Maths By Sujit Kumar Coaching Centre - MyNotesAdda€¦ · Maths By Sujit Kumar Coaching Centre 1....

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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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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


(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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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


(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


(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


(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


(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



[6]


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



[7]


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



[8]


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



[9]


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



[10]


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



[11]


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



[12]


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



[13]


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



[14]


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



[15]


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



[16]


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)



[17]


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



[18]


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



[19]


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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