Question

Let $R$ be set of points inside a rectangle of sides $a$ and $b$ $(a,b>1)$ with two sides along the positive direction of $X$-axis and $Y$-axis and $C$ be the set of points inside a unit circle centred at origin, then

• A. $R=\{(x,y):0\le x\le a,0\le y\le b\}$
• B. $R=\left\{\right(x,y):0<x<a,0<y<b\}$
• C. $C=\{(x,y):x^2+y^2>1\}$
• D. $R\cup C=R$

Answer 1

The correct option is B $R=\left\{\right(x,y):0<x<a,0<y<b\}$

The points in $R$ lie inside a rectangle (not on the rectangle) in the first quadrant with one vertex at origin, and the remaining vertices at $(a,0),(a,b)$ and $(0,b)$. Hence, for any point $P\in R,(0,0)<(x,y)<(a,b)$

Hence $R=\left\{\right(x,y):0<x<a,0<y<b\}$

The equation of a unit circle centred at origin is $x^2+y^2=1$.

For a point to lie inside the circle, $x^2+y^2<1$

$\therefore C=\left\{\right(x,y):x^2+y^2<1\}$

Hence, only option $B$ is correct.