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
Define a relation R on the interval $[0, π/2)$ by $x$ R $y$ if and only if $\sec^2x - \tan^2y = 1$. Then R is :
NUMERICAL
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.
NUMERICAL
Let $A=\{0,3,4,6,7,8,9,10\}$ and $R$ be the relation defined on $A$ such that $R=\{(x, y) \in A \times A: x-y$ is odd positive integer or $x-y=2\}$. The minimum number of elements that must be added to the relation $R$, so that it is a symmetric relation, is equal to ____________.
MCQ_SINGLE
If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :
NUMERICAL
26 The sum of all the elements of the set $$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$ is __________.
View All Questions