Class JEE Mathematics Sets, Relations, and Functions Q #1011
KNOWLEDGE BASED
APPLY
4 Marks 2025 JEE Main 2025 (Online) 23rd January Evening Shift MCQ SINGLE
Let $A = {(x, y) ∈ R × R : |x + y| ⩾ 3}$ and $B = {(x, y) ∈ R × R : |x| + |y| ≤ 3}$. If $C = {(x, y) ∈ A ∩ B : x = 0$ or $y = 0}$, then $\sum_{(x, y) ∈ C} |x + y|$ is :
(A) 18
(B) 24
(C) 15
(D) 12
Prev Next
Correct Answer: D
Explanation
From the image, we can determine that the points in set C are $(3,0)$, $(-3,0)$, $(0,3)$ and $(0,-3)$.
Thus, $C = {(3, 0), (-3, 0), (0, 3), (0, -3)}$.
$\sum |x + y| = |3 + 0| + |-3 + 0| + |0 + 3| + |0 + (-3)| = 3 + 3 + 3 + 3 = 12$.

More from this Chapter

MCQ_SINGLE
Define a relation $R$ over a class of $n imes n$ real matrices $A$ and $B$ as "$ARB$ iff there exists a non-singular matrix $P$ such that $PAP^{-1} = B$". Then which of the following is true?
MCQ_SINGLE
Let $Z$ be the set of integers. If $A = {x \in Z : 2(x + 2) (x^2 - 5x + 6) = 1}$ and $B = {x \in Z : -3 < 2x - 1 < 9}$, then the number of subsets of the set $A \times B$, is
MCQ_SINGLE
Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $R = {(x, y) ∈ N × N: x^3 - 3x^2y - xy^2 + 3y^3 = 0}$. Then the relation $R$ is :
MCQ_SINGLE
If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :
NUMERICAL
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.
View All Questions