( x − a)( x − b)

1. For real x , the function will assume all real values provided.
( x − c)
(a) a  b  c (b) a  b  c (c) a  c  b (d) a  c  b
2. Solution of 0 < |x-3|  5 is

(a) [-2, 8] (b) [-2,3) U (3,8] (c) [-2, 9) (d) none

( x − 3 )( x + 5 )( x − 7 )
3. Solution of  0 is
| x − 4 | (x + 6)

(a) (-6, -5] U [3,7] (b) [3,7]

(c) (-6, -5]  [3, 4)  (4,7] (d) none

4. If [x]2 – 5[x] + 6 = 0 (where [.] denotes the greatest integer function), then x belongs to

(a) [2,4) (b) [2,4) – {3} (c) {3} (d) {2}

5. The values of b and c for which the identity f (x + 1) – f(x) = 8x + 3 is satisfied, where f(x) = bx2 + cx +
d, are

(a) 4, 1 (b) 4, –1 (c) –1, 4 (d) none

6. If A contains 10 elements, then total number of functions defined from A to A is
(a) 10 (b) 210 (c) 10 10 (d) 210 − 1
x−| x |
7. If f (x ) = , then f (−1) =
| x|

(a) 1 (b) – 2 (c) 0 (d) 2

1 1
8. If f (x ) = + for x  2, then f (11) =
x + 2 2x − 4 x − 2 2x − 4
7 5 6 5
(a) (b) (c) (d)
6 6 7 7
1
9. Domain of the function is
2
x −1
(a) (−, − 1)  (1, ) (b) (−, − 1]  (1, ) (c) (−, − 1)  [1, ) (d) none
1
10. The domain of the function f (x ) = is
| x | −x

(a) R+ (b) R− (c) R0 (d) R

11. The domain of the function f (x ) = (2 − 2 x − x 2 ) is

(a) − 3  x  3 (b) − 1 − 3  x  −1 + 3 (c) −2  x  2 (d) none
12. If the domain of function f (x ) = x 2 − 6 x + 7 is (−, ) , then the range of function is
(a) (−, ) (b) [ − 2, ) (c) (−2, 3) (d) (−, − 2)

13. The domain of the function f (x ) = x − x 2 + 4+x + 4−x is

(a) [−4, ) (b) [−4, 4] (c) [0, 4 ] (d) [0, 1]
 1+ x2
14. The range of is
x2

(a) (0, 1) (b) (1, ) (c) [0, 1] (d) [1, )

x+2
15. The range of the function f (x ) = is
| x + 2|

(a) {0, 1} (b) {– 1, 1} (c) R (d) R − {−2}

x2 + x + 2
16. Range of the function f (x ) = ; x  R is
x2 + x +1
(a) (1, ) (b) (1, 11 / 7) (c) (1, 7 / 3] (d) (1, 7 / 5]

17. The domain of the function log( x 2 − 6 x + 6) is

(a) (−, ) (b) (−,3 − 3 )  (3 + 3 , ) (c) (−, 1] [5, ) (d) [0, )
1
18. Find the value of x satisfying =2
4log2 x
(a) 4 (b) -4 (c) ±4 (d) -3
19. The domain of the function f (x ) = log 3 + x (x − 1) is 2

(a) (−3, − 1)  (1, ) (b) [−3, − 1) [1, )

(c) (−3,−2)  (−2, − 1)  (1, ) (d) [−3, − 2)  (−2, − 1)  [1, ]
20. Logarithm of 32 4 to the base 2 2 is
5

(a) 3.6 (b) 5 (c) 5.6 (d) none

21. The number log 2 7 is
(a) An integer (b) A rational number (c) An irrational number (d) A prime number
22. If log 10 3 = 0.477 , the number of digits in 3 is 40

(a) 18 (b) 19 (c) 20 (d) 21

23. Which is the correct order for a given number  in increasing order
(a) log 2 , log 3 , log e , log10  (b) log10 , log 3 , log e , log 2 
(c) log10 , log e , log 2 , log 3  (d) log 3 , log e , log 2 , log10 
24. If log 0.3 (x − 1)  log 0.09 (x − 1), then x lies in the interval
(a) (2, ) (b) (– 2, –1) (c) (1, 2) (d) none
(l 2 + lm + m 2 ) (m 2 + nm + n 2 ) (n 2 + nl + l 2 )
 l   xm   xn 
25. For x  0,  xm 


 xn



 xl

 =
x     
(a) 1 (b) x (c) does not exist (d) none
1 1 1
26. If 2 x =4 =8 y z
and xyz = 288 , then + + =
2x 4y 8z
(a) 11/48 (b) 11/24 (c) 11/8 (d) 11/96
n +1 n −1
2 .3 + 7 .3
27. =
3 n + 2 − 2(1 / 3)1 −n
(a) 1 (b) 3 (c) –1 (d) 0
x +2 2−2 x
2 3
28. If   =  , then x=
3 2
(a) 1 (b) 3 (c) 4 (d) 0
( x 2 + 2) ( x 2 + 2)
29. The equation 4 − 9.2 + 8 = 0 has the solution
(a) x = 1 (b) x = −1 (c) x = 2 (d) x = − 2
30. The greatest number among 3 9 , 4 11 , 6 17 is
(a) 3 9 (b) 4 11 (c) 6
17 (d) cannot be determined
31. If x = 3 ( 2 + 1) − 3 ( 2 − 1); then x 3 + 3 x =
(a) 2 (b) 6 (c) 6x (d) none
32. If f(x) = log1 2 ( x − 2x + 2 ) , then domain of f(x) is
2

(a) R (b) {1} (c) R+ (d) {2}

33. If f(x) = logx2 x , then the domain of f(x) is
(a) R+ (b) R – {1} (c) R+ – {1} (d) none
x + e
2
34. If f(x) = n  2  , then range of f(x) is
 x +1 
(a) (0, 1) (b) [0, 1] (c) [0, 1) (d) (0, 1]
2
35. The value of x, satisfying the inequality log0.3(x + 8) > log0.39x, lies in
(a) 1 < x < 8 (b) 8 < x < 13 (c) x > 8 (d) none
36. The value of |logba + logab| where a and b are positive numbers is always
(a)  2 (b)  2 (c) = 2 (d) none
loga n − logb n
37. If a > 0, c > 0, b = ac , a  1, c  1, ac  1 and n > 0, then the value of is equal to
logb n − logc n
loga n logn a
(a) (b) (c) logca (d) none
logc n logn c
38. Values of x satisfying the equation log( 2x +3 ) ( 6x 2 + 23x + 21) = 4 − log( 3x +7 ) ( 4x 2 + 12x + 9 ) are
1 1 1 1
(a) −1, − (b) −2, − (c) −1, − (d) −2, −
3 4 4 3
 x 
6 log10  
39. Value of x, satisfying the equation aloga x. log10 a.loga 5 − 3  10  = 9log100 x +log4 2 is
5
(a) 50 (b) 100 (c) 150 (d) 200
1 1 1 1
40. + + + ....... + =
log2 n log3 n log4 n log43 n
logn 1
(a) (b) (c) log43! n (d) none
log(43!) log 43! n
loga ( logb a )
41. The value of is
logb ( loga b )
(a) logab (b) logba (c) − logab (d) none
42. The values of x, satisfying the equation 2logx a + logax a + 3loga2x a = 0  a > 0 are
(a) a−2, a−1 (b) a−1/2, a−1 (c) a−3, a−1 (d) a−4/3, a−1/2
1
(log 2 x − 2 )
43. The solutions of the equation x 2 = 16 are
1 1
(a)  2 2 (b) 4, − 2 (c) 16 , (d) 4 ,
4 16
1+ x
If f (x ) = log then f 
2x 
44. , 2
is equal to
1 − x  1 + x 
(a) [ f (x )]
2
(b) [ f (x )]3 (c) 2 f (x ) (d) 3 f (x )
45. The value of log 3 4 log 4 5 log 5 6 log 6 7 log 7 8 log 8 9 is
(a) 1 (b) 2 (c) 3 (d) 4
46. If x = log a (bc), y = log b (ca), z = log c (ab) , then which of the following is equal to 1
(a) x + y + z (b) (1 + x )−1 + (1 + y)−1 + (1 + z)−1
(c) xyz (d) none
 The equation x3 / 4(log x) +log x −(5 / 4) = 2 has
2
47. 2 2

(a) at least one real solution (b) exactly three real solutions
(c) exactly one irrational solution (d) complex roots
48. The least value of the expression 2log10x – logx(0.10), for x  1, is
(a) 10 (b) -0.01 (c) 2 (d) none
49. The domain of the function (log05 x ) is –
(a) [ 1,  [ (b) ] 0,  [ (c) ] 0, 1] (d) ] 0.5, 1]
50. The domain of the definition of the function f ( x ) = log x − 4 ( 4 − x ) is −
(a) (− , − 4)  (4 , ) (b) (− , − 5) (c) (−, − 5)  (−5 , − 4) (d) (− , − 5)  (−4 , 4)
 x 
51. Domain of the function f ( x ) = log 1/ 3  2  is −
 x − 1
 1− 5   1+ 5 
(a) (−1, 0)  (1, ) (b) (− , − 1)  (0 , 1) (c)  , 1   ,  (d) none
 2   2 
   
log 0.3 ( x − 1)
52. The domain of the function f ( x) = is
x 2 − 3x − 18
(a) [2,6] (b) (2,6) (c) [2,6) (d) none
53. What is domain of logarithmic function
(a) ( 0,  ) (b) R (c) ( −,  ) (d) ( −, 0 )
54. If f ( x) = log x , g ( x) = x3 then f ( g (a)) + f ( g (b)) =
(a) f  g (a) + g (b) (b) 3 f (ab) (c) g ( f (ab)) (d) g ( f (a) + f (b))
2𝑥−1
55. The domain of the function f(x)=√−log 𝑥−4 (log 2 ) is
2 3+𝑥
(a) (-4, -3) ᴜ (4, ∞) (b) (-∞, -3) ᴜ (4, ∞) (c) (-∞, -4) ᴜ (3, ∞) (d) none
𝑥−5 3
56. The domain of the function 𝑓(𝑥)= log10 𝑥 2 −10𝑥+24 - √𝑥 + 5 is
(a) (-5, ∞) (b) (5, ∞) (c) (2,5) ᴜ (5, ∞) (d) (4,5) ᴜ (6, ∞)
57. The domain of the function f (x) = log x is equal to
2

(a) R − 0 (b) ( 0, ) (c) R (d) none

58. The domain of real valued function f (x) = loge |loge X | is
(a) (1,+ ) (b) ( 0, ) (c) ( e ,  ) (d) none

59. log 7 log 7 7( 7 7 ) =

(a) 3log 2 7 (b) 1 − 3log3 7 (c) 1 − 3log 7 2 (d) none
60. If A = log 2 log 2 log 4 256 + 2 log 2
2, then A is equal to
(a) 2 (b) 3 (c) 5 (d) 7
61. If log x : log y : log z = ( y − z):( z − x) : ( x − y) then
(a) x y . y z .z x = 1 (b) x x y y z z = 1 (c) x
x y
y z z =1 (d) none

62. The solution of the equation log 7 log 5 ( x 2 + 5 + x ) = 0

(a) x = 2 (b) x = 3 (c) x = 4 (d) x = −2
63. If a, b, c are distinct positive numbers, each different from 1, such that
[logb a logc a − log a a] + [log a b logc b − logb b] + [log a c logb c − log c c] = 0, then abc =
 (a) 1 (b) 2 (c) 3 (d) none
1 1
64. If +  x, then x be
log3  log 4 
(a) 2 (b) 3 (c) 3.5 (d) 

1
65. If  log 0.1 x  2 then........
2
1 1 1
(a) The maximum value of x is (b) x lies between and
10 100 10
1 1 1
(c) x does not lie between and (d) The minimum value of x is
100 10 100
x+2
66. The set of real values of x for which log 0.2  1 is
x
 5 5 
(a)  −, −   (0, +) (b)  , +   (c) (−, − 2)  (0, + ) (d) none
 2 2 
67. The set of real values of x satisfying log1/2 ( x 2 − 6 x + 12)  −2 is
(a) ( −, 2 (b) [2, 4] (c)  4, + ) (d) none
68. Logarithm of 32 5 4 to the base 2 2 is
(a) 3.6 (b) 5 (c) 5.6 (d) none
15
69. The value of is
10 + 20 + 40 − 5 − 80

(a) 5 (5 + 2 ) (b) 5 (2 + 2 ) (c) 5 (1 + 2 ) (d) 5 (3 + 2 )

70. The rationalizing factor of a1 / 3 + a−1 / 3 is
(a) a1 / 3 − a −1 / 3 (b) a 2 / 3 + a −2 / 3 (c) a 2 / 3 − a −2 / 3 (d) a 2 / 3 + a −2 / 3 − 1

71. (3 + 5 ) is equal to
1
(a) 5 +1 (b) 3+ 2 (c) ( 5 + 1) / 2 (d) ( 5 + 1)
2

72. [10 − (24 ) − (40 ) + (60 )] =

(a) 5+ 3+ 2 (b) 5+ 3− 2 (c) 5− 3+ 2 (d) 2+ 3− 5

73. 4
(17 + 12 2 ) =

(a) 2 +1 (b) 21 / 4 ( 2 + 1) (c) 2 2 +1 (d) none

74. 3
(61 − 46 5 ) =

(a) 1 − 2 5 (b) 1− 5 (c) 2− 5 (d) none

75. The equation (x + 1) − (x − 1) = (4 x − 1) , x  R has

(a) One solution (b) Two solution (c) Four solution (d) No solution
76. The remainder obtained when the polynomial x 64
+ x + 1 is divided by
27
(x + 1) is
(a) 1 (b) – 1 (c) 2 (d) – 2
  1
77. If a = log1/ 2 0.125 and b = log3   then
 24 − 17 
 (a) a> 0, b > 0 (b) a < 0, b < 0 (c) a > 0, b < 0 (d) a < 0, b > 0

78. The value of x, satisfying 34log9 ( x+1) = 22log2 x + 3 , is

(a) x = 0 (b) x = 1 (c) x = 2 (d) x = 3

f ( x) − 5
79. Let f : R → R be a function defined by f ( x + 1) = x  R then which of the following
f ( x) − 3
statements is /are true?
(a) f (2008) = f (2004) (b) f (2006) = f (2010) (c) f (2006) = f (2002) (d) f (2006) = f (2018)

x 2 + 14 x + 9
80. If x is real, then value of the expression lies between
x 2 + 2x + 3
(a) 5 and 4 (b) 5 and – 4 (c) – 5 and 4 (d) none
81. Range of the function f (x) = x − x 2
is

(a) (0,1) (b) R − [ 0, 1] (c) R − [ 0, 1/ 2 ] (d) [ 0, 1/ 2 ]

82. Range of the function f (x) = 9x − 3x + 1 is

(a) [3 / 4, ) (b) [0, ) (c) [3 / 4, 3 / 2] (d) [1, )

x2 − 2 x + 4
83. If f ( x) = , x  R then range of function is
x2 + 2 x + 4

 1 1 
(a) [– 3, 3] (b)  − ,  (c) (3, + ) (d)  , 3
 3 3 

84. Solutions of inequality x2 + x+ | x | +1  0 is

(a) (1,2) (b) (0,1) (c) no solution (d) none

85. Solution of x 2 + 3x + x 2 − 2  0 is

 2
(a) ( −,1) (b) ( 0,1) (c)  −, −  (d) none
 3

86. What is the domain of the f ( x) = x

(a) ( 0,  ) (b) ( −, 0 ) (c) real number (d) none

87. What the domain of f ( x ) = 2005

(a) real number (b) (−,0) (c) (0, 2005) (d) (2005,0)

88. What is domain of logarithmic function

 (a) ( 0,  ) (b) R (c) ( −,  ) (d) ( −, 0 )

1
89. What is the range of is
x
(a) R − 0 (b) 0 (c) R − 1 (d) R − 

90. What is the value [x]+[-x] =……. if x is not an integer

(a) -1 (b) 1 (c) 0 (d) ±1

91. What is the domain of f ( x) = x − 2 + 2009 x − 3

(a)  2,  ) (b)  2,3 (c) ( −, 2 (d) (2,3)

𝑥−[𝑥]
92. Let 𝑓(𝑥)=1+𝑥−[𝑥] x ϵ R, then the range of 𝑓 is

(a) [0,1] (b) [0,1/2] (c) [0,1/2) (d) (0,1)

1
93. Let 𝑓(𝑥) = 𝑥 2 +4 and 𝑔(𝑥) = , then
√𝑥−1

(a) dom (𝑓+ 𝑔) = (0, ∞) ̴ (0,1) (b) range 𝑓∩range 𝑔 = [4 ∞)

(c) range g= (0, ∞) (d) range 𝑓ᴜ range 𝑔 = (0, ∞)
𝑥−5 3
94. The domain of the function 𝑓(𝑥)= log10 𝑥 2 −10𝑥+24 - √𝑥 + 5 is

(a) (-5, ∞) (b) (5, ∞) (c) (2,5) ᴜ (5, ∞) (d) (4,5) ᴜ (6, ∞)

 x −5
95. If f ( x ) =   is a real valued function, its domain is
 3− x 
(a)  x : x  3 or x  5 (b) 3 < 𝑥 ≤ 5 (c) 3 ≤ 𝑥 < 5 (d) 3 < 𝑥 < 5
96. If f is a function such that f (0) = 2, f (1) = 3 , f ( x + 2) = 2 f ( x) − f ( x + 1) , then f (5) is
(a) -7 (b) -3 (c) 7 (d) 13
97. Given, y = sgn( x) , then
(a) | x |= x sgn( x) (b) sgn(sgn( x)) = sgn( x) (c) x =| x | sgn( x) (d) all of (a), (b), (c)

98. If f : R → R, g : R → R, be two given functions, then 2 min.  f ( x ) − g ( x ) ,0 =

(a) f ( x ) + g ( x ) − |g ( x ) − f ( x )| (b) f ( x ) + g ( x ) + |g ( x ) − f ( x )|
(c) f ( x ) − g ( x ) + |g ( x ) − f ( x )| (d) f ( x ) − g ( x ) − |g ( x ) − f ( x )|