Question 1 :
The relation $"$iscongruent to$"$ on the set of all triangles in a plane is
Question 2 :
Let $f: N \rightarrow N$ be defined by $f(x) = x^2 + x + 1, x \in N$. Then $f$ is
Question 3 :
Let $f ( x ) = \left\{ \begin{array} { c l } { ( x - 1 ) \sin \dfrac { 1 } { x - 1 } } & { \text { if } x \neq 1 } \\ { 0 } & { \text { if } x = 1 } \end{array} \right.$Then which one of the following is true?
Question 4 :
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 5 :
If $f(x)=\left | x-1 \right |+\left | x-2 \right |+\left | x-3 \right |$ when $2<x<3$ is
Question 6 :
The function${\text{f}}\left( {\text{x}} \right){\text{ = co}}{{\text{t}}^{{\text{ - 1}}}}{\text{x + x}}$ increases in the interval
Question 8 :
The Set $A$ has $4$ elements and the Set $B$ has $5$ elements then the number of injective mappings that can be defined from $A$ to $B$ is
Question 9 :
The number of possible surjection from $A=\{1,2,3,...n\}$ to $B = \{1,2\}$ (where $n \geq 2)$ is $62$,then $n=$
Question 10 :
Let $f:Z\rightarrow Z$ be given by $f(x)=\begin{cases} \cfrac { x }{ 2 } ,\quad \text{if}\ x \ \text{is even} \\ 0,\quad \text{if }\ x \ \text{is odd} \end{cases}$. Then, $f$ is
Question 11 :
Write the properties that the relation "is greter that" satisfies in the set of all positive integers
Question 12 :
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 13 :
Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A into B is :
Question 14 :
Number of one-one functions from A to B where $n(A)=4, n(B)=5$.
Question 15 :
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 16 :
$f:(0,\infty )\rightarrow (0,\infty )$ defined by <br/>$f(x)=\begin{cases}2^{x} & x\in (0,1) \\5^{x} & x\in [1,\infty ) \end{cases}$ is
Question 17 :
If $A =\{1, 2, 3\}$ and $ B = \{4, 5\}$ then the number of function $f : A \rightarrow B$ which is not onto is ______
Question 18 :
If the function $f : R \rightarrow R$ is defined by $f(x) = (x^2+1)^{35} \forall \in R$, then $f$ is
Question 20 :
The minimum number of elements that must be added to the relation $R =\{(1,2)(2,3)\}$ on the set of natural numbers so that it is an equivalence is
Question 21 :
Give a relation R={(1,2), (2,3)} on the set of natural numbers, add a minimum number of ordered pairs.  
Question 22 :
Let N denote the set of all natural numbers. Define two binary relations on N as $R_1=\{(x, y)\epsilon N\times N : 2x+y=10\}$ and $R_2=\{(x, y)\epsilon N\times N:x+2y=10\}$. Then.
Question 23 :
Let $A = \left \{1, 2, 3\right \}$. Then number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive is<br/><br/>
Question 24 :
Let R be a reflexive relation on a finite set A having n elements, and let there be m ordered pairs in R. Then:
Question 25 :
Let $R$ be a relation defined as $aRb$ if $1 + ab > 0$, then the relation $R$ is:
Question 26 :
$R$ is a relation defined in $R\times T$ by $(a,b) R (c,d)$ iff $a-c$ is an integer and $b=d$. The relation $R$ is
Question 27 :
If $f:R\rightarrow R$ given by $f(x)={ x }^{ 3 }+({ a+2)x }^{ 2 }+3ax+5$ is one-one, then $a$ belongs to the interval<br>
Question 28 :
The number of bijection from the set $A$ to itselfwhen $A$ contains $106$ elements is
Question 29 :
If $f : A \rightarrow B $ defined as $f(x) = x^2+2x+\frac{1}{1+(x+1)^2}$ is onto function, then set B is equal to
Question 30 :
Let $R$ be a relation defined on the set $Z$ of all integers and $xRy$ when $x + 2y$ is divisible by $3$. Then
Question 31 :
Let $A=\left \{ 1, 2, 3 \right \}$. Then number of equivalence relations containing (1, 2) is:
Question 32 :
Total number of equivalence relations defined in the set $S =\{a,b,c\}$ is
Question 33 :
Consider the set $A=\left\{1,2,3\right\}$ and the relation $R=\left\{(1,2),(1,3)\right\} . R$ is a transitive relation.
Question 36 :
If the function $f:R\rightarrow A$ given by $f(x)=\cfrac { { x }^{ 2 } }{ { x }^{ 2 }+1 } $ is surjection, then $A=$
Question 37 :
The function $f:(0,\infty )\rightarrow R$ given by $ f(x)=\cfrac { x }{ x+1 } $ is<br>
Question 38 :
In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.<br/>It is sufficient, if $R$
Question 39 :
Let $A = [-1,1]= B $then which of the following functions from $A$ to $B$ is bijective function?
Question 40 :
Assertion: $ \displaystyle f:R \rightarrow \left [0,\frac {\pi}{2} \right )$ defined by $ \displaystyle f(x)=\tan^{-1}(x^{2}+x+a)$ is onto for all $ a \in \left ( -\infty ,\dfrac{1}{4} \right )$
Reason: For onto function codomain of $f=$ Range of $f$.
