JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Application +4 | -1

If a set

A

has 10 elements, then the ratio of total no. of reflexive relations to total no. of symmetric relations is

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Correct option: A

2^{35}

Option A (

2^{35}

) is correct because the ratio of reflexive relations to symmetric relations on a set with 10 elements is calculated as 2^{(n^2-n)} / 2^((n²⁺n)/2) = 2^((n^2-3n)/2), and substituting n=10 gives 2³⁵.

More Questions from RELATIONS

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In the set

\mathrm{Z}

of all integers, which of the following relation

R

is not an equivalence relation? Let

\mathrm{N}

denote the set of all natural numbers and

\mathrm{R}

be the relation on

\mathrm{N} \times \mathrm{N}

defined by

(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})

a d(b+c)=b c(a+d)

, then

\mathrm{R}

is Let

W

denote the words in the English dictionary. Define the relation

R

by:

R=\{(x, y) \in W \times W \mid

the words

x

and

y

have at least one letter in common

\}

Let

S

be the set of all real numbers. Then, the relation

R = \{ \left( {a,\;b} \right):1 + ab > 0\}

S

is Let

X

be a family of sets and

R

be a relation on

X

defined by '

A

is disjoint from

B

'. Then

R

is:

R

is relation on

N

given by

R = \left\{ {\left( {x,\;y} \right):4x + 3y = 20} \right\}

. Which of the following belongs to

R