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 \({1 \over {\left[ x \right]}} + \sqrt {2x - {x^2}} \) is
  • A
    \(\left[ {0,1} \right)\)
  • B
    \(\left[ {1,2} \right)\)
  • C
    \(\left[ {1,2} \right]\)
    Correct
  • D
    \(\left[ {0,2} \right]\)
2
If A = {(x, y) : \({x^2} + {y^2} = 5\) } and B = {(x, y) : 2x = 5y}, then \(A \cap B\) contains
  • A
    one-point
  • B
    two points
    Correct
  • C
    infinite points
  • D
    no point
3
If f : R \( \to \) R is given by f (x) = | x | and \(A = \{ x \in R:x < 0\} \) , then \({f^{ - 1}}(A)\) equals
  • A
    \({\text{A U }}\left\{ 0 \right\}\)
  • B
    A
  • C
    \(\phi \)
    Correct
  • D
    R
4
If f : N \( \times \)N \( \to \)N is such that f (m, n) = m + n where N is the set of natural number, then which of the following is true ?
  • A
    f is neither one-one nor onto
    Correct
  • B
    f is on-one but not onto
  • C
    f is one-one and onto
  • D
    f is onto but not one-one
5
The function sin \(\left( {\sin {x \over 3}} \right)\) is periodic with period
  • A
    \(2\pi \)
  • B
    \(6\pi \)
    Correct
  • C
    \(8\pi \)
  • D
    \(4\pi \)
6
If A = [a, b], B = [c,d], C = [d, e] then {(a, c), (a, d), (a,e), (b,c), (b, d), (b, e)} is equal to
  • A
    \(A \times (B\; \cap C)\)
  • B
    \(A \cap (B\; \cup C)\)
  • C
    \(A \times (B\; \cup C)\)
    Correct
  • D
    \(A \cup (B\; \cap C)\)
7
The function f(x) = \({10^x}\) from R to [0, \(\infty \)) is
  • A
    an identity function
  • B
    a constant function
  • C
    one-one and into
    Correct
  • D
    one-one and onto
8
For all x \( \in \) (0, 1)
  • A
    \({\log _e}(1 + x) < x\)
    Correct
  • B
    sin x \( > \) x
  • C
    \({e^x} < 1 + x\)
  • D
    \({\log _e}x > x\)
9
The domain of the function \(f(x) = \sqrt {x - 1} + \sqrt {6 - x} \)
  • A
    none of these
  • B
    [1, 6]
    Correct
  • C
    [1, 6]
  • D
    (-\(\infty \), 6)
10
Let f (x) = \({x^2}\) and g (x) = \(\sqrt x ,\) then
  • A
    (fog) (2) = 4
  • B
    (gof) (2) = 4
  • C
    (gof) (- 2) = 2
    Correct
  • D
    (fog) (3) = 6.
11
Suppose that g (x) = 1 + \(\sqrt x \) and f ( g (x)) = 3 + 2 \(\sqrt x \) + x, then f (x) is
  • A
    2 + x
  • B
    1+ x
  • C
    \(1 + 2{x^2}\)
  • D
    \(2 + {x^2}\)
    Correct
12
If f : [1, \(\infty \infty \)) \( \to \) [2, \(\infty \infty \)) is given by \(f(x) = x + {1 \over x}then{f^{ - 1}}(x)\) equals]
  • A
    \(1 + \sqrt {{x^2} - 4} \)
  • B
    \({{x + \sqrt {{x^2} - 4} } \over 2}\)
    Correct
  • C
    \({x \over {1 + {x^2}}}\)
  • D
    \({{x\sqrt {{x^2} - 4} } \over 2}\)
13
The minimum value of (x -\(\alpha \)) (x – \(\beta \)) is
  • A
    \({1 \over 4}{(\alpha - \beta )^2}\)
  • B
    \( - {1 \over 4}{(\alpha - \beta )^2}\)
    Correct
  • C
    \(\alpha {\rm{ }}\beta \)
  • D
    0
14
If f (x) = \({(25 - {x^4})^{1/4}}\) for 0 < x <\(\sqrt 5 \), then \(f\left( {f\left( {{1 \over 2}} \right)} \right) = \)
  • A
    \({2^{ - 4}}\)
  • B
    \({2^{ - 2}}\)
  • C
    \({2^{ - 3}}\)
  • D
    \({2^{ - 1}}\)
    Correct
15
Two functions \(f:R \to R\) and g : \(R \to R\)are defined as follows : \(f\left( x \right) = \left\{ \begin{gathered} 0\left( {xRational} \right) \\ 1\left( {xIrrational} \right) \\ \end{gathered} \right\},g\left( x \right) = \left\{ \begin{gathered} - 1\left( {xRational} \right) \\ 0\left( {xIrrational} \right) \\ \end{gathered} \right\}\) , then (gof)(e) + (fog)( \(\pi \)) =
  • A
    1
  • B
    2
  • C
    0
  • D
    - 1
    Correct