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

MCQ_SINGLE
Let $A = {2, 3, 4, 5, ....., 30}$ and '$\simeq$' be an equivalence relation on $A \times A$, defined by $(a, b) \simeq (c, d)$, if and only if $ad = bc$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4, 3)$ is equal to :
MCQ_SINGLE
Consider the relations $R_1$ and $R_2$ defined as $aR_1b \Leftrightarrow a^2 + b^2 = 1$ for all $a, b \in R$ and $(a, b)R_2(c, d) \Leftrightarrow a+ d = b + c$ for all $(a, b), (c, d) \in N \times N$. Then:
NUMERICAL
Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.
MCQ_SINGLE
An organization awarded $48$ medals in event 'A', $25$ in event 'B' and $18$ in event 'C'. If these medals went to total $60$ men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
MCQ_SINGLE
Let R be a relation defined on $N$ as $aRb$ if $2a + 3b$ is a multiple of $5$, $a, b \in N$. Then R is
View All Questions