1
JEE Main 2025 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements

(S1): The number of elements in R is 18, and

(S2): The relation R is symmetric but neither reflexive nor transitive

A

both are false

B

only (S1) is true

C

only (S2) is true

D

both are true

2
JEE Main 2025 (Online) 7th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let A = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : |$\alpha$ - 1| $\leq 4$ and |$\beta$ - 5| $\leq 6$ }

and B = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : 16($\alpha$ - $2)^2 $+ 9($\beta$ - $6)^2$ $\leq 144$ }.

Then

A

A $\subset$ B

B

B $\subset$ A

C

neither A $\subset$ B nor B $\subset$ A

D

$A \cup B=\{(x, y):-4 \leqslant x \leqslant 4,-1 \leqslant y \leqslant 11\}$

3
JEE Main 2025 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by $x \mathrm{R} y$ if and only if $2 x-y \in\{0,1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then $l+\mathrm{m}+\mathrm{n}$ is equal to:

A
17
B
18
C
15
D
16
4
JEE Main 2025 (Online) 4th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Consider the sets $A=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x^2+y^2=25\right\}, B=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x^2+9 y^2=144\right\}$, $C=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}: x^2+y^2 \leq 4\right\}$ and $D=A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

A
15120
B
18290
C
17160
D
19320
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