Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 1>Q 19

HARD

JEE Main

IMPORTANT

Earn 100

Let $S$ denotes a set of all integers. Define a relation $R$ on $S$ as $' a R b'$ if $a b \geq 0$ , where $a, b \in S$ . Then, $R$ is

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Important Questions on Set Theory and Relations

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 1>Q 20

Let

P = \{(x, y) ∣ x^{2} + y^{2} = 1, x, y \in R\} .

Then

P

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 1

What is the number of natural numbers less than or equal to

1000

which are neither divisible by

10

nor

15

nor

25

?

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 2

The value of

(A \cup B \cup C) \cap {(A \cap B^{c} \cap C^{c})}^{c} \cap C^{c}

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 3

A survey shows that

63 %

of the Americans like cheese whereas

76 %

like apples. If

x %

of the Americans like both cheese and apples, then

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 4

A school awarded

38

medals in football,

15

in basketball and

20

in cricket. Suppose these medals went to a total of

58

students and only three students got medals in all three sports. If only

5

students got medals in football and basketball, then the number of medals received in exactly two of the three sports is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 5

Let

R

be a relation on the set

N

of natural numbers defined by

' n R m \Leftrightarrow n

is a factor of

m'

. Then, which one of the following is correct?

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 6

If we define a relation

R

on the set

N \times N

as

(a, b) R (c, d) \Leftrightarrow a + d = b + c

for all

(a, b), (c, d) \in N \times N

, then the relation is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 26 - Set Theory and Relations>Level 2>Q 7

Let

S = {1, 2, 3, \dots, 24}

. Define a relation

' ~'

on

S

as

x ~ y

if the product of the digits in

x

is same as that of the digits of

y

(Note that if

x

is a single digit number then the product of the digits in will be considered to be

x

). Then the number of equivalence classes for this equivalence relation is