Let A= ( , ) R R:| -1| 4 and | -5| 6 and B= ( , ) R R: 16( -2)^ 2… - Vidyadip

MCQ

Let
$A=\{(\alpha, \beta) \in \mathbf{R} \times \mathbf{R}:|\alpha-1| \leq 4$ and $|\beta-5| \leq 6\}$
and
$B=\left\{(\alpha, \beta) \in \mathbf{R} \times \mathbf{R}: 16(\alpha-2)^{2}+9(\beta-6)^{2} \leq 144\right\}$.
Then

A
$\mathrm{B} \subset \mathrm{A}$
B
$\mathrm{A} \cup \mathrm{B}=\{(\mathrm{x}, \mathrm{y}):-4 \leq \mathrm{x} \leq 4,-1 \leq \mathrm{y} \leq 11\}$
C
neither $\mathrm{A} \subset \mathrm{B}$ nor $\mathrm{B} \subset \mathrm{A}$
D
$\mathrm{A} \subset \mathrm{B}$

✓

Answer

A. $\mathrm{B} \subset \mathrm{A}$
A : $|x-1| \leq 4$ and $|y-5| \leq 6$
$\Rightarrow-4 \leq \mathrm{x}-1 \leq 4 \Rightarrow-6 \leq y-5 \leq 6$
$\Rightarrow-3 \leq \mathrm{x} \leq 5 \quad \Rightarrow-1 \leq \mathrm{y} \leq 11$
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 $\mathrm{B} \subset \mathrm{A}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "SECTION - A [MATHS - MCQ]" from JEE Main 7-April-2025 Paper - Shift 2→JEE Main 7-April-2025 Paper - Shift 2 — all question types→JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is

$\int_{ - 1}^1 {{x^{17}}{{\cos }^4}x} \,dx = $

The value of $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{(2 j-1)+8 n}{(2 j-1)+4 n}$ is equal to:

$\int_0^\infty {\frac{{\log \,(1 + {x^2})}}{{1 + {x^2}}}} \,dx = $

The solution of $\frac{{dy}}{{dx}} = \frac{{{e^x}({{\sin }^2}x + \sin 2x)}}{{y(2\log y + 1)}}$ is

The function $f(x) = \left\{ \begin{array}{l}x,\,\,{\rm{if \,\,0}} \le x \le {\rm{1}}\\{\rm{1,\,\,}}\,{\rm{ if}}\,1 < x \le 2\end{array} \right.$ is

If $\tan y = {{2t} \over {1 - {t^2}}}$ and $\sin x = {{2t} \over {1 + {t^2}}},$ then ${{dy} \over {dx}} = $

$f\left( x \right) = \int {\frac{{dx}}{{{{\sin }^6}\,x}}} $ is a polynomial of degree

If the position vectors of the points $ A, B, C, D $ be $i + j + k,\,\,2\,i + 5\,j,\,\,3\,i + 2\,j - 3k$and $i - 6\,j - k,$ then the angle between the vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ is

Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to