Relations And Functions CBSE Questions & Answers

Relations And Functions

This is Mathematics Class 11 Relations and Functions CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Which of the following functions is not one-one ?
  • A
    none of these.
  • B
    \(\sqrt x \)
  • C
    \({x^2} + 1\)
    Correct
  • D
    \({{3 - x} \over {3 + x}}\)
2
If f (x) = \(\left\{ \begin{gathered} 2x - 3,x \leq 2 \\ \;\;\;\;\;\;x,x < 2 \\ \end{gathered} \right.\) then f (1) is equal to
  • A
    \({1 \over 2}f(2)\)
  • B
    - f (2)
  • C
    2 f (2)
  • D
    f (2)
    Correct
3
The domain of the real-valued function \(f(x) = {{(x - 3)(x - 1)} \over {\sqrt {{x^2} - 4} }}\) is
  • A
    (-\(\infty \), - 2) \( \cup \) ( 1, \(\infty \))
  • B
    (-\(\infty \), - 1) \( \cup \) ( 1, \(\infty \)).
  • C
    (1, 2)
  • D
    (-\(\infty \), - 2) \( \cup \) (2, \(\infty \))
    Correct
4
A condition for a function y = f (x) to have an inverse is that it should be
  • A
    an even function
  • B
    continuous every where
  • C
    defined for all x
  • D
    strictly monotone and continuous in the domain
    Correct
5
Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is
  • A
    12
  • B
    144
  • C
    24
    Correct
  • D
    64
6
The range of the function \(f(x) = {{{x^2} - x + 1} \over {{x^2} + x + 1}}\) is
  • A
    [3, \(\infty \))
  • B
    none of these
  • C
    \(\left[ {{1 \over 3},\;3} \right]\)
    Correct
  • D
    R
7
On the set Z of all integers define f ; Z \( \to \) Z as follows : f ( x ) = x/2 if x is even , and f ( x ) = 0 if x is odd , then f is
  • A
    one-one but not onto
  • B
    onto but not one-one
    Correct
  • C
    into
  • D
    one-one and onto
8
Let f : R \( \to \) R be defined by f (x) = 3x – 4, then \({f^{ - 1}}\) (x) is equal to
  • A
    \({{x + 4} \over 3}\)
    Correct
  • B
    none of these
  • C
    3x + 4
  • D
    \({x \over 3} - 4\)
9
The number of bijective functions from the set A to itself when A constrains 106 elements is
  • A
    \({(106)^2}\)
  • B
    \({2^{106}}\)
  • C
    \(\left| \!{\underline {\, {106} \,}} \right. \)
    Correct
  • D
    106
10
In the set W of whole numbers an equivalence relation R defined as follow : aRb iff both a and b leave same remainder when divided by 5. The equivalence class of 1 is given by
  • A
    {4, 9, 14, 19, …}.
  • B
    [0, 5, 10, 15,…}
  • C
    {2, 7, 12, 17…}
  • D
    {1, 6, 11, 16, ….}
    Correct
11
If f (x) \( = {{x - 1} \over {x + 1}},\) then \(\left( {f{1 \over {f(x)}}} \right)\)equals
  • A
    x
  • B
    \({1 \over x}\)
    Correct
  • C
    0
  • D
    1
12
If \(A = \{ (x,y):{x^2} + {y^2} = 25\} \) and \(B = \{ (x,y):{x^2} + 9{y^2} + {y^2} = 144\} ,\) then \(A \cap B\) contains
  • A
    one point
  • B
    two points
  • C
    four points
    Correct
  • D
    one point
13
If f(x) = \({x \over {x - 1}} = {1 \over y},\) then f (y) =
  • A
    x
  • B
    1 – x
    Correct
  • C
    x – 1
  • D
    1 + x
14
The function f (x) = log \(\left( {{{1 + x} \over {1 - x}}} \right)\) satisfies the equation
  • A
    \(f({x_1}) + f({x_2}) = f\left( {{{{x_1} + {x_2}} \over {1 + {x_1}{x_2}}}} \right)\)
    Correct
  • B
    \(f(x) + f(x + 1) = f({x^2} + x)\)
  • C
    \(f({x_1}) + f({x_2}) = f({x_1} + {x_2})\)
  • D
    \(f({x_1}) + f({x_2}) = f({x_1} + {x_2})\)
15
If f (x + y + z) = f (x) f (y ) f (z) for all x , y z and if f (2) = 4, f’ (0) = 5 and f (0) \( \ne \)0, then f’ (2) is equal to
  • A
    \( \pm 80\)
  • B
    \( \pm 100\)
  • C
    \( \pm 30\)
  • D
    \( \pm 20\)
    Correct