Mathematics · JEE

Relations, type of relations, equivalence relations Mock Test for JEE

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Syllabus context

Part of Sets, Relations and Functions in JEE Main Mathematics.

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Q1MathsUnit 1: Sets, Relations and Functions

Which of the following is NOT equivalent to

\boldsymbol{p} \rightarrow \boldsymbol{q} ?

Q2MathsUnit 1: Sets, Relations and Functions

Assertion The relation

\boldsymbol{R}

given by

\boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}

on a set

A=\{1,2,3,4\}

is not symmetric. Reason For symmetric relation

\boldsymbol{R}=\boldsymbol{R}^{-1}

Q3MathsUnit 1: Sets, Relations and Functions

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

Q4MathsUnit 1: Sets, Relations and Functions

The contrapositive statement of statement "If

x

is prime number, then

x

is odd" is

Q5MathsUnit 1: Sets, Relations and Functions

x^{2}=x y

is a relation (defined on set

R

) which is

Q6MathsUnit 1: Sets, Relations and Functions

Consider the following two statements:

P:

If 7 is an odd number, then 7 is divisible by 2. Q: If 7 is a prime number, then 7 is an odd number If

V_{1}

is the truth value of the contrapositive of

\mathrm{P}

and

V_{2}

is the truth value of contrapositive of

Q,

then the ordered pair

\left(V_{1}, V_{2}\right)

equals:

Q7MathsUnit 1: Sets, Relations and Functions

Which of the following statements is the inverse of "Our pond floods whenever there is a thunderstorm."?

Q8MathsUnit 1: Sets, Relations and Functions

\mathrm{R}

is a relation in

\mathrm{A}

and

(\mathrm{a}, \mathrm{b}) \notin \mathrm{r},

implies (b, a)

\notin \mathrm{R}

then

\mathrm{R}

is said to be relation

Q9MathsUnit 1: Sets, Relations and Functions

Find the HCF of 92690,7378 and 7161 by Euclid's division algorithm.

Q10MathsUnit 1: Sets, Relations and Functions

Let

\rho

be a relation defined on

N,

the set of natural numbers, as

\boldsymbol{\rho}=\{(\boldsymbol{x}, \boldsymbol{y}) \in \boldsymbol{N} \times \boldsymbol{N}: \mathbf{2} \boldsymbol{x}+\boldsymbol{y}=\mathbf{4 1}\}

then

Q11MathsUnit 1: Sets, Relations and Functions

Give a relation

\mathrm{R}=\{(1,2),(2,3)\}

on the set of natural numbers, add a minimum number of ordered pairs. This question has multiple correct options

Q12MathsUnit 1: Sets, Relations and Functions

According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers

a

and

b

with

a>b

enables us to find the

Q13MathsUnit 1: Sets, Relations and Functions

\operatorname{Let} \boldsymbol{R}=

\{(1,3),(4,2),(2,4),(2,3),(3,1)\} be a relation on the set

A=\{1,2,3,4\} .

The relation

\boldsymbol{R}

Q14MathsUnit 1: Sets, Relations and Functions

What type of a relation is "Less than" in the set of real numbers?

Q15MathsUnit 1: Sets, Relations and Functions

Let

A=\{1,2,3\}

and

R=

\{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3) then the relation

R

and

A

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