Class JEE Mathematics Sets, Relations, and Functions Q #1052
KNOWLEDGE BASED
APPLY
4 Marks 2021 JEE Main 2021 (Online) 26th February Morning Shift MCQ SINGLE
Let $R = {(P, Q) | P$ and $Q$ are at the same distance from the origin} be a relation, then the equivalence class of $(1, −1)$ is the set :
(A) $S = {(x, y) | x^2 + y^2 = \sqrt{2}}$
(B) $S = {(x, y) | x^2 + y^2 = 2}$
(C) $S = {(x, y) | x^2 + y^2 = 1}$
(D) $S = {(x, y) | x^2 + y^2 = 4}$
Prev Next
Correct Answer: B
Explanation
Given $R = {(P, Q) | P$ and $Q$ are at the same distance from the origin}.
Then the equivalence class of $(1, -1)$ will contain all such points that lie on the circumference of the circle with the center at the origin and passing through the point $(1, -1)$.
The radius of the circle $= \sqrt{1^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}$. Therefore, the equation of the circle is $x^2 + y^2 = (\sqrt{2})^2 = 2$.
Required equivalence class of $(S) = {(x, y) | x^2 + y^2 = 2}$.

More from this Chapter

MCQ_SINGLE
Let $S = {1, 2, 3, …, 10}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R = {(A, B) : A ∩ B ≠ 𝜙; A, B ∈ M}$ is :
MCQ_SINGLE
Let $A = {1, 2, 3, …, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n$ and $gcd(m, n) = 1}$. Then $n(B)$ is equal to :
MCQ_SINGLE
Let $R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}$ be a relation on the set $A = \{3, 6, 9, 12\}$. The relation is :
NUMERICAL
Let $S=\left\{p_1, p_2 \ldots, p_{10}\right\}$ be the set of first ten prime numbers. Let $A=S \cup P$, where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y), x \in S$, $y \in A$, such that $x$ divides $y$, is ________ .
MCQ_SINGLE
Let $A = {-3, -2, -1, 0, 1, 2, 3}$. Let R be a relation on A defined by $xRy$ if and only if $0 \le x^2 + 2y \le 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l + m$ is equal to
View All Questions