Question 1 :
If $A=\left\{ 1,2,3 \right\} $, then a relation $R=\left\{ \left( 2,3 \right) \right\} $ on $A$ is
Question 2 :
Let $f:R\rightarrow R$ be defined as $f(x)=x^{3}+2x^{2}+4x+\sin \left(\dfrac{\pi}{2}\right)$ and $g(x)$ be the inverse function of $f(x)$, then $g'(8)$ is equal to
Question 3 :
Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F is
Question 4 :
If $f: A \rightarrow B$is a bijective function and if n(A) = 5, then n(B) is equal to
Question 5 :
Let $f(x,y)=xy^{2}$ if $x$ and $y$ satisfy $x^{2}+y^{2}=9$ then the minimum value of $f(x,y)$ is
Question 6 :
The relation $R=\left\{ \left( 1,1 \right) ,\left( 2,2 \right) \left( 3,3 \right)  \right\} $ on the set $A=\left\{ 1,2,3 \right\} $ is
Question 7 :
Let $A = \left\{ {1,2,3} \right\}$ and $R = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {2,2} \right),\left( {2,1} \right),\left( {3,3} \right)} \right\}$, then the relation $R$ and $A$ is
Question 8 :
If $A=\left\{ a,b,c,d \right\} $, then a relation $R=\left\{ \left( a,b \right) ,\left( b,a \right) ,\left( a,a \right) \right\} $ on $A$ is
Question 9 :
For real number $x$ and $y$, define $xRy$ iff $x-y+\sqrt{2}$ is an irrational number. Then the relation $R$ is
Question 12 :
Assertion: Domain of $f(x)$ is singleton.
Reason: Range of $f(x)$ is singleton.
Question 13 :
The relation $R$ in $N\times N$ such that $(a,b)R(c,d)\Leftrightarrow a+d=b+c$ is
Question 14 :
If the relation is defined on $R-\left\{ 0 \right\} $ by $\left( x,y \right) \in S\Leftrightarrow xy>0$, then $S$ is ________
Question 15 :
Which one of the following relations on R (set of real numbers) is an equivalence relation
Question 16 :
In the set $Z$ of all integers, which of the following relation $R$ is an equivalence relation?
Question 17 :
If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then
Question 18 :
Given the relation R= {(1,2), (2,3) } on the set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is
Question 21 :
a R b if "a and b are animals in different zoological parks" then R is
Question 22 :
Let Z be the set of all integers and let R be a relation on Z defined by $a$ R $b\Leftrightarrow (a-b)$ is divisible by $3$. Then, R is?
Question 23 :
Let $R$ be a reflexive relation in a finite set having $n$ elements and let there be $m$ ordered pairs in $R$. Then,
Question 24 :
$f:\left ( -\dfrac{\pi }{2},\dfrac{\pi }{2} \right )\rightarrow \left ( -\infty ,\infty \right )$defined by $f(x)=1+3x$ is
Question 25 :
A function $f$ from the set of natural numbers to the set of integers defined by<br/>$f(n)=\begin{cases} \cfrac { n-1 }{ 2 } ,\quad \text{when n is odd} \\ -\cfrac { n }{ 2 } ,\quad \text{when n is even} \end{cases}$
