Sample QuestionsPART - 1 CH - 2 Relations and Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The range of function $f(x)=\cos \frac{x}{3}$ is :
Answer: C.
View full solution →If $f: R \rightarrow R , f(x)=\sin \pi x$ then the range of $f$ is :
Answer: D.
View full solution →If $f(x)=2|x-2|-3|x-3|$, then for $2 < x < 3$. the value of $f(x)$ is :
- A
$5-x$
- B
$x-5$
- ✓
$5 x-13$
- D
$5+x$
Answer: C.
View full solution →The domain of function $y=\sqrt{x+1}$ is :
- A
$(-1,0)$
- B
$(1,0)$
- C
$(1, \infty)$
- ✓
$[-1, \infty]$
Answer: D.
View full solution →The domain of function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is :
- A
$R ^{+}$
- ✓
$R ^{-}$
- C
$R _0$
- D
$R$
Answer: B.
View full solution →Real function $f(x)=\frac{1}{x+2}$, then domain is $R -\{-2\}$.
View full solution →If $f: X \rightarrow R , f(x)=x^3+1$ then $f(9)=730$.
View full solution →If $A =\{-2,-1,0,1,2\}$ and $B =\{0,1,2,3,4,5,6\}$ and $f(x)=x^2, f: A \rightarrow B$ then the range of $f$ is $\{(0,1)\}$.
View full solution →If set $a$ contains $n$ elements then the number of relations defined in A is $2^{n^2}$.
View full solution →Both the domain and range of a real function are the set of real numbers of a subset of it.
If $f(x)=\tan x$ then write the value of $f(x)+f(\pi-x)$.
View full solution →If $A =\{2,3,5,7\}$ and $f: A \rightarrow N , f(x)=x^3+2$, then find the range of function.
View full solution →A relation R is defined on set N such that $R =\{(x, y)$ / $y=x+2,1 < x < 5\}$ then write the domain of relation R.
View full solution →If $f(x)=\frac{x}{x+1}$, then write the value of $f\left(\frac{p}{q}\right)$.
View full solution →If $f(x)=\log x$, then find the value of $f(e)$.
View full solution →If $f: R \rightarrow R , f(x)=e^x$, then find -
(i) Set of images of R under $f$.
(ii) $\{f / f(y)=1\}$
(iii) Is $f(x+y)=f(x) \cdot f(y)$ is true?
View full solution →Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ is a function? If $g$ is represented by $g(x)=\alpha x+\beta$ then find the value of $\alpha$ and $\beta$.
View full solution →A relation $R$ is defined from set $A=\{2,3,4,5\}$ $B=\{3,6,7,10\}$ such that $x R y \Leftrightarrow x$, is coprime to $y$. Write the relation R in the form of ordered pairs and also find the domain and range of $R$.
View full solution →A relation $R$ is defined from the set of real numbers $R$ to the set of complex numbers $C$ such that $x R y \Leftrightarrow|x|=y$, then tell with reason which of the following are true or false-
(i) $(1+i) R 3$
(ii) $3 R (-3)$
(iii) $(2+3 i) R 13$
(iv) $(1+i) R 1$
View full solution →Find the domain of functions $f$ and $g$ for which $f(x)=2 x^2-1$ and $g(x)=1-3 x$ are equal. Find domain for which these functions are not equal.
View full solution →If $R=\{(1,2),(1,3),(2,3),(3,2)\}$ is a realtion then $R^{-1}=$ __________.
View full solution →The domain of function $f(x)=\log |x|$ is _________.
View full solution →The range of function $f(x)=|x|$ is __________.
View full solution →If $n(A)=m$ and $n(B)=n$ then ___________ relations can be defined from $A$ to $B$.
View full solution →$R \times R =\{(x, y) \mid x, y \in R \}$ is a set of all points in _________ plane.
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