EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 16th April 2018>Q 27

EASY

JEE Main

IMPORTANT

Earn 100

Let $N$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_{1} = \{(x, y) \in N \times N : 2 x + y = 10\}$ and $R_{2} = \{(x, y) \in N \times N : x + 2 y = 10\}$ . Then

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Important Questions on Set Theory and Relations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 10th April 2015>Q 28

In a certain town,

25 %

of the families own a phone and

15 %

own a car;

65 %

families own neither a phone nor a car and

2000

families own both a car and a phone. Consider the following three statements:

(i)

5 %

families own both a car and a phone.

(i i)

35 %

families own either a car or a phone.

(i i i)

40000

families live in the town.

Then,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 4th April 2015>Q 29

Let

A

and

B

be two sets containing four and two elements respectively. Then the number of subsets of the set

A \times B

, each having at least three elements is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 9th April 2014>Q 30

Let

P

be the relation defined on the set of all real numbers such that

P = \{(a, b) : \sec^{2} a - \tan^{2} b = 1\}

. Then,

P

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 7th April 2013>Q 31

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 24 June 2022 Shift 2>Q 32

Let

x \times y = x^{2} + y^{3}

and

(x \times 1) \times 1 = x \times (1 \times 1)

. Then a value of

2 \sin^{- 1} (\frac{x^{4} + x^{2} - 2}{x^{4} + x^{2} + 2})

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 24 June 2022 Shift 2>Q 33

The sum of all the elements of the set

\{α \in \{1, 2, \dots . . 100\} : H C F (α, 24) = 1\}

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 25 June 2022 Shift 2>Q 34

Let

A = \{x \in R : |x + 1| < 2\}

and

B = \{x \in R : |x - 1| \geq 2\}

. Then which one the following statements is NOT true?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 1 - Set Theory and Relations>JEE Main - 28 June 2022 Shift 1>Q 35

Let

R_{1}

and

R_{2}

be relations on the set

\{1, 2, \dots, 50\}

such that

R_{1} =

{

(p, p^{n}) : p

is a prime and

n \geq 0

is an integer} and

R_{2} =

{

(p, p^{n}) : p

is a prime and

n = 0

or

1

}. Then, the number of elements in

R_{1} - R_{2}

is ____.