Test Details

Relation And Fuction

For NDA

Dec 03, 9:00 PM

60 minutes

Dec 03, 10:00 PM

40.0 marks

MCQ

25 questions

satyanarayan sir

I am maths faculty (NITian)

Class Details

Maths

Class 12th IIT JEE

Maths

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Question Text

Question 1 :
If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then

Question 2 :
Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto functions from E to F 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 :
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 5 :
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 6 :
$\displaystyle x^{2} = xy$ is a relation (defined on set R) which is

Question 7 :
Find number of all such functions $y = f(x)$ which are one-one?

Question 8 :
In the set $Z$ of all integers, which of the following relation $R$ is an equivalence relation?

Question 9 :
If the relation is defined on $R-\left\{ 0 \right\} $ by $\left( x,y \right) \in S\Leftrightarrow xy>0$, then $S$ is ________

Question 10 :
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 11 :
Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is

Question 12 :
Let $f : Z$ $\rightarrow$ $Z$ be defined as f(x) $=x^2, x \in Z$. $f$ is

Question 13 :
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 :
Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l}_{1}$ and ${l}_{2}$ are said to be related by the relation $R$ if ${l}_{1}$ is parallel to ${l}_{2}$. Then the relation $R$ is-

Question 16 :
Let $Z$ be the set of integers and$f:Z\rightarrow Z$ is a bijective function then

Question 18 :
The number of bijection from the set $A$ to itselfwhen $A$ contains $106$ elements is

Question 19 :
Number of one-one functions from A to B where $n(A)=4, n(B)=5$.

Question 20 :
Which one of the following is an elementary symmetric function of  $x_{1},x_{2},x_{3},x_{4}$.

Question 21 :
If $f\left( x+y+1 \right) =\left( \sqrt { f\left( x \right)  }  \right)^2 +\left( \sqrt { f\left( y \right)  }  \right) ^{ 2 }\forall x,y\epsilon N$ and $f\left( 0 \right) =1,$ then $f\left( +3 \right) =$ 

Question 22 :
Let $Z$ be the set of integers and $aRb$, where $a, b\epsilon Z$ if an only if $(a - b)$ is divisible by $5$. Consider the following statements: $1.$ The relation $R$ partitions $Z$ into five equivalent classes. $2.$ Any two equivalent classes are either equal or disjoint. Which of the above statements is/are correct?

Question 23 :
Which one of the following relations on $R$ is equivalence relation

Question 24 :
Let $A = [-1,1]= B $then which of the following functions from $A$ to $B$ is bijective function?

Question 25 :
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 $f$.

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