New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sets and Relations question

2025 · 23 Jan · Shift 2 · Q32

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Sets and Relations
2025 · 23 Jan · Shift 2 · Q32

Sets and Relations question

2025 · 23 Jan · Shift 2 · Q32

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Let

\mathrm{X}=\mathbf{R} \times \mathbf{R}

. Define a relation R on X as :

\left(a_1, b_1\right) R\left(a_2, b_2\right) \Leftrightarrow b_1=b_2

Statement I:

\quad \mathrm{R}

is an equivalence relation. Statement II : For some

(\mathrm{a}, \mathrm{b}) \in \mathrm{X}

, the

\operatorname{set} \mathrm{S}=\{(x, y) \in \mathrm{X}:(x, y) \mathrm{R}(\mathrm{a}, \mathrm{b})\}

represents a line parallel to

y=x

. In the light of the above statements, choose the correct answer from the options given below :

A
Both Statement I and Statement II are true
B
Statement I is true but Statement II is false
C
Both Statement I and Statement II are false
D
Statement I is false but Statement II is true

More from Sets and Relations

Let $A = {(x, y) \in R \times R : ∣ x + y ∣ ⩾ 3}$ and $B = {(x, y) \in R \times R : ∣ x ∣ + ∣ y ∣ \leq 3}$ . If $C = {(x, y) \in A \cap B : x = 0$ or $y = 0}$ , then $\sum_{(x, y) \in C} ∣ x + y ∣$ …2025 · MCQ
Let $S = {p_{1}, p_{2} \dots, p_{10}}$ 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 $(x, y), x \in S$ , $y \in A$ …2025 · Numerical
Let $A = {x \in (0, π) - {\frac{π}{2}} : lo g_{(2/ π)} ∣ sin x ∣ + lo g_{(2/ π)} ∣ cos x ∣ = 2}$ and $B = {x ⩾ 0 : x (x - 4) - 3∣ x - 2∣ + 6 = 0}$ . Then $n (A \cup B)$ …2025 · MCQ
The relation $R = {(x, y) : x, y \in Z$ and $x + y$ is even $}$ is:2025 · MCQ
Define a relation R on the interval $[0, \frac{π}{2})$ by $x$ R $y$ if and only if $sec^{2} x - tan^{2} y = 1$ . Then R is :2025 · MCQ
Let $S = N \cup {0}$ . Define a relation R from S to $R$ by : $R = {(x, y) : lo g_{e} y = x lo g_{e} (\frac{2}{5}), x \in S, y \in R} .$ Then, the…2025 · MCQ
Let $A = {1, 2, 3, \dots, 20}$ . Let $R_{1}$ and $R_{2}$ two relation on $A$ such that $R_{1} = {(a, b) : b$ is divisible by $a} R_{2} = {(a, b) : a$ is an integral multiple of $b}$ . Then, number of elements in $R_{1} - R_{2}$ is equal to …2024 · Numerical
Consider the relations $R_{1}$ and $R_{2}$ defined as $a R_{1} b \Leftrightarrow a^{2} + b^{2} = 1$ for all $a, b \in R$ and $(a, b) R_{2} (c, d) \Leftrightarrow a + d = b + c$ for all $(a, b), (c, d) \in N \times N$ . Then :2024 · MCQ