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[1]
Maths By Sujit KumarCoaching Centre
1. If a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equalto ?
(a) 22 (b) 24 (c) 26 (d) 28
2. If p × q = p + q + qp
, the value of 8 × 2 is ?
(a) 6 (b) 10 (c) 14 (d) 16
3. Two numbers x and y (x > y) are such that theirsum is equal to three times their difference. The
value of 2223
yxxy will be ?
(a) 32
(b) 1 (c) 1 21
(d) 1 32
4. The value of
311
211
11111
xxxx is ?
(a) 411
x (b) x + 4
(c) x1
(d) 44x
5. If a * b = 2 (a + b), then 5 * 2 is equal to ?
(a) 3 (b) 10 (c) 14 (d) 20
6. If 34
2
baba
, then find the value of baba
2
?
(a) 95
(b) 72
(c) 910
(d) 710
7. If a = 4.965, b = 2.343 and c = 2.622, then thevalue of a3 – b3 – c3 – 3abc is ?
(a) – 2 (b) – 1 (c) 0 (d) 9.93
8. If a * b = a + b + ab, then 3 * 4 – 2 * 3 is equalto ?
(a) 6 (b) 8 (c) 10 (d) 12
9. If a = 1.21, b = 2.12 and c = –3.33 then, the valueof a3 + b3 + c3 – 3abc is ?(a) 0 (b) 1 (c) 2 (d) 3
10. If x y = 3x + 2y. Then 2 3 + 3 4 is equalto ?
(a) 18 (b) 29 (c) 32 (d) 38
11. If 743cba
then ccba
is equal to ?
(a) 0 (b) 1 (c) 2 (d) 3
12. If x4.14
144.0144
, then the value of x is ?
(a) 1.44 (b) 14.4 (c) 1.44 (d) 0.014413. If 1 < x < 2, then the value of
22 31 xx ?
(a) 1 (b) 2 (c) 3 (d) 2x – 414. If a b = (a × b) + b, then 5 7 equals to ?
(a) 12 (b) 35 (c) 42 (d) 5015. If a = 0.1039, then the value of
aaa 3144 2 is ?
(a) 0.1039 (b) 0.2078 (c) 1.1039 (d) 2.1039
16. If a = 0.25, b = – 0.05, c = 0.5, then the value of
222
222
22
cabbabccba
is ?
(a) 87
(b) 1714
(c) 1 (d) 1625
17. If x * y = x2 + y2 – xy, then the value of 9 * 11 is ?(a) 93 (b) 103 (c) 113 (d) 121
18. If p = 999, then the value of 3 2 133 pppis ?
(a) 1000 (b) 999 (c) 998 (d) 100219. If 55x+5 = 1, then x equals ?
(a) 0 (b) – 1 (c) 1 (d) – 54
ALGEBRATYPE – 1
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Maths By Sujit KumarCoaching Centre
20. If 3x+3 + 7 = 250, then x is equal to ?(a) 5 (b) 3 (c) 2 (d) 1
21. If .....125
104
83
62
41
x21
6431
, the value of
x is ?(a) 31 (b) 32 (c) 36 (d) 37
22. The value of 1
125
3.93.243
nn
nn
is ?
(a) 1 (b) 9 (c) 3 (d) 3n
23. If x = 0.5 and y = 0.2, then value of 6.0 × (3y)x
is equal to ?(a) 1.0 (b) 0.5 (c) 0.6 (d) 1.1
24. If xxx xxx , then x equals ?
(a) 94
(b) 32
(c) 49
(d) 23
25. If a = 7, b = 5 and c = 3, then the value of a2 +b2 + c2 – ab – bc – ca is ?(a) 12 (b) – 12 (c) 0 (d) 8
26. If 7x = 3431
, then the value of x is ?
(a) 3 (b) –3 (c) 31
(d) 71
27. If * is an operation such that x * y = 3x + 2y,then 2 * 3 + 3 * 4 is equal to ?(a) 18 (b) 29 (c) 32 (d) 38
28. If 0.13 p2 = 13, then p is equal to ?(a) 10 (b) 0.01 (c) 0.1 (d) 100
29. If a = 4.36, b = 2.39 and c = 1.97, then the valueof a3 – b3 – c3 – 3abc is ?(a) 3.94 (b) 2.39 (c) 0 (d) 1
30. For what value(s) of a is 2
41 axx a perfect
square ?
(a) 181 (b) 8
1 (c) 51 (d) 4
1
31. If a b, then which of the following statementsis true ?
(a) abba
2 (b) ab
ba
2
(c) abba
2 (d) All of the above
32.
xx
xx
11
1
11
12
22
2
xx
xx is
equal to ?
(a) 66 1
xx (b) 8
8 1x
x
(c) 88 1
xx (d) 6
6 1x
x
33. If x, y are t wo p os it ive real numbers andx1/3 = y1/4, then which of the following relationsis true ?(a) x3 = y4 (b) x3 = y(c) x = y4 (d) x20 = y15
34. If a2x+2 = 1, where a is a positive real numberother than 1, then x is equal to ?(a) – 2 (b) – 1 (c) 0 (d) 1
35. If x is real, then the minimum value of (x2 – x +1) is ?
(a) 43
(b) 0 (c) 1 (d) 41
36. If ba
72727
, then the value of a is ?
(a) 311
(b) 34 (c) 3
4(d)
374
37. If (125)x = 3215, then the value of x is ?
(a) 51
(b) 53
(c) 35
(d) 75
38. If xxx 13125 , the x is equal to ?
(a) 425
(b) 4 (c) 9 (d) 16
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Maths By Sujit KumarCoaching Centre
39. If 22x–y = 16 and 2x+y = 32, the value of xy is ?
(a) 2 (b) 4 (c) 6 (d) 8
40. If1263
53
53
53
x
, then x is equal to ?
(a) – 2 (b) 2 (c) – 1 (d) 1
41. If a = 11 and b = 9, t hen the value of
33
22
baabba
is ?
(a) 21
(b) 2 (c) 201
(d) 20
42. If a and b be p osit ive int egers such t hata2 – b2 = 19, then the value of a is ?
(a) 19 (b) 20 (c) 9 (d) 10
43. 23333
xxxx
then x is equal to ?
(a) 125
(b) 512
(c) 75
(d) 57
44. If a = 1227 and b = 1227 , t hen
33 ba is equal to ?
(a) 40 (b) 44 (c) 48 (d) 52
45. If23x , then the value of
xxxx
1111
is ?
(a) 3 (b) – 1 (c) 1 (d) 3
46. If x = 19 and y = 18, t hen t he value of
33
22
yxxyyx
is ?
(a) 1 (b) 37 (c) 324 (d) 361
47. If 44x + 1 = 641
, then the value of x is ?
(a) 21
(b) – 1 (c) – 21
(d) – 61
48. If4444
xxxx
= 2 then x is equal to ?
(a) 2.4 (b) 3.2 (c) 4 (d) 5
49. If x2 = 256, then the value of x is ?
(a) 14 (b) 16 (c) 18 (d) 20
50. If p55557 , then the value of p is ?
(a) 5 (b) 2 (c) 23
(d) 1
51. If53
1001
3
x
, then x equals ?
(a) 2 (b) 4 (c) 16 (d) (136)1/3
52. If a b = 2a + 3b – ab, t hen t he value of(3 5 + 5 3) is ?
(a) 10 (b) 6 (c) 4 (d) 2
53. If3
139
1 x
, then the value of x is ?
(a) 91439
(b) 160 (c) 91443
(d) 169
54. If 61848
2534ba
, then the values of a
and b are respectively ?
(a) 154,
159 (b) 33
4,113
(c) 52,
109
(d) 154,
53
55. If
10
675
43
2
x
, then the value of x is ?
(a) 1351276
(b) 653
(c) 4.35 (d) 9
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56. If a * b = ab, then the value of 5 * 3 is ?
(a) 125 (b) 243 (c) 53 (d) 15
57. If ba 3.03.03.003.0 value of ba
is ?
(a) 0.009 (b) 0.03 (c) 0.09 (d) 0.08
58. If x * y = (x + 3)2 (y – 1), then the value of 5 * 4is ?
(a) 192 (b) 182 (c) 180 (d) 172
59. If 147129 x , then x = ?
(a) 2 (b) 3 (c) 4 (d) 5
60. If X * Y = X2 + Y2 then 11 * 13 is ?
(a) 117 (b) 147 (c) 290 (d) 433
61. If 3132
9611
x, then the value of x is ?
(a) 63 (b) 61 (c) 65 (d) 64
62. If ba 4.0004.04.004.0 , then t he
value of ba
is ?
(a) 16×10–3 (b) 16×10–4 (c) 16×10–5 (d) 16×10–6
63. If the sum of ba
and its reciprocal is 1 and a O,
b O, then the value of a3 + b3 is ?
(a) 2 (b) –1 (c) 0 (d) 1
64. If 2x+3 = 32, then the value of 3x+1 is equal to ?
(a) 27 (b) 81 (c) 72 (d) 9
65. The value of the expression x4 – 17x3 + 17x2 –17x + 17 at x = 16 is ?
(a) 0 (b) 1 (c) 2 (d) 3
66. If a = 23 and b = 29 then the value of 25a2 + 40ab+ 16b2 is ?
(a) 1 (b) –1 (c) 0 (d) 2
67. If 9771
21
32 nnnn then the value of n is ?
(a) 40 (b) 42 (c) 44 (d) 46
68. If x – y = 2 and x2 + y2 = 20, the value of (x + y)2
is ?
(a) 38 (b) 36 (c) 16 (d) 12
69. 1 + 2 + 3 + .... + 100 = x, then x is ?
(a) 5,050 (b) 5,000 (c) 10,100 (d) 10,000
70. If x = 2 – 21/3 + 22/3, then the value of x3 – 6x2 +18x + 18 is ?
(a) 22 (b) 33 (c) 40 (d) 45
71. If x2 + y2 – 4x – 4y + 8 = 0 then the value ofx – y is ?
(a) 4 (b) – 4 (c) 0 (d) 8
72. If a3 – b3 – c3 – 3abc = O, then ?
(a) a = b = c (b) a + b + c = 0
(c) a + c = b (d) a = b + c
73. If p, q, rare all real numbers, then (p – q)3 +(q – r)3 + (r – p)3 is equal to ?
(a) (p – q) (q – r) (r – p)
(b) 3(p – q) (q – r) (r – p)
(c) 0 (d) 1
74. 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
(c) a – b + c (d) a + b – c
75. If (a – 1)2 + (b + 2)2 + (c + 1)2 = 0, then the valueof 2a – 3b + 7c is ?
(a) 12 (b) 3 (c) –11 (d) 1
76. (x – z)3 + (z – x)3 + (x – y)3 is equal to ?
(a) 3 (y – z) (z + y) (y – z)
(b) (x – y) (y + z) (x – z)
(c) 3 (y – z) (z – x) (x – y)
(d) (y – z) (z – x) (x – y)
77. If x varies inversely as (y 2 – 1) and is equal to 24when y = 10, then the value of x when y = 5 is ?
(a) 99 (b) 12 (c) 24 (d) 100
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78. If a = 2.361, b = 3.263 and c = 5.624, then thevalue of a3 + b3 – c3 + 3abc is ?
(a) 35.621 (b) 0 (c) 19.277 (d) 1
79. If x2 + 2 = 2x, then the value of x4 – x3 + x2 + 2is ?
(a) 0 (b) 1 (c) – 1 (d) 2
80. For real a, b, c if a2 + b2 + c2 = ab + bc + ca, then
the value of bca
is ?
(a) 1 (b) 2 (c) 3 (d) 0
81. If (3a + 1)2 + (b – 1)2 + (2c – 3)2 = 0, then thevalue of (3a + b + 2c) is equal to ?
(a) 3 (b) – 1 (c) 2 (d) 5
82. The value of the express ion
))((
)( 2
accbba
))(()( 2
acbacb
))((
)( 2
cbbaac
is ?
(a) 0 (b) 3 (c) 31
(d) 2
83. If (a – 3)2 + (b – 4)2 + (c – 9)2 = 0, then the valueof cba is ?
(a) – 4 (b) 4 (c) 4 (d) 2
84. If a3b = abc = 180, a, b, c are positive integers,then the value of c is ?
(a) 110 (b) (c) 4 (d)
85. If a + b + c = 6, a2 + b2 + c2 = 14 and a3 + b3 + c3
= 36, then the value of abc is ?
(a) 3 (b) (c) 9 (d)
86. If a, b are rational numbers and (a + 1) 2 + 3 =
b 2 + a, the value of (a + b) is ?
(a) – 5 (b) (c) – 3 (d)
87. The value of (x + y + z)3 – (y + z – x)3 – (z + x –y)3 – (x + y – z)3 is ?
(a) 12 xyz (b) 24 xyz (c) 36 xyz (d) 0.
88. If x – y = 2, xy = 24, then the value of (x2 + y2)is ?
(a) 25 (b) 36 (c) 63 (d) 52
89. If the expression 4
2
2
2 ytxyx
is a perfect square,
then the values of t is ?
(a) 1 (b) 2 (c) 0 (d) 3
90. If a + b = 1 and a3 + b3 + 3ab = k, then the valueof k is ?
(a) 1 (b) (c) 5 (d)
91. If a = x + y, b = x – y, c = x + 2y, then a2 + b2 + c2
– ab – bc – ca is ?
(a) 4y2 (b) 5y2 (c) 6y2 (d) 7y2
92. If 64x+1 = x464
, then the value of x is ?
(a) 1 (b) 0 (c) 21
(d) 2
93. If ax2 + bx + c = a (x – p)2, then the relationamong a, b, c would be ?
(a) abc = 1 (b) b2 = ac
(c) b2 = 4ac (d) 2b = a + c
94. If a = 34, b = c = 33, then the value of a3 + b3 + c3
– 3abc is ?
(a) 0 (b) 111 (c) 50 (d) 100
95. If a2 + b2 + c2 = ab + bc + ca, where a, b, care non zero real numbers, then the value of
cba
is ?
(a) 2 (b) 1 (c) 0 (d) – 1
96. If a + b + c + d = 1, then the maximum value of(1 + a) (1 + b) (1 + c) (1 + d) is ?
(a) 1 (b) 3
2
(c) 3
43
(d) 3
45
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97. x varies inversely as square of y. Given thaty = 2 for x = 1, the value of x for y = 6 will beequal to ?
(a) 3 (b) 9 (c) 31
(d) 91
98. If x = – 1, then the value of 979899
111xxx
949596
111xxx
11
x is ?
(a) 1 (b) 0 (c) – 2 (d) – 1
99. If a2 + b2 + c2 + 3 = 2 (a – b – c), then the value of2a – b + c is ?(a) 3 (b) 4 (c) 0 (d) 2
100. If x2 – y2 = 80 and x – y = 8, then the average ofx and y is ?(a) 2 (b) 3 (c) 4 (d) 5
101. If cba
3333
24124
1 and a, b, c are
rational numbers, then a + b + c is equal to ?(a) 0 (b) 1 (c) 2 (d) 3
102. T he t hird p rop ort ional t o
xy
yx
and
22 yx is ?
(a) xy (b) xy (c) 3 xy (d) 4 xy
103. If x2 + 9y2 = 6xy, then x : y is ?(a) 1 : 3 (b) 3 : 2 (c) 3 : 1 (d) 2 : 3
104. If 34x
+ 2P = 12 for what value of P, x = 6 ?
(a) 6 (b) 4 (c) 2 (d) 1
105. The value of 347334
is ?
(a) 835 (b) 835
(c) 538 (d) 538
106. If a2 + b2 + 4c2 = 2 (a + b – 2c) – 3 and a, b, c arereal, then the value of (a2 + b2 + c2) is ?
(a) 3 (b) 3 41
(c) 2 (d) 2 41
107. If x = y = 333 and z = 334, then the values ofx3 + y3 + z3 – 3xyz is ?
(a) 0 (b) 667 (c) 1000 (d) 2334
108. If bacx
acbx
cbax
222
= 4(a + b + c), then
x is equal to ?(a) (a + b + c)2 (b) a2 + b2 + c2
(c) ab + bc + ca
(d) a2 + b2 + c2 – ab – bc – ca
109. Out of the given responses, one of the factors of(a2 – b2)3 + (b2 – c2)3 + (c2 – a2)3 is ?
(a) (a + b) (a – b) (b) (a + b) (a + b)
(c) (a – b) (a – b) (d) (b – c) (b – c)
110. Let a = 56 , b = 25 , c = 2 – 3 . Thenpoint out the correct alternative among the fouralternatives given below.(a) b < a < c (b) a < c < b
(c) b < c < a (d) a < b < c
111. If a = ab
b
2
then the value of a3 + b3 is ?
(a) 6 ab (b) 0 (c) 1 (d) 2
112. Number of solutions of the two equations4x – y = 2 and 2y – 8x + 4 = 0 is ?
(a) zero (b) one
(c) two (d) infinitely many
113. If x = 35
154
, the value of 1212
2020
xx
xx
is ?
(a) 1 (b) 2 (c) 3 (d) 5
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Maths By Sujit KumarCoaching Centre
114. ))(()(
))(()(
))(()( 222
cbbaca
acbacb
accbba
where a b c, is ?
(a) 1 (b) 2 (c) 3 (d) 5
115. If x = 5 – 21 , then the value of
21232 xx
is ?
(a) 732
1 (b) 37
21
(c) 372
1 (d) 37
21
116. If 6x – 5y = 13, 7x + 2y = 23 t hen 11x +18y = ?
(a) – 15 (b) 51 (c) 33 (d) 15
117. The value of (xb+c)b–c (xc+a)c–a (xa+b) a–b (x 0) is ?
(a) 1 (b) 2 (c) – 1 (d) 0
TYPE – 2
1. If p = 99, then value of p(p 2 + 3p + 3) is ?(a) 999 (b) 9999 (c) 99999 (d) 999999
2. If p = 999, then the value of 3 2 1)33( pppis ?(a) 1000 (b) 999 (c) 998 (d) 1002
3. If p = 101, then the value of 3 2 1)33( pppis ?(a) 100 (b) 101 (c) 102 (d) 1000
4. If p = 124, 3 2 1)33( ppp = ?
(a) 5 (b) 7 (c) 123 (d) 125
5. If x = 1515
, then, the value of 5x2 – 5x – 1
is ?(a) 0 (b) 3 (c) 4 (d) 5
6. The expression x4 – 2x2 + k will be a perfectsquare when the value of k is ?(a) 2 (b) 1 (c) – 1 (d) – 2
7. If p – 2q = 4, then the value of p 3 – 8q3 – 24pq –64 is :(a) 2 (b) 0 (c) 3 (d) – 1
8. If the expression x2 + x + 1 is written in the
form 22
21
qx
, then the possible values of
q are ?
(a) 31
(b) 23
(c) 32
(d) 21
9. If a2 – 4a – 1 = 0, then value of a2 + aa
a331
2
is ?(a) 25 (b) 30 (c) 35 (d) 40
10. If a2 + 1 = a, then the value of a12 + a6 + 1 is ?(a) – 3 (b) 1 (c) 2 (d) 3
11. The minimum value of (x – 2) (x – 9) is ?
(a) 411 (b) 4
49(c) 0 (d) 4
49
12. One of t he fact ors of t he exp ress ion
32534 2 xx is ?
(a) 34 x (b) 4x + 3
(c) 4x – 3 (d) 34 x
13. If 53 x , then the value of x2 – 16x + 6is ?(a) 0 (b) – 2 (c) 2 (d) 4
14. If x = 3 5 +2, then the value of x3 – 6x2 + 12x –13 is ?(a) – 1 (b) 1 (c) 2 (d) 0
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TYPE – 3
1. If x = 7 – 4 3 , then the value of
xx
1 is ?
(a) 33 (b) 38
(c) 3814 (d) 14
2. If p = 85
, q = 127
, r = 1613
and s = 2916
then ?
(a) p < q < r < s (b) s < q < p < r
(c) p < r < q < s (d) s < r < p < q
3. Given that 100.48 = x, 100.70 = y, and x2 = y2, thenthe value of z is close to ?
(a) 1.45 (b) 1.88 (c) 2.9 (d) 3.7
4. If x = 3 + 2 2 , then the value of xx
1 is ?
(a) 1 (b) 2 2 (c) 2 (d) 33
5. If x = 1313
and y = 1313
the value of x2 + y2
is ?
(a) 14 (b) 13 (c) 15 (d) 10
6. If 47.2506 = 4A + B7
+ 2C + D5
+ 6E, then the
value of 5A + 3B + 6C + D + 3E is ?
(a) 53.6003 (b) 53.603
(c) 153.6003 (d) 213.0003
7. If x = 7 – 4 3 then xx
1 is equal to ?
(a) 1 (b) 2 (c) 3 (d) 4
8. If 43
yx
, the value of xyxy
76
is ?
(a) 1 (b) 72
(c) 73
(d) 1 73
9. If a = 1515
and b = 1515
, then the value of
22
22
babababa
is ?
(a) 43
(b) 34
(c) 53
(d) 35
10. If x = 23
, then x
xx
x
111
111
is equal
to ?
(a) 1 (b) 2 / 3 (c) 2 – 3 (d) 2
11. If for non-zero, x, x2 – 4x – 1 = 0, the value of
22 1
xx is ?
(a) 4 (b) 10 (c) 12 (d) 18
12. If x = 3 + 8 , then x2 + 2
1x is equal to ?
(a) 38 (b) 36 (c) 34 (d) 30
13. If 11 b
a and 11 c
b , then ac 1 is equal to ?
(a) 0 (b) 21
(c) 1 (d) 2
14. If x2 – 3x + 1 = 0, then the value of xx 1 is ?
(a) 0 (b) 1 (c) 2 (d) 3
15. If x = 23 , then the value of
3
3 1x
x is ?
(a) 6 3 (b) 12 3 (c) 18 3 (d) 24 3
16. If x + y = 7, then the value of x3 + y3 + 21xy is ?
(a) 243 (b) 143 (c) 343 (d) 443
17. If 31
31
31
zyx , then {(x + y – z)3 + 27 xyz}
equals :(a) – 1 (b) 1 (c) 0 (d) 27
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18. If 41
xx , then
xx
1 is equal to ?
(a) 25 (b) 52 (c) 24 (d) 54
19. If x = 3 + 8 , then the value of
2
2 1x
x is ?
(a) 34 (b) 24 (c) 38 (d) 36
20. If 21
4 22
bb , then the value of 3
3 18
bb is ?
(a) 0 (b) 1 (c) 2 (d) 5
21. It 41
2 p
p the value of 33
81p
p is ?
(a) 4 (b) 5 (c) 8 (d) 15
22. If 1.5 a = 0.04 b then abab
is equal to ?
(a) 7773
(b) 3377
(c) 752
(d) 275
23. If x = 5 + 2 6 , then the value of
xx
1
is ?
(a) 2 2 (b) 3 2 (c) 2 3 (d) 3 3
24. If x = 3112 , the value of
3
3 1x
x is ?
(a) 0 (b) 2 (c) – 2 (d) 23
25. If 32
11
2
2
xxxx
, then the value of
xx 1
is ?
(a) 4 (b) 5 (c) 6 (d) 826. For a > b, if a + b = 5 and ab = 6, then the value
of (a2 – b2) is ?(a)1 (b) 3 (c) 5 (d) 7
27. If x = 3 + 8 , the value of
2
2 1x
x is ?
(a) 32 2 (b) 34 (c) 38 (d) 40 2
28. If a4 + b4 = a2b2, then (a6 + b6) equals ?(a) 0 (b) 1(c) a2 + b2 (d) a2b4 + a4b2
29. If 3fe
dc
ba
, then
222
222
432432
fbbeca
= ?
(a) 2 (b) 3 (c) 4 (d) 9
30. If 1.5x = 0.04y, then the value of 22
22
2 xxyyxy
is ?
(a) 77730
(b) 7773
(c) 77073
(d) 7774
31. If 31
a = 11, then the value of a2 – 331a is ?
(a) 1331331 (b) 1331000(c) 1334331 (d) 1330030
32. If x2 + y2 + 22
11yx
= 4, then the value of x2 + y2
is ?(a) 2 (b) 4 (c) 8 (d) 16
33. If x2 = y + z, y2 = z + x, z2 = x + y, then the value
of 11
11
11
zyx is ?
(a) – 1 (b) 1 (c) 2 (d) 4
34. If x + 31 x then the value of x18 + x12 + x6 + 1
is ?(a) 0 (b) 1 (c) 2 (d) 3
35. If a2 + b2 = 2 and c2 + d2 = 1, then the value of(ad – bc)2 + (ac + bd)2 is ?
(a) 94
(b) 21
(c) 1 (d) 2
36. If 0,21 xx
x then value of 32 1
xx is equal
to ?(a) 1 (b) 2 (c) 3 (d) 4
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37. If oboaab
ba
,,1 the value of a3 + b3 is ?
(a) 0 (b) 1 (c) – 1 (d) 238. If a2 + b2 + c2 + 3 = 2 (a + b + c) then the value of
(a + b + c) is ?(a) 2 (b) 3 (c) 4 (d) 5
39. If oppp
p
,
41
122
2 , then the value of
pp
1 is ?
(a) 4 (b) 5 (c) 10 (d) 12
40. If 51
xx , then 2
2 1x
x is ?
(a) 5 (b) 25 (c) 27 (d) 23
41. If x = 3 + 2 2 , then the value of xx
1
is ?
(a) 1 (b) 2 (c) 2 2 (d) 3 3
42. If x, y and z are real numbers such that (x – 3)2 +(y – 4)2 + (z – 5)2 = 0 then (x + y + z) is equal to ?
(a) – 12 (b) 0 (c) 8 (d) 12
43. If 532cba , then c
cba is equal to ?
(a) 2 (b) 4 (c) 5 (d) 6
44. If 31 x
x , then the value of 1
1
2
3
xxx
x is ?
(a) 23
(b) 25
(c) 27
(d) 211
45. If )(011 oaa
a then the value of (a4 – a)
is ?
(a) 0 (b) 1 (c) 2 (d) – 1
46. If x = 23 , then the value of
2
2 1x
x is ?
(a) 4 (b) 6 (c) 9 (d) 10
47. If 69
xx , then the value of
2
2 9x
x is ?
(a) 8 (b) 9 (c) 10 (d) 12
48. If aax
1 and a
ay1
, then the value of x4
+ y4 – 2x2y2 is ?
(a) 24 (b) 18 (c) 16 (d) 12
49. If 221
xx , find the value of 8x3 + 3
1x ?
(a) 48 (b) 88 (c) 40 (d) 44
50. If 21
xx and x is real, then the value of
1917 1
xx is ?
(a) 1 (b) 0 (c) 2 (d) – 2
51. If 2x + x31
= 5, find the value of 12065
2 xxx
?
(a) 41
(b) 61
(c) 51
(d) 71
52. If for two real constants a and b, the expressionax3 + 3x2 – 8x + b is exactly divisible by (x + 2)and (x – 2), then ?
(a) a = 2, b = 12 (b) a = 12, b = 2
(c) a = 2, b = – 12 (d) a = – 2, b = 12
53. If x2 – 3x + 1 = 0, then the value of 33 1
xx is ?
(a) 9 (b) 18 (c) 27 (d) 1
54. If x2 + y2 + 2x + 1 = 0, then the value of x31 + y35
is ?
(a) – 1 (b) 0 (c) 1 (d) 2
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55. If 23ba
, then value of baba
2332
is ?
(a) 512
(b) 125
(c) 1 (d) 712
56. If 23
41
xx , find the value of 3
3
81
8x
x ?
(a) 18 (b) 36 (c) 24 (d) 16
57. If )(4
baba
abx
, the value of
bxbx
axax
22
22
is ?
(a) a (b) b (c) 2 ab (d) 2
58. If 42
1
mm , find the value of
22
21
)2(
m
m ?
(a) – 2 (b) 0 (c) 2 (d) 4
59. If a2 = b + c, b2 = c + a and c2 = a + b, then the
value of cba
11
11
11
is ?
(a) abc (b) a2b2c2 (c) 1 (d) 0
60. If cc
bb
aa
111 = 1, t hen t he value of
cba
11
11
11
is ?
(a) 1 (b) 2 (c) 3 (d) 4
61. If a2 + b2 + 2b + 4a + 5 = 0, then the value of
baba
is ?
(a) 3 (b) – 3 (c) 31
(d) – 31
62. If ),0,0(111
yxyxyxyx
t hen, t he
value of x3 – y3 is ?
(a) 0 (b) 1 (c) – 1 (d) 2
63. If x = a (b – c), y = b (c – a) and z = c (a – b), then
333
cz
by
ax
?
(a) abcxyz
3 (b) 3 xyzabc
(c) abcxyz3
(d) abcxyz
64. If xy (x + y ) = 1, t hen t he value of
3333
1yx
yx ?
(a) 0 (b) 1 (c) 3 (d) – 2
65. If 61
252 2 xx
x, value of
xx
1 is ?
(a) 2 (b) 21
(c) – 21
(d) – 2
66. If 21
22
yxyx
, then value of yxyx
33
is ?
(a) 51
(b) 53
(c) 54
(d) 1
67. If 51 x
x , then 3532
2 xxx
is equal to ?
(a) 5 (b) 51
(c) 3 (d) 31
68. If 11914
4 x
x and x > 1, t hen the value of
33 1
xx is ?
(a) 54 (b) 18 (c) 72 (d) 36
69. If x – y = 47xyyx
, the numerical value of xy
is ?
(a) 34
(b) 43
(c) 41
(d) 31
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70. If x + y + z = 0, then xyz
zxy
yzx 222
?
(a) (xyz)2 (b) x2 + y2 + z2
(c) 9 (d) 3
71. If a + b + c = 0 then the value of ))((
1cbba
))((1
abca ))((1
bcac is ?
(a) 1 (b) 0 (c) – 1 (d) – 2
72. If 3x + x21
= 5, then the value of 33
271
8x
x
is ?
(a) 118 21
(b) 30 2710
(c) 0 (d) 1
73. If a, b, c are real and a2 + b2 + c2 = 2 (a – b – c)– 3, then the value of 2a – 3b + 4c is ?
(a) – 1 (b) 0 (c) 1 (d) 2
74. If x + y = z, then the expression x3 + y3 – z3 +3xyz will be equal to ?
(a) 0 (b) 3xyz (c) – 3xyz (d) z3
75. If 21
xx = 3, then the value of )x72 + x66 + x54
+ x36 + x24 + x6 + 1) is ?
(a) 1 (b) 2 (c) 3 (d) 4
76. If a + b + c = 0, then the value of bca
cba
2
222
is ?
(a) 0 (b) 1 (c) 2 (d) 3
77. If n = 7 + 4 3 , then the value of
nn
1
is ?
(a) 2 3 (b) 4 (c) – 4 (d) – 2 3
78. If 21
xx = 3, then the value of x206 + x200 + x90
+ x84 + x18 + x12 + x6 + 1 is ?
(a) 0 (b) 1 (c) 84 (d) 206
79. If x = 23 , then the value of 1
xx is ?
(a) 2 2 (b) 2 3 (c) 2 (d) 3
80. If p + q = 10 and pq = 5, then the numerical
value of pq
qp will be ?
(a) 16 (b) 20 (c) 22 (d) 18
81. If 31
aa , then the value of 2
16
6 a
a will
be ?
(a) 1 (b) 2 (c) 3 3 (d) 5
82. If x3 + y3 = 35 and x + y = 5, then the value of
yx11
will be ?
(a) 31
(b) 65
(c) 6 (d) 32
83. If x = 3 + 2 2 and xy = 1, then the value of
22
22
33
yxyxyxyx
is ?
(a) 3130
(b) 3170
(c) 3135
(d) 3134
84. If a3 – b3 = 56 and a – b = 2, then the value ofa2 + b2 will be ?
(a) 48 (b) (c) 22 (d)
85. If (a2 + b2)3 = (a3 + b3)2, then ab
ba is ?
(a) 31
(b) 32
(c) – 31
(d) – 32
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86. If 51
xx , then t he value of
11353
4
234
xxxxx
is ?
(a) 2343
(b) 2147
(c) 2341
(d) 2145
87. If a2 + b2 + c2 = ab + bc + ca, where a, b, care non zero real numbers, then the value of
cba
is ?
(a) 2 (b) 1 (c) 0 (d) – 1
88. If ax + by = 3, bx – ay = 4, and x2 + y2 = 1, thenthe value of a2 + b2 is ?
(a) 17 (b) 16 (c) 9 (d) 25
89. If x is real, 01
xx and 0
13
3 x
x , then the
value of 41
xx is ?
(a) (b) (c) 16 (d)
90. If 31 x
x , then the value of
5
5 1x
x is ?
(a) 322 (b) (c) 123 (d)
91. If 31 x
x , the value of 33 1
xx is ?
(a) 32 (b) 36 (c) 40 (d) 49
92. If 11914
4 m
m , then mm 1 = ?
(a) 3 (b) 4 (c) 2 (d) 1
93. If x + y + z = 6, then the value of (x – 1)3 +(y – 2)3 + (z – 3)3 is ?
(a) 3 (x – 1) (y + 2) (z – 3)
(b) 3 (x + 1) (y – 2) (z – 3)
(c) 3 (x – 1) (y – 2) (z + 3)
(d) 3 (x – 1) (y – 2) (z – 3)
94. If x + y = 2z then the value of zyz
zxx
is ?
(a) 1 (b) 3 (c) 21
(d) 2
95. If x2 + 1 = 2x, then the value of 13
1
2
24
xxx
x is ?
(a) 0 (b) 1 (c) 2 (d) – 2
96. If x3 + y3 = 35 and x + y = 5, then the value of
yx11
will be ?
(a) 31
(b) 65
(c) 6 (d) 32
97. If baz
acy
cbx
, then ?
(a) caxz
bczy
abyx
(b) cz
by
ax
(c) cxz
bzy
cyx
(d) None of the above is true
98. If x = 23 , then the value of 33 1
xx is ?
(a) 14 2 (b) 14 3 (c) 22 2 (d) 10 2
99. If ax + by = 3, bx – ay = 4 and x2 + y2 = 1, thenthe value of a2 + b2 is ?(a) 17 (b) 16 (c) 9 (d) 25
100. If x is real, 01 x
x and 013
3 x
x , then the
value of 41
xx is ?
(a) 4 (b) 9 (c) 16 (d) 25
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101. If x > 1 and 22 1
xx = 83, then 3
3 1x
x is ?
(a) 764 (b) 750 (c) 756 (d) 760
102. If 21
aa = 3, then 3
3 1a
a = ?
(a) 2 3 (b) 2 (c) 3 3 (d) 0
103. If xaax 11
, then the value of x – x2 is ?
(a) – a (b) a1
(c) – a1
(d) a
104. If 31
122 xx
x, then the value of 3
3 1x
x
is :(a) 81 (b) 110 (c) 125 (d) 27
105. If 41
xx , then the value of 4
4 1x
x is ?
(a) 64 (b) 194 (c) 81 (d) 124106. If x2 + y2 + z2 = 2(x – y – z) – 3 then the value of
2x – 3y + 4z is (assume that x, y, z are all realnumbers) ?
(a) 9 (b) 1 (c) 3 (d) 0107. If a + b + c = 0, t hen t he value of
bac
acb
cba
bac
acb
cba
is ?(a) 8 (b) – 3 (c) 9 (d) 0
108. If a, b, c are non-zero, 11 b
a and 11 c
b ,
then the value of abc is ?
(a) – 1 (b) 3 (c) – 3 (d) 1
109. If 42
1
a
a , then t he value of
2
2
212
aa is ?
(a) 0 (b) 2 (c) – 2 (d) 4
110. If a + b + c = 2s, then
222
2222
cbascsbsas
is equal to ?
(a) a2 + b2 + c2 (b) 0
(c) 1 (d) 2
111. If xy (x + y) = 1 then, the value of 33
33
1yx
yx
is ?
(a) 3 (b) – 3 (c) 1 (d) – 1
112. If x + y + z = 6 and s2 + y2 + z2 = 20 then thevalue of x3 + y3 + z3 – 3xyz is ?
(a) 64 (b) 70 (c) 72 (d) 76
113. If x = 1 – 2 , the value of 31
xx is ?
(a) – 8 (b) 8 (c) 2 2 (d) 1
114. If 01 ab
ba
, then the value of a3 + b3 is ?
(a) 3 (b) 0 (c) 1 (d) – 1
115. If 991 x
x , find the value of 21022100
2 xxx
?
(a) 61
(b) 21
(c) 31
(d) 41
116. If x = 3 + 2 2 , the value of 22 1
xx is ?
(a) 36 (b) 30 (c) 32 (d) 34
117. If (a + b + c) = 0, then
abc
cab
bca 222
is ?
(a) 3 (b) – 1 (c) 0 (d) 1
118. If 1111
c
cb
ba
a, then the value of
cba
11
11
11
is ?
(a) 1 (b) 3 (c) 4 (d) 0
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119. If (x – 3)2 + (y – 5)2 + (z – 4)2 = 0, then the value
of 16259
222 zyx is ?
(a) 12 (b) 9 (c) 3 (d) 1
120. If xxx
323
, then the value of 2
2 1x
x is ?
(a) 2 91
(b) 2 94
(c) 3 91
(d) 3 94
121. If x2 = y + z, y2 = z + x and z2 = x + y, then the
value of zyx
11
11
11
is ?
(a) – 1 (b) 1 (c) 2 (d) 0
122. If x2 – 3x + 1 = 0, then t he value of
22 11
xxxx is ?
(a) 10 (b) 2 (c) 6 (d) 8
123. If 0343434
z
zy
yx
x, then the value
of zyx111
is ?
(a) 9 (b) 3 (c) 4 (d) 6124. If x = a – b, y = b – c, z = c – a, then the numerical
value of the algebraic expression x3 + y3 + z3 –3xyz will be ?(a) a + b + c (b) 0(c) 4 (a + b + c) (d) 3 abc
125. If a2 + b2 = 5ab, then the value of
2
2
2
2
ab
ba
is ?(a) 32 (b) 16 (c) 23 (d) – 23
126. If 2323
x and 2323
y , then t he
value of x3 + y3 is?(a) 950 (b) 730 (c) 650 (d) 970
127. If (x – a) (x – b) = 1 and a – b + 5 = 0, then the
value of 3
3 1ax
ax
is ?
(a) – 125 (b) 1 (c) 125 (d) 140128. If a2 + b2 + c2 = 2 (a – b – c) – 3, then the value
of 4a – 3b + 5c is ?(a) 2 (b) 3 (c) 5 (d) 6
129. If 2x + x2
= 3, then the value of 33 1
xx + 2
is :
(a) 89
(b) 825
(c) 87
(d) 11
130. If xy + yz + zx = 0, then
xyzzxyyzx 222
111 0,, zyx is
equal to ?(a) 3 (b) 1(c) x + y + z (d) 0
131. If a2 + b2 + c2 = 2(a – b – c) – 3 then the value of2a – 3b + 4c is ?
(a) 7 (b) 2 (c) 3 (d) 1132. If a + b + c = 9, (where a, b, c are real numbers)
then the minimum value of a2 + b2 + c2 is ?
(a) 100 (b) 9 (c) 27 (d) 81133. If a + b + c = 15 and a2 + b2 + c2 = 83 then the
value of a3 + b3 + c3 – 3 abc = ?
(a) 200 (b) 180 (c) 190 (d) 210
134. If x2 – 3x + 1 = 0, then the value of 55 1
xx
is equal to ?
(a) 87 (b) 123 (c) 135 (d) 201
135. If a – b = 3 and a3 – b3 = 117 then |a + b| is equalto ?
(a) 3 (b) 5 (c) 7 (d) 9
136. If 11
x
x = 1, then 5
5
111
x
x equals ?
(a) 1 (b) 2 (c) 4 (d) 8
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137. If baba
111, then the value of a3 + b3 is ?
(a) 0 (b) – 1 (c) 1 (d) 2
138. If a2 + b2 + c2 = ab + bc + ca, then bca
is equal
to ?
(a) 1 (b) 2 (c) 3 (d) 4
139. If a + b + c = 0, then a3 + b3 + c3 is equal to ?
(a) a + b + c (b) abc
(c) 2 abc (d) 3 abc
140. If bzx
xza
yxxy
, and czy
yz
, where a,
b, c are all non-zero numbers, then x equals to ?
(a) acbcababc
2
(b) bcacababc
2
(c) abbcacabc
2
(d) acbcababc
2
141. If x + y + z = 13 and x2 + y2 + z2 = 69, then xy +z (x + y) is equal to ?
(a) 70 (b) 40 (c) 50 (d) 60
142. If 3 32 x , then the value of 33 1
xx is ?
(a) 8 (b) 9 (c) 2 (d) 4
TYPE – 4
1. If (2x)(2y) = 8 and (9x) (3y) = 81, then (x, y) is ?
(a) (1, 2) (b) (2, 1) (c) (1, 1) (d) (2, 2)
2. The lines 2x + y = 5 and x + 2y = 4 intersect atthe point ?
(a) (1, 2) (b) (2, 1) (c) ( 25
, 0) (d) (0, 2)
3. The graph of the linear equation 3x + 4y = 24 isa straight line intersecting x-axis and y-axis atthe points A and B respectively. P(2, 0) and Q
23
,0 are two points on the sides OA and OB
respectively of OAB, where O is the origin ofthe co-ordinate system. Given that AB = 10 cm,then PQ = ?
(a) 20 cm (b) 2.5 cm (c) 40 cm (d) 5 cm
4. The length of the intercept of the graph of theequation 9x – 12y = 108 between the two axesis ?
(a) 15 units (b) 9 units (c) 12 units (d) 18 units
5. The x-intercept of the graph of 7x – 3y = 2 is ?
(a) 43
(b) 73
(c) 52
(d) 72
6. If 2x + y = 6 and x = 2 are two linear equations,then graph of two equations meet at a point :
(a) (2, 0) (b) (0, 2) (c) (2, 2) (d) (1, 2)
7. An equation whose graph passes through theorigin, out of given equations 2x + 3y = 2, 2x –3y = 3, –2 + 3y = 5 and 2x + 3y = 0 is ?
(a) 2x – 3y = 3 (b) –2x + 3y = 5
(c) 2x + 3y = 0 (d) 2x + 3y = 2
8. In a linear equation is of the form x = k where kis a constant, then graph of the equation will be ?
(a) a line parallel to x-axis
(b) a line cutting both the axes
(c) a line marking positive acute angle with x-axis
(d) a line parallel to y-axis
9. The graph of the equation 2x – 3y = 6 intersectsthe y-axis at the point ?
(a) (–2, 0) (b) (0, –2) (c) (2, 3) (d) (2, –3)
10. The graphs of the equations 25x + 75y = 255and x = 9 meet at the point ?
(a) (0, 9) (b) (9, 0) (c) (3, 0) (d) (0, 3)
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11. The area bounded by the lines x = 0, y = 0,x + y = 1, 2x + 3y = 6 (in square units) is ?
(a) 2 (b) 2 31
(c) 2 21
(d) 3
12. The graph of the equation 4x – 5y = 20 intersectsthe x-axis at the point ?(a) (2, 0) (b) (5, 0) (c) (4, 5) (d) (0, 5)
13. If x and y are positive real numbers and xy = 8,then the minimum value of 2x + y is ?
(a) 9 (b) 17 (c) 10 (d) 814. The graph of 2x + 1 = 0 and 3y – 9 = 0 intersect
at the point ?
(a) (– 21
, – 3) (b) (– 21
, 3)
(c) ( 21
, – 3) (d) None of these
15. An equation of the form ax + by + c = 0 wherea 0, b 0, c = 0 represents a straight line whichpasses through
(a) (0, 0) (b) (3, 2)(c) (2, 4) (d) None of these
16. The linear equation such that each point on itsgraph has an ordinate four times its abscissa is ?(a) y + 4x = 0 (b) y = 4x
(c) x = 4y (d) x + 4y = 017. If the graphs of the equations 3x + 2y = 18 and
3y – 2x = 1 intersect at the point (p, q), then thevalue of p + q is ?
(a) 7 (b) 6 (c) 5 (d) 418. If the grap hs of the equations x + y = 0 and
5y + 7x = 24 intersect at (m, n), then the value ofm + n is ?
(a) 2 (b) 1 (c) 0 (d) – 119. The area of the triangle formed by the graphs of
3x + 4y = 12, x-axis and y-axis (in sq. units) is ?
(a) 4 (b) 12 (c) 6 (d) 8
20. Equat ion of the straight line parallel to x-axisand also 3 units below x-axis is ?(a) x = – 3 (b) y = 3 (c) y = – 3 (d) x = 3
21. The straight line 2x + 3y = 12 passes through ?(a) 1st, 2nd and 3rd quadrant(b) 1st, 2nd and 4th quadrant(c) 2nd, 3rd and 4th quadrant(d) 1st, 3rd and 4th quadrant
TYPE – 5
1. If 32
ba
and 54
cb
, then the ratio cbba
equal
to ?
(a) 2720
(b) 2027
(c) 86
(d) 68
2. If a : b = 2 : 3 and b : c = 4 : 5, find a2 : b2 : bc ?
(a) 4 : 9 : 45 (b) 16 : 36 : 45
(c) 16 : 36 : 20 (d) 4 : 36 : 40
3. If A : B = 83:
21
, B : C = 95:
31
and C : D = 43:
65
then the ratio A : B : C : D is ?
(a) 6 : 4 : 8 : 10 (b) 6 : 8 : 9 : 10
(c) 8 : 6 : 10 : 9 (d) 4 : 6 : 8 : 10
4. If x : y = 3 : 2, then the ratio 2x2 + 3y2 : 3x2 – 2y2
is equal to ?
(a) 12 : 5 (b) 6 : 5 (c) 30 : 19 (d) 5 : 3
5. If A : B : C = 2 : 3 : 4, then AC
CB
BA :: is equal
to ?
(a) 8 : 9 : 16 (b) 8 : 9 : 12
(c) 8 : 9 : 24 (d) 4 : 9 : 16
6. If A : B = 1 : 2, B : C = 3 : 4 and C : D = 5 : 6, findD : C : B : A ?
(a) 6 : 5 : 4 : 2 (b) 6 : 3 : 2 : 1
(c) 6 : 4 : 2 : 1 (d) 48 : 40 : 30 : 15
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[18]
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7. If 74
6352
baba
then a : b is equal to ?
(a) 21 : 36 (b) 2 : 59 (c) 59 : 2 (d) 36 : 21
8. If 53
,97
cb
ba
, then the value of a : b : c is ?
(a) 7 : 9 : 15 (b) 7 : 9 : 5
(c) 21 : 35 : 45 (d) 7 : 3 : 15
9. If x : y = 7 : 3, then the value of 22
2
yxyxy
is ?
(a) 43
(b) 34
(c) 73
(d) 37
10. If baba
5353
= 5, then a : b is equal to ?
(a) 2 : 1 (b) 5 : 3 (c) 3 : 2 (d) 5 : 2
11. If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) :(mq + ns + ou) equals ?
(a) 3 : 2 (b) 2 : 3 (c) 1 : 3 (d) 1 : 2
12. If x : y = 3 : 4, then (7x + 3y) : (7x – 3y) is equalto ?
(a) 5 : 2 (b) 4 : 3 (c) 11 : 3 (d) 37 : 19
13. If a : b : c = (y – z) : (z – x) : (x – y) then the valueof ax + by + cz is ?
(a) 1 (b) 3 (c) 0 (d) – 1
14. If 50% of (p – q) = 30% of (p + u), then p : q isequal to ?
(a) 5 : 3 (b) 4 : 1 (c) 3 : 5 (d) 1 : 4
15. If x : y = 2 : 1, then (5x2 – 13xy + 6y2) is equalto ?
(a) 43
(b) 34
(c) 0 (d) 455
16. If y : x = 4 : 15, then the value of
yxyx
is ?
(a) 1911
(b) 1119
(c) 114
(d) 1915
17. If x : y = 3 : 4, then the value of yxyx
2725
= ?
(a) 257
(b) 237
(c) 297
(d) 177
18. The work done by (x – 1) me in (x + 1) days andthe work done by (x + 1) men in (x + 2) days arein the ratio 5 : 6. x is ?
(a) 16 (b) 10 (c) 8 (d) 6
19. If 54
ba
and 1615
cb
, then 22
22
2045718
acac
is equal
to ?
(a) 31
(b) 52
(c) 43
(d) 41
TYPE – 6
1. If [p] means the greatest integer less than or equal
to p, then 3414
41
is equal to ?
(a) 4 (b) 5 (c) 6 (d) 7
2. If is an operation such that for positive integersa and b, b, a b = – a + b – (–2), then the valueof 4 3 is ?
(a) 1 (b) – 1 (c) + 3 (d) – 3
3. If 1ab
ba
, then the value of (a3 + b3) is ?
(a) 0 (b) 1 (c) 2 (d) 3
4. If is an operation such that a b = 2a whena > b = a + b when a < b = a2 when a = b, then,
31115553
4475 is equal to ?
(a) 31
(b) 2314
(c) 32
(d) 1314
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[19]
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5. If is an operation such that a b = a + b when
a > 0, b > 0. a b = 22 ba for all other values
of a and b. The value of is ?
(a) 51
(b) 54
(c) 56
(d) 52
6. If p and q represent digits, what is the possiblemaximum value of q in the statement 5p9 + 327+ 2q8 = 1114 ?
(a) 9 (b) 8 (c) 7 (d) 6
7. If x + y = a and xy = b2, then the value of x3 – x2y– xy2 + y3 in terms of a and b is :
(a) (a2 + 4b2) a (b) a3 – 3b2
(c) a3 – 4b2 a (d) a3 + 3b2
8. The value of for which the expression x3 + x2 –5x + will be divisible by (x – 2) is ?
(a) 2 (b) – 2 (c) – 3 (d) 4
9. The number of pairs of natural numbers, thedifference of whose squares is 45 will be ?
(a) 2 (b) 3 (c) 6 (d) 5
10. The expression x4 – 2x2 + k will be a perfectsquare when the value of k is ?
(a) 2 (b) 1 (c) – 1 (d) – 2
11. If a + b + c + d = 1, then the maximum value of(1 + a)(1 + b) (1 + c) (1 + d) is ?
(a) 1 (b) 3
21
(c) 3
43
(d) 4
45
12. I read 83
of a book on one day and 54
of the
remainder on another day. If there were 30 poagesunread now, how many pages did the bookcontain ?
(a) 200 (b) 60 (c) 240 (d) 65
13. If x = 3 323 32 baabaa , then x3 +
3bx is equal to ?
(a) 0 (b) a (c) 2a (d) 1
14. If x 0, y 0 and z 0 and 222
111zyx
zyyzxy111
then the relation among x, y, z is ?
(a) x + y + z = 0 (b) x + y = z
(c) 0111
zyx (d) x = y = z
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