QJEEAdv21Ma4a7a: JEE Advanced 2021 Mathematics - Class 12 JEEAdv21Ma4a7a Solution: The area of the region { ( x , y ) : 0 ≤ x ≤ 9 4 , 0 ≤ y ≤ 1 ,…

Required area = Shaded region

On solving x + y = 2 and x = 3y, we get

$A \equiv \left( {{3 \over 2},{1 \over 2}} \right)$

On solving y = 0 and x + y = 2, we get

B ≡ (2, 0)

On solving x = ${9 \over 4}$ and x = 3y, we get

D ≡ $\left( {{9 \over 4},{3 \over 4}} \right)$

and C ≡ $\left( {{9 \over 4},0} \right)$

Required area = Area of ∆OCD − Area of ∆OBA

= ${1 \over 2} \times \left( {{9 \over 4} - 0} \right) \times {3 \over 4} - {1 \over 2} \times \left( {2 - 0} \right) \times {1 \over 2}$

= ${{27} \over {32}} - {1 \over 2}$

= ${{11} \over {32}}$