 29
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 1 1 (C) 198 (D) 232
If x  53 then the value of x  x 2 is :
2
97. = 106. =?
x 10  2 6  2 10  2 15
(A) 7 (B) 7 53
(A) 2 3 5 (B) 2 3 5
(C) 4 53 (D) 6 53
(C) 3 5 2 (D) 2 5 3
1 1
98. If x  = 2 10 then the value of x  3 is :
3
ab bc
x x 107. If ab +bc + ca = 1 then the value of +
1  ab 1  bc
(A) 216 (B) 204
(C) 234 (D) 230 ca
+ is :
1  ac
1 1
If x  13 then the value of x  x 5 is :
5
99. = 1
x
(A) abc (B)
(A) 390 (B) 393 abc
(C) 396 (D) 400 (C) 1 (D) a+b+c

  + a  
1 1
3 3
108. If x = a  a  b a 2  b3
2 3
1 1 then the
100. If x  = 4 2 then the value of x  x 4 is :
4

x
value of x3+ 3bx - 2a is :
(A) 1150 2 (B) 816 2 (A) 0 (B) 1
(C) 1156 2 (D) 1614 2 (C) 2a3 (D) 2b3
1 1
1 109. The value of + +
1 x5  3 a 2  ax  x 2 a 2  ax  x 2
101. If x  = 4 then the value of x is :
x x2  2x  1 2ax
is:
(A) 256 (B) 128 a4  a 2 x2  x4
(C) 64 (D) 97 (A) 1 (B) -1
(C) 2 (D) 0
1
1 x4  2 110. If p=99 then the value of p (p2+3p+3) is :
102. If x  = 5 then the value of x is : (A) 10000000 (B) 999000
x x 2  3x  1
(C) 999999 (D) 990099
(A) 110 (B) 55
(C) 23 (D) 140    
111. If 2  3 a = 2  3 b = 1 then the value of

1 2 1009 1 1
103. If + y2 + = 1 then the value of  is
x 1 z  1009 a b
(A) 1 (B) 2
x y z
+ + is : (C) 2 3 (D) 4
x 1 x2 z  1009
2 2
(A) 0 (B) 2 112. The factors of (a +4b +4b-4ab-2a-8) are :
(A) (a-2b-4) (a-2b+2) (B) (a-b+2) (a-4b-4)
(C) 3 (D) 4
(C) (a+2b-4) (a+2b+2) (D) (a+2b-1) (a-2b+1)
 2 1  (ax  by )
104. If x = 7 + 4 3 then the valueof 2  x  x 2  + 3
  113. If x :a = y:b = z:c, then the value of (a  b)( x  y ) +

 3 1  (by  cz ) (cz  ax)

 x  x 3  is . +
  (b  c)( y  z ) (c  a )( z  x) is :
(A) 8494 (B) 8449 (A) 0 (B) 1
(C) 8444 (D) 8489 (C) 2 (D) 3
1 114. If x2 + x = 5, then the value of
105. If x = 3 + 2 2 then find the value of x2+x3+ 2 +
x 1
(i) ( x  3)  ?
3

1 ( x  3)3
is. (A) 125 (B) 110
x3
(A) 216 (B) 234 (C) 140 (D) 100

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115. If a 2 +b 2 = x and ab = y then the value of
1
(C) n (D) n
a 4  b4 2
is :
a 2  2 ab  b 2 x y x– y ab
124. If a = and b = then the value of
(A) x+2b (B) x+ 2 y 1 – xy 1  xy 1– ab
(C) 2 x+y (D) 2x+y is :
116. If (x+y+z)= 2 andxy+yz+zx =1then the value of (x+y)2+ x 2x
(A) (B)
(y+z)2 + (z+x)2 is : 1 y2 1 y
(A) 12 (B) 6
(C) 10 (D) 16 2x 2x
(C) (D)
117. The least ositive integer that should be added to 1 y2 1 – x2
123456× 12358 so that the product is a porfect square 125. If a 2 +b 2 = x and ab = y then the value of
is :
a 4  b4
(A) 123456 (B) 123458 is :
(C) 1 (D) 0 a 2  2ab  b 2
(A) x+2y (B) x-2y
x y z
118. If = = then the value of xy+yz + zx is : (C) x+ 2 y (D) x- 2 y
a b c
1 1 1
x 2 (a  b  c)2  b 2 ( x 2  y 2  z 2 ) 126. If a   b   c  then the value of abc is:
(A) b c a
2b 2
(A) 1 (B) –1
x 2 (a  b  c)2  a 2 ( x 2  y 2  z 2 ) (C) 1 (D) 2
(B)
2a 2 2
127. If x + x = 11 the the value of

x 2 (a  b  c)2  c 2 ( x 2  y 2  z 2 ) 1
(i)  x  4 
3
?
(C) ( x  4)3
2c 2
(D) All of above (A) 322 (B) 343
(C) 310 (D) 47
128. Fine the value of
119. If x = 3 - 5 then the value of x2-16x+6 is :
(A) 0 (B) 1  2 xy   x 3  y 3 
(C) 2 (D) 3  x 2  y 2    x  y  3 xy  ?
1 

120. If x = 2+ 3 4 + 3 3 2
2 then the value of x -6x + 6x-2 is: 1 1
(A) (B)
(A) 0 (B) 1 2
x –y 2
x  y2
2

(C) 4 (D) 6 1 1
(C) (D)
x  a2 x  b2 x  c2 x y x y
121. If 2 + 2 2 + 2 = 3 then the value of 129. If x2 + y2 + 2x + 1 = 0, then x31 + y35 = ?
b c
2
c a a  b2
(A) – 1 (B) 0
x is :
(C) 1 (D) 2
(A) a2+b2 (B) a2+b2+c2
(C) abc (D) 0 5 1 5 1
130. If x and y  then the value of
122. If a+b+c =0 then find the value of
1
+
5 1 5 1
a 2  b2  c2
x 2  xy  y 2
1 1 is:
2 + is : x 2  xy  y 2
b c a
2 2
a  b2  c2
2
3 4
(A) 0 (B) 1 (A) (B)
(C) -1 (D) 2
4 3
3 5
 1   2  (C) (D)
123. Find the sum of 1 –  + 1   5 3
n 1  n 1  2
 1 1
131. If  x    3, then x  6  ?
6
 3   n   x  x
+ 1 –  + ...... + 1 – 
n 1 n 1 (A) 90 (B) 100
(A) 0 (B) 1
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 (C) 110 (D) 120 (A) 1 (B) 2
132. If a2 + b2 + c2 = 16, x2 + y2 + z2 = 25 and ax + by + cz = (C) 4 (D) 0
a bc 141. If x2 + y2 + 6x + 5 = 4(x – y), then x – y = ?
20, then the value of is: (A) 1 (B) – 1
x yz
(C) 0 (D) 4
3 5 142. If a = 299, b = 298, c = 297, then the value of 2a3 + 2b3
(A) (B) + 2c3 – 6abc is:
5 3
(A) 5154 (B) 5267
4 5 (C) 5364 (D) 5456
(C) (D)
5 4 1
133. If a3 = 117 + b3 and a = 3 + b, then the value of a + b 143. If x   3 , then x18 + x12 + x6 + 1 = ?
is: x
(A) 0 (B) 1
(A) 7 (B) 49 (C) 2 (D) 3
(C) 13 (D) 0
144. If x = 1 + 2  3 , then 2x4 – 8x3 – 5x2 + 26x – 28
134. If a + b + c = 0, then find the value of
1 1 1 =?
 
(a  b)(b  c) (b  c)(c  a ) ( c  a )( a  b) (A) 2 2 (B) 6 6
(A) 0 (B) 1
(C) 3 (D) 2 (C) 5 5 (D) 3 5
135. If x4 + 2x3 + ax2 + bx + 9 is a perfect square, where a 1 1 1
and b are real positive numbers, then find the value 145. If a + = 1 and b + = 1, then the value of c +
of a and b?
b c a
(A) a = 5, b = 6 (B) a = 6, b = 7 is:
(C) a = 7, b = 6 (D) a = 7, b = 8
(A) 0 (B) 2
x  a 2  2c 2 (C) 1 (D) 3
136. Find the value of x, which satisfies of
bc 146. If x = y + z, then the value of x3 – y3 – z3 is:
x  b 2  2a 2 x  c 2  2b 2 (A) 0 (B) 3xyz
  (C) – 3xyz (D) 1
ca ab
(A) (a2 + b2 + c2) (B) – (a2 + b2 + c2) 147. If x = 11, then x5 – 12x4 + 12x3 – 12x2 + 12x – 1 = ?
(C) (a2 + 2b2 + c2) (D) – (a2 + b2 + 2c2)
(A) 11 (B) 10
1
137. If a   2, then a1000 + a-1000 = ? (C) 12 (D) – 10
a 1 1 1
(A) 2 (B) 0 148. If a  b  c (where a  b  c ) ,
b c a
1 then abc = ?
(C) 1 (D) (A) + 1 (B) – 1
2
(C) + 1 and – 1 (D) None of these
1 1
138. If x   c  , then find the value of x ? 2ab
x c 149. If ax + by = 1 and bx + ay = , then the value
(A) C, 1/C (B) C, C2 a  b2
2

(C) C, 2C (D) C, 2C of (x2 - y2) (a2 +b2) will be equal to –

139. Find the factors of x4 + 64.gh (A) 1 (B) 2
(C) 0.5 (D) 0
(A) x 2
 82  150. If a3 – 7a – 6 has three factors x, y, z, the find the
value of x + y + z.
(B) x 2
 82  x 2 – 8 (A) 8 (B) 3
(C) 6 (D) 0
(C) x 2
 4 x  8 x 2 – 4 x – 8 151. If x2 + x = 29 then find the value of
(D) x 2
 4 x  8 x 2 – 4 x  8
 x  63 
1
?
140. If a + b = 1, then the value of a4 + b4 – a3 – b3 – 2a2b2 ( x  6)3
+ ab will be equal to: (A) 1331 (B) 1310
(C) 1298 (D) 1320

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 161. If x + y + z = 0, Then what is the value of
ssc mains 2017 (3y2 + x2 + z2)(2y2 - xz)?
152. What is the value of 10062 - 1007 × 1005 (A) 2 (B) 1
+ 1008 × 1004 - 1009 × 1003? (C) 3/2 (D) 5/3
(A) 6 (B) 3 162. If P = 7 + 4 3 and PQ = 1, then what is
(C) 12 (D) 24 the value of 1/P2 + 1/Q2?
153 . If a2 + b2 = 4b + 6a - 13, then what is (A) 196 (B) 194
the value of a + b? (C) 206 (D) 182
(A) 3 (B) 2 163. If a3 + 3a2 + 9a = 1, then what is the value
(C) 5 (D) 10 of a3 + (3/a)?
154. X and Y are Positive integers. If x4 + y4 + (A) 31 (B) 26
x2y2 = 481 and xy = 12, then What is the (C) 28 (D) 24
value of x2 - xy + y2? 164. x, y and z are real number. If x3 + y3 +
(A) 16 (B) 13 z3 = 13, x + y + z = 1 and xyz = 1, then
(C) 11 (D) 15 what is the value of xy + yz + zx?
(A) - 1 (B) 1
155. If A = 1 + 2P and B = 1 + 2-P , then What is
(C) 3 (D) - 3
the value of B?
(A) (A + 1)/(A - 1) (B) (A +21)/(A + 1) 165. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then
(C) A /(A - 1) (D) (A - 2)/(A + 1) what is the value of (a + c)/b?
(A) 9/5 (B) 11/7
156. If a and b are root of the equation ax2 + bx
(C) 7/11 (D) 7/4
+ c = o, then which equation will have root
(ab + a + b) and (ab - a - b)? 166. If z3 + y3 + z3 = 3(1+ xyz), P = y + z -x, Q = z +
(A) a2x2 + 2acx + c2 + b2 = 0 x - y and R = x + y - z,then what is the
(B) a2x2 - 2acx + c2 - b2 = 0 value of P3 + Q3 + R3 - 3PQR?
(C) a2x2 - 2acx + c2 + b2 = 0 (A) 9 (B) 8
(D) a2x2 + 2acx + c2 - b2 = 0 (C) 12 (D) 6
167 .If x1x2x3 = 4(4 + x1 + x2 + x3), then what is
3 the value of [1/(2 + x1)] + [1/(2 + x2)] + [1/(2
157. If (1  p 2 )(1  q 2  , then what is
2 + x3)]?
(A) 1 (B) 1/2
2 p 2  2q 2  2 pq  2 p 2  2q 2  2 pq (C) 2 (D) 1/3
=? 168 .If a and  are the roots of equation x2 - x +
(A) 2 (B) 1 = 0, then which equation will have roots
2
(C) 1 (D) None of these a3 and  3 ?
(A) x2 +2x + 1 = 0 (B) x2 - 2x - 1 = 0
158. If (a + b)2 - 2(a + b) = 80 and ab = 16, then (C) x2 - 3x - 1 = 0 (D) x2 - 3x + 1 = 0
what can be the value of 3a -19b?
(A) - 16 (B) - 14 169 .If 3x + 5y + 7z = 49 and 9x + 8y + 21z =
(C) - 18 (D) - 20 126, then what is the value of y?
(A) 4 (B) 2
159. If xy+z = 1, yx+z = 1024 and zx+y = 729 (x,y (C) 3 (D) 5
and z are natural numbes),then what is
the value of (z + 1)y+x+1? 170 .If X =  5  + 1 and Y =  5  - 1, then
(A) 6561 (B) 10000
what is the value of (x2/y2) + (y2/x2) +
(C) 4096 (D) 14641
160. If x + y + z = 1, x2 + y2 + z2 = 2 and x3 + y3 + 4[(x/y) + (y/x)] + 6?
z3 = 3, then what is the value of xyz? (A) 31 (B) 23 5
(A) 1/3 (B) 1/6 (C) 27 5 (D) 25
(C) 1/2 (D) 1/4

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171 .If x = 2 + 3, y =2- 3 and z = 1, then (C) 2 (D) 12
what is the value of (x/yz) + (y/xz) + (z/xy) 181. If a and  are the roots of the equation
+ 2 [(1/x) + (1/y) + (1/z)]? x2 + x - 1 = 0, then what is the equation
(A) 25 (B) 22 whose roots are a5 and  5 ?
(C) 17 (D) 43 (A) x2 + 7x - 1 = 0
172 .A root of rquation ax2 + bx + c = o(where (B) x2 - 7x - 1 = 0
(C) x2 - 11x - 1 = 0
a,b and c are rational numbers) is 5 + 3 3 .
(D) x2 + 11x - 1 = 0
what is the value of (a2 + b2 + c2)/(a + b +
c)? 182. If x and y are natural numbers such that
x + y = 2017, then what is the value of (-
(A) 35/3 (B) 37/3
1)X - (-1)Y ?
(C) - 105/11 (D) - 105/13
(A) 2 (B) - 2
173. If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (C) 0 (D) 1

 
(c/a) + (a/c), then what is the value of xyz
- x2 - y2 - z2? 183. If x + (1/x) = 3  1 / 2, then what is
(A) - 4 (B) 2 4
the value of x + (1/x )? 4

(C) - 1 (D) - 6
(A)  4 3 1 / 4 (B)  4 3  1 / 2
(C)   4 3  1 / 4 (D)   4 3  1 / 2
174. If [a + (1/a)]2 - 2[a - (1/a)] = 12, then which
of the following is a value of 'a'?
(A) - 8 + 3 (B) - 8 - 3 184. If a + a2 + a3 - 1 = o, then what is the
(C) - 8 + 5 (D) None of these value of a3 + (1/a)?
175. If x2 - 4x + 1 = 0, then what is the value of (A) 1 (B) 4
x9 + x7 - 194 x5 - 194x3? (C) 2 (D) 3
(A) 4 (B) - 4 185. If a - (1/a) = b, b - (1/b) = c and c - (1/c) =
(C) 1 (D) - 1 a then what is the value of (1+ ab) + (1/bc)
176. If x + y = 3, then what is the value of x3 + + (1/c a)?
y3 + 9xy? (A) - 3 (B) - 6
(A) 15 (B) 81 (C) - 1 (D) - 9
(C) 27 (D) 9 186. If the roots of the equation a (b - c)x2 + b(c-
177. A = (x8 - 1)/(x4 +1) and B = (y4 - 1)/(y2 + 1) if a) x + c(a - b) = o are equal, then which of
x = 2 and y = 9, then what is the value if A2 the following is true?
+2AB +AB2? (A) b = (a+c)/ac
(A) 96475 (B) 98625 (B) 2/b = (1/a)
(C) 92425 (D) 89125 (C) 2/b = (1/a) + (1/c)
(D) abc = ab + bc + ca
178. If x - 4y = o and x + 2y =24,then what is
the value of (2x +3y)/(2x - 3y)? 187. If (a2 + b2 + ab) + (a2 + b2 - ab) = 1
(A) 9/5 (B) 11/5 ,then what is the value of (1 - a2) (1 - b2)?
(C) 13/7 (D) 9/7 (A) 1/4 (B) 4/7
179. If (x/a) + (y/b) = 3 and (x/b) - (y/a) = 9, (C) 5/4 (D) 3/4
then what is the value of x/y? 188. If 3x + 4y - 11 = 18 and 8x - 6y +12 = 6,
(A) (b +3a)/(a - 3b) then what is the value of 5x - 3y - 9 =?
(B) (a +3b)/(b - 3a) (A) 18 (B) - 9
(C) (1 +3a)/(a + 3b) (C) - 27 (D) - 18
(D) (a +3b2)/(b - 3a2) 189. If a + b + c = 7/12, 3a - 4b + 5c = 3/4 and
3 3 3
180. p + q + r - 3pqr = 4, If a = q + r, b = r + p 7a - 11b - 13c = - 7/12, then what is the
and c = p+q then what is the value of a3 + value of a+c?
b3 + c3 - 3abc? (A) 1/2 (B) 5/12
(A) 4 (B) 8 (C) 3/4 (D) 1/4

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190. If x + y + z = 22 and xy + yz + zx = 35,then value of 46x + 131y?
what is the value of (x - y)2 + (y - z)2 + (z - (A) 414 (B) 364
x)2? (C) 384 (D) 464
(A) 793 (B) 681 200. If the difference between the roots of the
(C) 758 (D) 715 equation Ax2 - Bx + c = 0 is 4, then which
191. If (x + y)/z = 2, then what is the value of of the following is true?
[y/(y - z)] + [x/(x - z)] = ? (A) B2 - 16A2 = 4AC + 4B2
(A) 0 (B) 1 (B) B2 - 10A2 = 4AC + 6A2
(C) 2 (D) - 1 (C) B2 - 8A2 = 4AC + 10A2
192. If a and  are roots of equation x2 - 2x + 4 D) B2 - 16A2 = 4AC + 8B2
= 0, then what is the equation whose roots 201. a and  are the roots of quadratic
are a3/  2 and  3 /a2? equation. If a +  = 8 and a -  = 2 5 ,
(A) x2 - 4x + 8 = 0 then which of the following equation will
(B) x2 - 32x + 4 = 0
have roots a4 and  4 ?
(C) x2 - 2x + 4 = 0 (A) x2 - 1522x + 14641 = 0
(D) x2 - 16x + 4 = 0
(B) x2 + 1921x + 14641 = 0
193. If one root of the equation Ax2 + Bx + c = 0 (C) x2 - 1764x + 14641 = 0
is two and a half times the others, then (D) x2 + 2520x + 14641 = 0
which of the following is True? 202. If a and b are the roots of the equation Px2
(A) 7B2 = 3 CA (B) 7B2 = 4 CA
- Qx + R = o, then what is the value of (1/
2
(C) 7B = 36 CA (D) 10B2 = 49 CA a2) + (1/b2) + (a/b) + (b/a)?
194. If x2 - 12x + 33 = 0, then what is the value (Q 2  2 P )(2 R  P )
of (x - 4)2 + [1/(x - 4)2]? (A)
PR 2
(A) 16 (B) 14
(Q  2 PR)( R  P )
2
(C) 18 (D) 20 (B)
PR 2
195. If a4 + 1 = [a2/b2] (4b2 - b4 - 1), then what is
(Q  2 R )(2 P  R )
2
the value of a4 + b4? (C)
(A) 2 (B) 16 P2 R2
(C) 32 (D) 64 (Q  2 PR)( R  P )
2

(D)
PR 2
1 a a
196. 3  9  19  3 , then what is 203. If x2 - 16x - 59 = 0, then what is the value
a 1 a of (x - 6)2 + [1/(x - 6)2]?
the value of a ?
(A) 14 (B) 18
(A) 3/10, 7/10 (B) 1/10, 9/10
(C) 16 (D) 20
(C) 2/5, 3/5 (D) 1/5, 4/5
204. If A and B are the roots of the equation
a b Ax2 - A2x + AB = 0, then what is the value
197. If a + b = 10 and  13    11 then of A and B respectively?
b a
(A) 1, 0 (B) 1, 1
what is the value of 3ab + 4a2 + 5b2? (C) 0, 2 (D) 0, 1
(A) 450 (B) 300
205. a and  are the roots of the quadratic
(C) 600 (D) 750
equation x2 + x - 1 = 0. what is the value of
198. If 3x + 4y - 2z + 9 = 17, 7x + 2y + 11z + 8 = a8 +  8 ?
23 and 5x + 9y + 6z - 4 = 18, then what is (A) 47 (B) 54
the value of x + y + z -34? (C) 59 (D) 68
(A) - 28 (B) - 14
206. If a + b + c = 9, ab + ca = 26, a3 + b3 =91, b3
(C) - 31 (D) - 45
+ c3 = 72 and c3 + a3 = 35, then what is the
2z 2 value of abc?
199. x + 3y - = 6, x + (2y + 3z) = 33 and
4 3 (A) 48 (B) 24
1
(x + y + z) + 2z = 9, then what is the (C) 36 (D) 42
7
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207 . If x3 - 4x2 + 19 = 6(x - 1), then what is 208. If 2x + 3y - 5z = 18, 3x + 2y + z = 29 and x
the value of [x2 + (1/x - 4)]? + y + 3z = 17, then what is the value of xy
(A) 3 (B) 5 + yz + zx?
(C) 6 (D) 8 (A) 32 (B) 52
(C) 64 (D) 46

ANSWERS (LEVEL -2 )

1. (a) 2. (d) 3. (b) 4. (c) 5. (a) 6. (c) 7. (c) 8. (c) 9. (a) 10. (b)
11. (a) 12. (b) 13. (b) 14. b) 15. (c) 16. (c) 17. (d) 18. (d) 19. (d) 20. (b)
21. (d) 22. (b) 23. (d) 24. (a) 25. (c) 26. (b) 27. (a) 28. (a) 29. (d) 30. (d)
31. (b) 32. (a) 33. (c) 34. (d) 35. (b) 36. (c) 37. (b) 38. (c) 39. (b) 40. (a)
41. (d) 42. (c) 43. (c) 44. (a) 45. (c) 46. (b) 47. (b) 48. (c) 49. (c) 50. (c)
51. (a) 52. (a) 53. (c) 54. (b) 55. (c) 56. (b) 57. (c) 58. (c) 59. (c) 60. (b)
61. (b) 62. (d) 63. (b) 64. (b) 65. (a) 66. (a) 67. (c) 68. (c) 69. (b) 70. (c)
71. (c) 72. (a) 73. (a) 74. (c) 75. (b) 76. (c) 77. (d) 78. (c) 79. (a) 80. (a)
81. (a) 82. (c) 83. (a) 84. (b) 85. (d) 86. (b) 87. (d) 88. (c) 89. (a) 90. (a)
91. (b) 92. (b) 93. (b) 94. (a) 95. (c) 96. (c) 97. (b) 98. (c) 99. (b) 100. (b)
101. (d) 102. (b) 103. (b) 104. (a) 105. (d) 106. (a) 107. (b) 108. (a) 109. (d) 110. (c)
111. (d) 112. (a) 113. (d) 114. (b) 115. (b) 116. (b) 117. (c) 118. (b) 119. (c) 120. (a)
121. (b) 122. (a) 123. (d) 124. (d) 125. (d) 126. (c) 127. (a) 128. (b) 129. (a) 130. (b)
131. (c) 132. (c) 133. (a) 134. (a) 135. (c) 136. (b) 137. (a) 138. (a) 139. (b) 140. (d)
141. (a) 142. (c) 143. (a) 144. (d) 145. (c) 146. (b) 147. (b) 148. (c) 149. (a) 150. (d)
151. (c) 152. (a) 153. (c) 154. (b) 155. (c) 156. (b) 157. (b) 158. (b) 159. (b) 160. (b)
161. (a) 162. (b) 163. (c) 164. (d) 165. (d) 166. (c) 167. (b) 168. (a) 169. (c) 170. (d)
171. (a) 172. (c) 173. (a) 174. (d) 175. (b) 176. (c) 177. (b) 178. (b) 179. (a) 180. (b)
181. (d) 182. (c) 183. (c) 184. (c) 185. (a) 186. (c) 187. (d) 188. (b) 189. (b) 190. (c)
191. (c) 192. (c) 193. (d) 194. (b) 195. (a) 196. (b) 197. (b) 198.(c) 199. (a) 200. (b)
201. (a) 202. (b) 203. (b) 204. (a) 205. (a) 206. (b) 207. (c) 208. (b)

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