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  4. The area of the region (x, y) ; 0 ≤ x ≤ (9/4), 0 ≤ y ≤ 1, x ≥ 3 y, x+y ≥ 2 is

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Q. The area of the region $\left\{(x, y) ; \,\,0 \leq x \leq \frac{9}{4}, \,\, 0 \leq y \leq 1, \,\,x \geq 3 y, \,\,x+y \geq 2\right\}$ is

JEE AdvancedJEE Advanced 2021

Solution:

image
Area of shaded region
$=\frac{1}{2}\left(\frac{2}{3}+\frac{3}{4}\right) \frac{1}{4}+\frac{1}{2} \times \frac{2}{3} \times \frac{1}{2} $
$=\frac{11}{32}$