A relation R is defined on the set N of natural numbers as x R y ⇒ x 2 - 4 x y + 3 y 2 = 0 . Then which one of the following is correct?

R is reflexive, but neither symmetric nor transitive

R is reflexive and symmetric, but not transitive

R is reflexive and transitive, but not symmetric

R is reflexive, symmetric and transitive

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 2 Mathematics>Q 10

EASY

NDA & NA EE

IMPORTANT

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Let $S = \{2, 4, 6, 8, \dots \dots, 20\} .$ What are the maximum number of subsets of $S ?$

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Important Questions on Set Theory and Relations

EASY

NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 2 Mathematics>Q 11

A binary number is represented by

{(cdccddcccddd)}_{2},

where

c > d .

What is its decimal equivalent?

EASY

NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 1 Mathematics>Q 12

Suppose

X = {1, 2, 3, 4}

and

R

is a relation on

X .

If

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

then which one of the following is correct?

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NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 1 Mathematics>Q 13

A relation

R

is defined on the set

N

of natural numbers as

x R y \Rightarrow x^{2} - 4 x y + 3 y^{2} = 0 .

Then which one of the following is correct?

EASY

NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 1 Mathematics>Q 14

If

A = \{x \in Z : x^{3} - 1 = 0\}

and

B = \{x \in Z : x^{2} + x + 1 = 0\},

where

Z

is set of complex numbers, then what is

A \cap B

equal to?

MEDIUM

NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 1 Mathematics>Q 15

Consider the following statements for the two non-empty sets $A$ and $B$

1.

(A \cap B) \cup (A \cap \bar{B}) \cup (\bar{A} \cap B) = A \cup B

2. $(A \cup (\bar{A} \cap \bar{B})) = A \cup B$
Which of the above statements is/are correct?

EASY

NDA & NA EE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Set Theory and Relations>NDA & NA EE 2019 Paper 1 Mathematics>Q 16

Let $X$ be a non-empty set and let $A, B, C$ be subsets of $X .$ Consider the following statements.

1. $A \subset C \Rightarrow (A \cap B) \subset (C \cap B)$
$(A \cup B) \subset (C \cup B)$
2. $(A \cap B) \subset (C \cap B)$ for all sets $B \Rightarrow A \subset C$
3. $(A \cup B) \subset (C \cup B)$ for all sets $B \Rightarrow A \subset C$
Which of the above statements are correct?