Relations And Functions Test

Relations And Functions

This is Relations and functions Test-04 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The diagram given below shows that
Question 1 figure 1
  • A
    f is a bijection function from A to B
  • B
    f is a one – one function from A to B
  • C
    f is not a function
    Correct
  • D
    f is a function from A to B.
2
The domain of the function f = {(1,3), (3,5), (2,6)} is
  • A
    {3, 5, 6}
  • B
    3, 5 and 6.
  • C
    1, 3 and 2
  • D
    {1, 3, 2}
    Correct
3
The range of \(f(x) = \frac{{x - 3}}{{3 - x}},x \ne 3\;is\)
  • A
    {– 1}
    Correct
  • B
    {1}
  • C
    – 1
  • D
    1
4
The range of the function f(x) =\(\left| {x - 1} \right|\) is
  • A
    \(( - \infty ,0)\)
  • B
    \([0,\infty )\)
    Correct
  • C
    \((0,\infty )\)
  • D
    \(( - \infty ,\infty )\)
5
The function\(f(x) = \frac{{{{(1 + {2^x})}^2}}}{{{2^x}}}\)
  • A
    none of these
  • B
    is an odd function
  • C
    is a one – one function
  • D
    is an even function
    Correct
6
The domain of definition of the function \(y = f(x) = \sqrt { - x} \) is :
  • A
    \((1,\infty )\)
  • B
    \([0,\infty )\)
  • C
    none of these.
  • D
    \(( - \infty ,0]\)
    Correct
7
The range of the function \(\begin{gathered} f(x) = \left\{ {\frac{{\left| x \right|}}{{\mathop x\limits_0 }}} \right.for\;x\; \ne 0 & is \\\\\\ for\;x = 0 \\\\\\ \end{gathered} \)
  • A
    {–1, 0, 1}
    Correct
  • B
    none of these.
  • C
    [–1, 1]
  • D
    {–1, 1}
8
The range of the function f(x) = [sin x] is
  • A
    { – 1, 0, 1}
    Correct
  • B
    [1, 1].
  • C
    (–1, 1)
  • D
    {–1, 1}
9
The function \(f(x) = \frac{x}{{1 + \left| X \right|}}\)
  • A
    is an even function.
  • B
    is monotone decreasing
  • C
    is monotone increasing
    Correct
  • D
    is not one – one
10
The range of the function f(x) = x – [x] is
  • A
    [0, 1]
  • B
    (0, 1)
  • C
    [0, 1)
    Correct
  • D
    none of these.
11
The domain of the function \(f(x) = \frac{{{x^2} - x + 1}}{{{x^2} + x + 1}}\;\;is\)
  • A
    R – {– 1}
  • B
    R
    Correct
  • C
    R – {0, – 1}
  • D
    none of these.
12
The range of function f(x) = [x] is :
  • A
    Z
    Correct
  • B
    R
  • C
    none of these.
  • D
    R – Z
13
If f(x) = x – x2 , then f( a + 1 ) – f( a – 1) , a \( \in \) R is :
  • A
    2 – 4a
    Correct
  • B
    4 – 2a
  • C
    none of these
  • D
    2a + 4
14
The domain of the function \(\frac{f}{g}\) is
  • A
    none of these
    Correct
  • B
    \({D_f} - {D_g}\)
  • C
    \({D_f} \cup {D_g}\)
  • D
    \({D_f} \cap {D_g}\)
15
If \(f(x) = \frac{1}{{4x - 3}},then\;{D_f} = \)
  • A
    none of these.
  • B
    R
  • C
    \(\left ( \frac{3}{4},\infty \right )\)
  • D
    R – \(\left\{ {\frac{3}{4}} \right\}\)
    Correct