Let A_1, A_2 \and A_3 be the regions on R_2 defined by A_1 = \{(x, y) : x \geq0, y \geq 0, 2x + 2y -x^2 -y^2 > 1 > x + y\} A_2 = \{(x, y) : x \geq 0, y \geq0, x + y > 1 > x^2 + y^2\}, A_3 = \{(x, y) : x\geq 0, y\geq 0, x + y > 1 > x^3 + y^3\} Denote by |A_1|, |A_2| \and |A_3| the areas of the regions A_1, A_2, \and A_3 respectively. Then

Correct Answer is : |A1|=|A2|<|A3|

KVPY 2019 SB SX Exam Previous Papers

Question : 16 of 120

Marks: +1, -0

Let

A_1, A_2 \and A_3

be the regions on

R_2

defined by

A_1 = \{(x, y) : x ≥0, y ≥ 0,

2x + 2y -x^2 -y^2 > 1 > x + y\}

A_2 = \{(x, y) : x ≥ 0, y ≥0,

x + y > 1 > x^2 + y^2\}

A_3 = \{(x, y) : x≥ 0, y≥ 0,

x + y > 1 > x^3 + y^3\}

Denote by

|A_1|, |A_2| \and |A_3|

the areas of the regions

A_1, A_2, \and A_3

respectively. Then

Solution:

|A_1|=π/4-1/2

|A_2| =π/4-1/2

|A_3| > |A_2|

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