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
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
MCQ_SINGLE
If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :
NUMERICAL
Let X = {n $ \in $ N : 1 $ \le $ n $ \le $ 50}. If A = {n $ \in $ X: n is a multiple of 2} and B = {n $ \in $ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
NUMERICAL
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is _________.
MCQ_SINGLE
Consider the sets $A = \{(x, y) \in R \times R : x^2 + y^2 = 25\}$, $B = \{(x, y) \in R \times R : x^2 + 9y^2 = 144\}$, $C = \{(x, y) \in Z \times Z : x^2 + y^2 \le 4\}$ and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:
View All Questions