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Area (in sq. units) of the region outside ${|x|\over2}+{|y|\over3}=1$ and inside the ellipse ${x^2\over4}+{y^2\over9}=1$ is :

(1) 3($\pi$ – 2)

(2) 3(4 – $\pi$)

(3) 6($\pi$ – 2)

(4) 6(4 – $\pi$)
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Recent question of JEE(main)2020

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Ans. (3) $6(\pi-2)$

Sol. 

Area of Ellipse $=\pi ab=6\pi$

Area enclose by ${|x|\over2}+{|y|\over3}=1$ is

$={1\over2}(d_1d_2)={1\over2}(4)(6)=12$

so required Area is $= 6\pi-12=6(\pi-2)$

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