Relations And Functions Test

Relations And Functions

This is Relations and functions Test-05 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Which of the following is an even function?
  • A
    \(si{n^3}\;x\)
  • B
    none of these
  • C
    \(\sqrt x \)
  • D
    \(\begin{array}{*{20}{l}} {{x^2}\; + {\text{ }}si{n^2}x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} \end{array}\)
    Correct
2
The domain of the function \(f(x) = \sqrt {x - 1} + \sqrt {6 - x} \) is
  • A
    ( 1,6)
  • B
    \([0,\;\infty )\)
  • C
    none of these.
  • D
    [1,6]
    Correct
3
The function \(f\left( x \right){\text{ }} = {\text{ }}sin{\text{ }}{x^2}\) is
  • A
    an even function
    Correct
  • B
    one – one
  • C
    none of these.
  • D
    Periodic
4
The range of the function \(f(x) = \frac{{x + 2}}{{\left| {x + 2} \right|}},x \ne - 2,\;is\)
  • A
    {1}
  • B
    {–1}
  • C
    {1, –1}
    Correct
  • D
    {0, 1, –1}.
5
Which of the following is a polynomial function ?
  • A
    \(2{x^2} + \sqrt x + 1.\)
  • B
    \({x^3} + 3{x^2} - 4x + \sqrt 2 {x^{ - 2}}\)
  • C
    \(\frac{{{x^2} - 1}}{x},x \ne 0\)
  • D
    \(\frac{{3{x^3} + 7x - 1}}{3}\)
    Correct
6
If \(f(x) = \left\{ {\begin{array}{*{20}{c}} {1,x > 0} \\\\\\ {0,x = 0\;} \\\\\\ { - 1,x < 0,} \end{array}then\;f\;is} \right.\).
  • A
    The signum function
    Correct
  • B
    a constant function.
  • C
    the greatest integer function
  • D
    the absolute value function
7
The function \(f{\text{ }}\left( x \right){\text{ }} = {\text{ }}{x^2}\; + {\text{ }}sin{\text{ }}x\) is
  • A
    an even function
  • B
    an odd function
  • C
    neither even nor odd
    Correct
  • D
    a constant function.
8
The period of the function \(f\left( x \right){\text{ }} = {\text{ }}si{n^2}\;x{\text{ }} + {\text{ }}tan{\text{ }}x\) is
  • A
    \(3\pi \)
  • B
    none of these
  • C
    \(2\pi \)
  • D
    \(\pi \)
    Correct
9
Let A contain n distinct numbers. How many bijections from A to A can be defined?
  • A
    None of these.
  • B
    \({n^2}\)
  • C
    N
  • D
    $\left| \!{\underline {\, n \,}} \right. $
    Correct
10
Which of the following functions is an even function?
  • A
    \(f(x) = \frac{{{a^x} + 1}}{{{a^x} - 1}}\)
  • B
    \(f(x) = {\log _2}(x + \sqrt {{x^2} + 1} )\)
  • C
    \(f(x) = x\frac{{{a^x} - 1}}{{{a^x} + 1}}\)
    Correct
  • D
    \(f(x) = \frac{{{a^x} + {a^{ - x}}}}{{{a^x} - {a^{ - x}}}}\)
11
The function f: N\( \to \)N (N is the set of natural numbers) defined by f(n) = 2n + 3, is
  • A
    injective
    Correct
  • B
    surjective
  • C
    bijective
  • D
    none of these
12
Let \(p\left( x \right){\text{ }} = {\text{ }}{a^2}\; + {\text{ }}bx\) ,\(q\left( x \right){\text{ }} = {\text{ }}l{x^2}\; + {\text{ }}mx{\text{ }} + {\text{ }}n\) . If p(1) – q (1) = 0, p(2) – q(2) = 1 and p(3) – q(3) = 4, then p(4) – q(4) equals
  • A
    9
    Correct
  • B
    0
  • C
    6
  • D
    5
13
If the mappings f: A \( \to \)B and g: B \( \to \)C are both bijective, then the mapping A\( \to \)C is
  • A
    neither one – one nor onto
  • B
    onto but not one – one
  • C
    one – one and onto
    Correct
  • D
    one – one but not onto
14
The domain of the function \(f\left( x \right) = \sqrt {sinx} \;is:\)
  • A
    Option A
    Correct
  • B
    [0, 1]
  • C
    [1, 1]
  • D
    \(\left[ {0,\pi } \right]\)
15
The domain of the function $f\left( x \right)=\sqrt{\cos x}\ is:$
  • A
    \([0,2\pi ]\)
  • B
    \(\left\{ {x \in R:2n\pi - \frac{\pi }{2} \leqslant x \leqslant 2n\pi + \frac{\pi }{2},n \in I} \right\}\)
    Correct
  • C
    \([0,\pi ]\)
  • D
    \([0,\;\;\frac{\pi }{2}]\)