Let A= \(x,y)in R^2:yge0,\ 2xle ylesqrt4-(x-1)^2 \ and B= \(x,y)in Rtimes R:0le ylemin \2x,sqrt4-(x-1)^2 \ \ . Then the ratio of the area of A to the area of B is

Application of Integrals: Let A= \(x,y)in R^2:yge0,\ 2xle ylesqrt4-(x-1)^2 \ and B= \(x,y)in… | JEE Main 2023

JEE Main 2023 (Online) 29th January Morning ShiftQuestion 1

Let $A=\left\{(x,y)\in R^{2}:y\ge0,\ 2x\le y\le\sqrt{4-(x-1)^{2}}\right\}$ and $B=\left\{(x,y)\in R\times R:0\le y\le\min\left\{2x,\sqrt{4-(x-1)^{2}}\right\}\right\}$. Then the ratio of the area of $A$ to the area of $B$ is

Application of Integrals

$\frac{\pi-1}{\pi+1}$✓ Correct answer$\frac{\pi}{\pi-1}$$\frac{\pi}{\pi+1}$$\frac{\pi+1}{\pi-1}$

Solution

Line $y=2x$ meets the circle $(x-1)^2+y^2=4$ at its top $(1,2)$. $B$ = triangle $1$ + quarter disc $\pi$ = $\pi+1$; $A$ = upper half disc $2\pi-B=\pi-1$. Ratio $\frac{\pi-1}{\pi+1}$.

Application of Integrals - JEE Mathematics question (JEE Main 2023 (Online) 29th January Morning Shift)

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