Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202523 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 23 January · Evening Shift · Mathematics · Sets and Relations

Let A=\ (x, y) ∈ R × R:|x+y| ≥ 3\ and B=\ (x, y) ∈ R × R:|x|+|y| ≤...

Let A={(x,y)∈R×R:∣x+y∣⩾3}\mathrm{A}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geqslant 3\} and B={(x,y)∈R×R:∣x∣+∣y∣≤3}\mathrm{B}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}. If C={(x,y)∈A∩B:x=0\mathrm{C}=\{(x, y) \in \mathrm{A} \cap \mathrm{B}: x=0 or y=0}y=0\}, then ∑(x,y)∈C∣x+y∣\sum_{(x, y) \in \mathrm{C}}|x+y| is :

Options

  1. A15
  2. B24
  3. C18
  4. D12

Correct answer

D. 12

Step-by-step solution

A={(x,y)∈R×R:∣x+y∣≥3} and B={(x,y)∈R×R:∣x∣+∣y∣≤3}C={(x,y)∈A∩B:x=0 or y=0}\begin{aligned} & A=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geq 3\} \\ & \text{ and } B=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\} \\ & C=\{(x, y) \in A \cap B: x=0 \text{ or } y=0\}\end{aligned} A \cap Bwillhaveonlycommonpointslyingonthelinewill have only common points lying on the lineP Q and R SNow,Now,C=\{(-3,0),(3,0),(0,3),(0,-3)\} \sum_{(x, y) \in c}|x+y|=3+3+3+3=12
Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

Let S = \ 1, 2, 3, …, 10\ . Consider the set X = \ R : R is an equivalence relation on… JEE Advanced 2026Consider the relation R on the set \ -2,-1,0,1,2\ defined by (a, b) ∈ R if and only if… JEE Main 2026Let R = \ (x, y) ∈ ℕ × ℕ : _e(x + y) ≤ 2\ . Then the minimum number of elements, required… JEE Main 2026Let A = \ 1, 4, 7\ and B = \ 2, 3, 8\ . Then the number of elements, in the relation R =… JEE Main 2026Let A = \ 2, 3, 4, 5, 6\ . Let R be a relation on the set A × A given by (x, y) R (z, w)… JEE Main 2026Let R be a relation defined on the set \ 1,2,3,4\ ×\ 1,2,3,4\ by R=\ ((a, b),(c, d)): 2… JEE Main 2026Let A=\ 0,1,2, …, 9\ . Let R be a relation on A defined by (x, y) ∈ R if and only if… JEE Main 2026Let A=\ -2,-1,0,1,2,3,4\ . Let R be a relation on A defined by x Ry if and only if 2 x+y… JEE Main 2026The number of elements in the relation R=\ (x, y): 4 x^ 2 +y^ 2 <52, x, y ∈ Z\ is JEE Main 2026Let S be the set of the first 11 natural numbers. Then the number of elements in A=\ B ⊆… JEE Main 2026Let the relation R on the set M=\ 1,2,3, …, 16\ be given by R=\ (x, y): 4 y=5 x-3, x, y ∈… JEE Main 2026Let A=\ x:|x^ 2 -10| ≤ 6\ and B=\ x:|x-2|>1\ . Then JEE Main 2026Let A=\ 2,3,5,7,9\ . Let R be the relation on A defined by x R y if and only if 2 x ≤ 3 y… JEE Main 2026The number of relations, defined on the set \ a, b, c, d\ , which are both reflexive and… JEE Main 2026Let the set of all relations R on the set \ a, b, c, d, e, f\ , such that R is reflexive… JEE Advanced 2025Let A=\ 0,1,2,3,4,5\ . Let R be a relation on A defined by (x, y) ∈ R if and only if max… JEE Main 2025 Full Sets and Relations list Sets and Relations JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs