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.
If $A =\{a, b, c, d\}$ and $B =\{p, q, r, s\}$ then a realtion from A to B is :
- ✓
$\{(a, p),(b, r),(c, r)\}$
- B
$\{(a, p),(b, q),(c, r),(s, d)\}$
- C
$\{(b, a),(q, b),(c, r)\}$
- D
$\{(c, s),(d, s),(r, a),(q, b)\}$
Answer: A.
View full solution →If $f(x)=\cos (\log x)$ then
$f(x) \cdot f(y) \frac{1}{2}\left[f\left(\frac{x}{y}\right)+f(x \cdot y)\right]$ is equal to :
- A
$-1$
- ✓
$0$
- C
$\frac{1}{2}$
- D
$-2$
Answer: B.
View full solution →The range of function $f(x)=\cos \frac{x}{3}$ is :
Answer: C.
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 →If $f: R \rightarrow R , f(x)=\sin \pi x$ then the range of $f$ is :
Answer: D.
View full solution →Cartesian product of sets A and B is $A \times B =\{(a, b)$ : $a \in A, b \in B\}$
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 →A pair of elements grouped in a particular order is called an _____________.
A relation from set A to set B is always a _________ of ordered pair $A \times B$.
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 $f(x)=\log x$, then find the value of $f(e)$.
View full solution →A relation $R$ is defined on a set $A=\{1,2,3,4,5,6\}$ such that $x R y \Leftrightarrow x+2 y=8$, then write the domain of R.
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 →$A$ and $B$ are two different sets, each of which has two elements. Find the number of non-empty relation from set A to set B .
View full solution →If $f: R \rightarrow R$ is defined as-
$f(x)=\left\{\begin{array}{r}1 \text { if } x \in Q \\ -1 \text { if } x \notin Q \end{array}\right.$
then
(i) Find the value of the following-
$f\left(\frac{1}{2}\right), f(\pi), f(\sqrt{2})$
(ii) Find the set of images of set R under $f$.
(iii) Find the pre images of 1 and -1
View full solution →A relation $R$ is defined on the set of integers such that $x R y \Leftrightarrow x ^2+ y ^2= 2 5$ then write $R$ and $R^{-1}$ as the set of ordered pairs and also find its domain.
View full solution →If $x, y \in\{1,2,3\}$, then which of the relation are functions-
(i) $f_1=\{(x, y): x+y>3\}$
(ii) $f_2=\{(x, y): x>3\}$
(iii) $f_3=\{(x, y): y=x+1\}$
(iv) $f_4=\{(x, y): x+y=4\}$
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 →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 →