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 $R$ be the relation over the set of all straight lines in a plane such that ${l}_{1}$ $R$ ${l}_{2}\Leftrightarrow {l}_{1}\bot {l}_{2}$. Then, $R$ is
Question 3 :
For real number $x$ and $y$, define $xRy$ iff $x-y+\sqrt{2}$ is an irrational number. Then the relation $R$ is
Question 4 :
Which one of the following relations on R (set of real numbers) is an equivalence relation
Question 5 :
Let $A=\left\{ 1,2,3 \right\} $ and $R=\left\{ \left( 1,2 \right) ,\left( 2,3 \right) ,\left( 1,3 \right) \right\} $ be a relation on $A$. Then $R$ is
Question 6 :
Let $L$ denote the set of all straight lines in a plane, Let a relation $R$ be defined by $lRm$, iff $l$ is perpendicular to $m$ for all $l \in L$. Then, $R$ is
Question 7 :
Let $A=\left\{ 2,3,4,5,....,17,18 \right\} $. Let $\simeq $ be the equivalence relation on $A\times A$, cartesian product of $A$ with itself, defined by $(a,b)\simeq (c,d)$, iff $ad=bc$. The the number of ordered pairs of the equivalence class of $(3,2)$ is
Question 8 :
Let N denote the set of all natural numbers and R a relation on $N\times N$. Which of the following is an equivalence relation?
Question 9 :
$N$ is the set of positive integers. The relation $R$ is defined on N x N as follows: $(a,b) R (c,d)\Longleftrightarrow ad=bc$ Prove that
Question 10 :
In the set $Z$ of all integers, which of the following relation $R$ is an equivalence relation?
Question 11 :
The distinct linear functions which maps from $[-1,1]$ onto $[0,2]$ are
Question 12 :
If $N$ denote the set of all natural numbers and $R$ be the relation on $N\times N$ defined by $(a, b)R(c, d)$. if $ad(b + c) = bc (a + d)$, then $R$ is
Question 14 :
N is the set of positive integers and $\displaystyle \sim $ be a relation on $\displaystyle N\times N\:defined\:\left ( a,b \right )\sim \left ( c,d \right )$ iff ad=bc.<br/>Check the relation for being an equivalence relation. <br/>
Question 15 :
Let $A = \left\{p,q,r\right\}$. Which of the following is an equivalence relation in $A$?
Question 17 :
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 18 :
The relation 'is a sister of' in the set of human beings is____
Question 19 :
Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation $R$ is
Question 20 :
The number of possible surjection from $A=\{1,2,3,...n\}$ to $B = \{1,2\}$ (where $n \geq 2)$ is $62$,then $n=$
Question 21 :
Let $A=\{1,2,3\}, B =\{a, b, c\}$ and If $f=\{(1,a),(2,b),(3,c)\}, g=\{(1,b),(2,a),(3,b)\}, h=\{(1,b)(2,c),(3,a)\}$ then
Question 22 :
Let $f:R\rightarrow R$ be defined by $f(x)=2x+6$ which is a bijective mapping then ${ f }^{ -1 }(x)\quad $ is given by
Question 23 :
Let $f:A \to b$ be a function defined by f(x) =$\sqrt {1 - {x^2}} $<br/>
Question 24 :
Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?
Question 25 :
The function $f$ defined by $f\left( x \right) = {x^3} - 3{x^2} + 5x + 7,$ is:
Question 26 :
Let $\displaystyle f\left ( x \right )=\frac{ax^{2}+2x+1}{2x^{2}-2x+1}$, the value of $a$ for which $\displaystyle f:R\rightarrow \left [ -1,2 \right ]$ is onto , is<br>
Question 27 :
The function $f:\left[ -\dfrac {1}{2},\dfrac {1}{2} \right] \rightarrow \left[ -\dfrac {\pi }{2},\dfrac {\pi }{2} \right] $ defined by $f(x)=\sin ^{ -1 }{ \left( 3x-4{ x }^{ 3 } \right)  } $ is
Question 28 :
The function $f: [0, 3]$ $\rightarrow$ $[1, 29]$, defined by $f(x) = 2x^3-15x^2 + 36x+ 1$, is<br>
Question 29 :
In the following functions defined from $[-1, 1]$ to $[-1, 1]$, then functions which are not bijective are
Question 30 :
Consider the functions<br>$\displaystyle f: X\rightarrow Y$ and$\displaystyle g: Y\rightarrow Z$<br>then which of the following is/are incorrect?
Question 31 :
$f\left( x \right) =\begin{cases} x\left( \dfrac { { ae }^{ \dfrac { 1 }{ \left| x \right| } }+{ 3.e }^{ \dfrac { -1 }{ x } } }{ \left( a+2 \right) { e }^{ \dfrac { 1 }{ \left| x \right| } }-{ e }^{ \dfrac { -1 }{ x } } } \right) \\ 0 \end{cases},\begin{matrix} x\neq 0 \\ x=0 \end{matrix}$ is differentiable at $x=0$ then $[a]=$__ ([] denotes greatest integers function )
Question 32 :
Let$\displaystyle f:R \rightarrow R, g(x) = f(x) + 3x - 1$, then the least value of function$\displaystyle y = g(|x|)$ is
Question 34 :
Let $f:N\rightarrow N$ ($N$ being the set of positive integers) be a function defined by $f(x)=$ the biggest positive integer obtained by reshuffling the digits of $x$. For example, $f(296)=962$<br>$f$ is
Question 35 :
Let $f:{x, y, z}\rightarrow (a, b, c)$ be a one-one function. It is known that only one of the following statements is true:(i) $f(x)\neq b$<br/>(ii)$f(y)=b$<br/>(iii)$f(z)\neq  a$
