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
The domain of the function \(\sqrt {\cos x - } 1\) is
  • A
    { }
  • B
    R
  • C
    {2 n \(\pi \): n \( \in \) I}
    Correct
  • D
    none of these
2
The domain of the function \(f(x) = \sqrt {\left| x \right| - x} \) is
  • A
    \(( - \infty ,0]\)
  • B
    R
    Correct
  • C
    \([0,\infty )\)
  • D
    none of these
3
The domain of the function \(f(x) = \sqrt {1 - \cos x} \) is
  • A
    \(\{ {\rm{x }} = {\rm{ 2 n}}\pi :{\rm{ n}} \in {\rm{I}}\} \)
  • B
    none of these
  • C
    R
    Correct
  • D
    \([0,{\rm{ 2}}\pi ]\)
4
The domain of the function f (x) = \(\sqrt {\sin x - 1} \) is
  • A
    \(\left\{ {x \in R:x = 2n\pi \pm \;{\pi \over 2},n \in I} \right\}\)
  • B
    \(\left\{ {x \in R:x = 2n\pi + {\pi \over 2},n \in I} \right\}.\)
    Correct
  • C
    \( - \phi \)
  • D
    \(\left\{ {{\pi \over 2}} \right\}\)
5
Let x be any real, then [x + y] = [x] + [y] holds for
  • A
    y \( \in \) I
    Correct
  • B
    y \( \in \) R
  • C
    y \( \in \) Q
  • D
    y \( \in \) R, y \( \in \) Q.
6
The function f (x) = x + cos x
  • A
    assumes only positive values
  • B
    is defined for all reals
    Correct
  • C
    assumes only negative values
  • D
    none of these
7
If f \(x = {1 \over {\sqrt {x - \left| x \right|} }},\) then \({D_f}\) is equal to
  • A
    R
  • B
    \(\phi \)
    Correct
  • C
    \(( - \infty ,{\rm{ }}0)\)
  • D
    \((0,\infty )\)
8
If f (x) = tan x, \( - {\pi \over 2} < 0 < {\pi \over 2}\) and g (x) = \(\sqrt {3 - {x^2}} ,\) then domain of the function gof is
  • A
    \(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
  • B
    \(\left[ { - {\pi \over 3},{\pi \over 3}} \right]\)
    Correct
  • C
    \(\left( { - {\pi \over 3},{\pi \over 3}} \right)\)
  • D
    none of these
9
If f (x) = tan x, \( - {\pi \over 2} < 0 < {\pi \over 2}\) and g (x) = \(\sqrt {1 - {x^2}} \) , then domain of fog is
  • A
    \(\left[ { - {\pi \over 4},{\pi \over 4}} \right]\)
  • B
    (- 1, 1)
  • C
    [- 1, 1]
    Correct
  • D
    \(\left( { - {\pi \over 2},{\pi \over 2}} \right)\)
10
If f (x) =\(\sqrt { - x} \), then domain of fof is
  • A
    \(({\rm{ }}0,\infty )\)
  • B
    none of these
    Correct
  • C
    \(( - \infty ,{\rm{ }}0)\)
  • D
    \(( - \infty ,\infty )\)
11
If y = tan, \(\sqrt {{\pi \over 9} - {x^2}} \) then
  • A
    \(0 \le y \le 3\)
  • B
    none of these
  • C
    \( - \sqrt 3 \le y \le \sqrt 3 \)
  • D
    \(0 \le y \le \sqrt 3 \)
    Correct
12
The interval in which the values of f (x) lie where f (x) = 3 sin \(\sqrt {{{{\pi ^2}} \over {16}} - {x^2}} \) is
  • A
    [-3, 3]
  • B
    \(\left[ {0,{3 \over {\sqrt 2 }}} \right]\)
    Correct
  • C
    \(\left[ { - {\pi \over 4},{\pi \over 4}} \right]\)
  • D
    none of these
13
The range of the function \(f(x) = {{{x^2} - 3x + 2} \over {{x^2} + x - 6}}\) is
  • A
    R
  • B
    R – {1}
  • C
    \({\bf{R}} - \left\{ {{1 \over 5}} \right\}\)
  • D
    \({\bf{R}} - \left\{ {1,{1 \over 5}} \right\}\)
    Correct
14
If f(x) = log\(\left( {{{1 + x} \over {1 - x}}} \right)\), then \(f\left( {{{2x} \over {1 + {x^2}}}} \right)\) is equal to
  • A
    none of these
  • B
    4 f(x)
  • C
    f (x)
  • D
    2 f (x)
    Correct
15
If \(f(x) = {{\left| x \right|} \over x};x \ne 0;\) then f (x) – f (- x) | is equal to
  • A
    1
  • B
    2
    Correct
  • C
    none of these.
  • D
    0