Test Details

Relation And Functions

Chapter 1

Nov 21, 9:00 AM

30 minutes

Nov 22, 9:00 AM

20.0 marks

MCQ

20 questions

Neetesh Mishra

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Question Text

Question 1 :
Assertion: Domain of $f(x)$ is singleton. Reason: Range of $f(x)$ is singleton.

Question 2 :
The number of reflexive relation in set A = {a, b, c} is equal to

Question 3 :
The true set of real value of $x$ for which the function, $f(x)=x\ \mathrm{ln}\ x-x+1$ is positive is

Question 4 :
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 5 :
Which of the following is not an equivalence relation on $Z$?

Question 6 :
Let $A=\left\{ 1,2,3 \right\} $. Then, the number of equivalence relations containing $(1,2)$ over set A is

Question 7 :
The relation $R$ on the set $Z$ of all integer numbers defined by $(x,y)\ \epsilon \ R\\Leftrightarrow x-y$ is divisible by $n$ is

Question 8 :
$\displaystyle x^{2} = xy$ is a relation (defined on set R) which is

Question 9 :
If $A=\left\{ a,b,c \right\} $, then the relation $R=\left\{ \left( b,c \right) \right\} $ on $A$ is

Question 10 :
For real number $x$ and $y$, define $xRy$ iff $x-y+\sqrt{2}$ is an irrational number. Then the relation $R$ is

Question 11 :
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 14 :
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 15 :
If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then

Question 16 :
Consider the following two binary relations on the set $A = \left \{a, b, c\right \} : R_{1} = \left \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\right \}$ and $R_{2} = \left \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\right \}$ Then

Question 17 :
Which one of the following relations on R (set of real numbers) is an equivalence relation

Question 18 :
If $f:\mathbb{N} \rightarrow \mathbb{N}$ and $f(x) = x^{2}$ then the function is

Question 19 :
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 20 :
If $A=\left\{ 1,2,3 \right\} $, then a relation $R=\left\{ \left( 2,3 \right) \right\} $ on $A$ is

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