Q.1
If , then fof(x) is given as
jee-maths-relation-and-functions-mcq-1.png
  • x-1
  • x
  • -x
  • 1-x
Q.2
if $f(x) =log_{[x-1]} \frac {|x|}{x}$ The which one is false
  • Domain of f is $(3, \infty)$
  • Domain of f is $(2, \infty)$
  • Range of f is {0}
  • None of these
Q.3
For what real values of b does the range of the function  $y= \frac {x+1}{b+x^2}$ contain the interval [0,1]$
  • $(-\infty ,-1 ) \cup (-1,1/4)$
  • $(-\infty ,1 ) \cup (1,5/4)$
  • $(-\infty ,-1 ) \cup (-1,4/5)$
  • $(-\infty ,-1 ) \cup (-1,5/4)$
Q.4
The domain of the function $f(x)= log_{10} log_{10} (1+x^3)$
  • $[0, \infty)$
  • $(0, \infty)$
  • $(-1, \infty)$
  • $[-1, \infty)$
Q.5
The range of the function defined as $f(x) = \frac {|x-11|}{x-11}$
  • {5, -5}
  • (-1, 1)
  • [-1,1]
  • {-1,1}
Q.6
Range of function $f(x) = \frac {x^2 + x+ 2}{x^2 + x + 1}$ , $x \in R$ is?
  • $(1, 7/5]$
  • $(1 , 11/7]$
  • $(1, 7/3]$
  • $(1, \infty)$
Q.7
if then fof(x) is given by  
jee-maths-relation-and-functions-mcq-3.png
  • $x^4 \ for \ x \geq 0 , -x^2 \ for \ x < 0$
  • $x^2 \ for \ x \geq 0 , x \ for  \ x < 0$
  • $x^4 \ for \ x \geq 0 , x^2 \ for \ x < 0$
  • $x^4 \ for \ x \geq 0 , x \ for \ x < 0$
Q.8
if $f(x) + 2f(1-x) = x^2 + 2$ , $x \in R$, then f(x) is given by
  • $f(x) =\frac {(x-2)^2}{3}$
  • $f(x) =x^2 -2$
  • $f(x) =1$
  • $f(x) =x -2$
Q.9
The domain of definition of $f(x) = \frac {log_2 (x+3)}{x^2 + 3x +2 }$
  • $(-3, \infty) - \left \{ -1,-2 \right \}$
  • $(-2, \infty)$
  • R – {-1, -2,-3}
  • R – {-1, -2}
Q.10
Domain of $f(x) =\frac {1}{3 -log_3 (x-3)}$
  • $(3,\infty)$
  • $(30,\infty)$
  • $(3,30 ) \cup (30,\infty)$
  • $[3,30 ) \cup (30,\infty)$
Q.11
Range of the function defined as $F(x)= \frac {x-2}{3-x}$
  • R –{3}
  • R – {-1}
  • R –{2}
  • R –{1}
Q.12
Domain of $f(x) = \frac {1}{\sqrt {\left \{ x \right \} -x^2 + 2x}}$  where {.} denotes the fractional part of x
  • $\left ( 2, \frac {3+ \sqrt {13}}{2} \right ) - \left \{ 0,1 \right )$
  • $\left ( 2, \frac {3+ \sqrt {13}}{2} \right ) –\left \{ 0 \right )$
  • $\left ( 2, \frac {3+ \sqrt {13}}{2} \right )$
  • $ \left ( \frac {3- \sqrt {13}}{2},2 \right )$
Q.13
if $f(x) = x^3  - \frac {1}{x^3}$ then f(x) + f(1/x) is
  • $x^3$
  • 1
  • 0
  • $\frac {1}{x^3}$
Q.14
Let function f: R -> R be defined as f(x) = 2x + sin(x) , $x \in R$, then f is
  • neither one to one nor onto
  • one to one but not onto
  • onto but not one to one
  • one to one and onto
Q.15
The real function $f(x) = cos^{-1} \sqrt {x^2 + 3x + 1} + cos^{-1} \sqrt {x^2 + 3x}$ is defined on the set then which of them is incorrect
  • [-3,0]
  • (-3,0)
  • {0,-3}
  • {0,3}
0 h : 0 m : 1 s