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

Question

The area of the region (x, y) ; 0 ≤ x ≤ (9/4), 0 ≤ y ≤ 1, x ≥ 3 y, x+y ≥ 2 is (A) (11/32) (B) (35/96) (C) (37/96) (D) (13/32)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a87a61bed09f8962e79b8e1d73caa212-.png" /> Area of shaded region =(1/2)((2/3)+(3/4)) (1/4)+(1/2) × (2/3) × (1/2) =(11/32)

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

$\frac{11}{32}$

$\frac{35}{96}$

$\frac{37}{96}$

$\frac{13}{32}$

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

Q. The area of the region {(x,y);0≤x≤49​,0≤y≤1,x≥3y,x+y≥2} is

3211​

9635​

9637​

3213​