JEE Advanced2013MathematicsStraight LinesActual

Paragraph: Let S=S₁ S₂ S₃ , where S₁= z C :|z| 0 and S₃= z C : Re z>0 . Question: Area of S=

Options

A1 0 π 3
B2 0 π 3
C1 6 π 3
D 3 2 π 3

Correct answer

B. 2 0 π 3

Step-by-step solution

S 1 : x 2 + y 2 < 16 S 2  :  z - 1 + 3 i 1 - i 3 = x - 1 + i  y + 3 1 - 3 i = x - 1 + i  y + 3   1 + 3   i 1 + 3 S 2  :  x - 1 3 + y + 3 9 > 0 S 2  :  3 x + y > 0  &  S 3  :  x > 0 A = 1 2 r 2 θ = 1 2 × 1 6 × 5 π 6 = 4 0 π 6 = 2 0 π 3

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