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

NUMERICAL
Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ______.
NUMERICAL
Let $A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $ and $B = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\max \,\{ i,j\} } } $. Then A + B is equal to _____________.
MCQ_SINGLE
Let $R$ be a relation on $Z \times Z$ defined by $(a, b)R(c, d)$ if and only if $ad - bc$ is divisible by $5$. Then $R$ is
NUMERICAL
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is _________.
NUMERICAL
Let $A=\{1,2,3,4\}$ and $\mathrm{R}$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $\mathrm{R}$ is ____________.
View All Questions