Class JEE Mathematics Sets, Relations, and Functions Q #995
KNOWLEDGE BASED
APPLY
4 Marks 2025 JEE Main 2025 (Online) 7th April Evening Shift MCQ SINGLE
Let $A = { (\alpha, \beta ) \in R \times R : |\alpha - 1| \leq 4$ and $|\beta - 5| \leq 6 }$

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

Then
(A) A $A \subset B$
(B) B $B \subset A$
(C) C neither $A \subset B$ nor $B \subset A$
(D) D $A \cup B = { (x, y) : -4 \leqslant x \leqslant 4, -1 \leqslant y \leqslant 11 }$
Prev Next
Correct Answer: B
Explanation
$A: |x-1| \leq 4$ and $|y-5| \leq 6$
$\Rightarrow -4 \leq x-1 \leq 4 \Rightarrow -6 \leq y-5 \leq 6$
$\Rightarrow -3 \leq x \leq 5 \Rightarrow -1 \leq y \leq 11$
$B : 16(x-2)^{2} + 9(y-6)^{2} \leq 144$
$B : \frac{(x-2)^{2}}{9} + \frac{(y-6)^{2}}{16} \leq 1$

From Diagram $B \subset A$

More from this Chapter

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
If $R = {(x, y) : x, y \in Z, x^2 + 3y^2 \le 8}$ is a relation on the set of integers $Z$, then the domain of $R^{-1}$ is :
MCQ_SINGLE
The number of non-empty equivalence relations on the set ${1, 2, 3}$ 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 $R = \{(1, 2), (2, 3), (3, 3)\}$ be a relation defined on the set $\{1, 2, 3, 4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, is:
View All Questions