NIMCET 2009 Question Paper with solutions

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Question : 33 of 120

Marks: +1, -0

The smaller of the areas bound by

y=2-x

and

x^{2}+y^{2}=4

, is

$(π-1)$ sq units
$(π-2)$ sq units
$(2 π-1)$ sq units
$(2 π-2)$ sq units

Solution:

From the above figure, shaded area is the smaller area bounded by the given line and circle.

=\;{1}/{4} \;\text " (Area of circle) "\;-\;\text " Area of "\; ∆ A O B

=

\;{1}/{4} π(2)^{2}-\;{1}/{2} × 2 × 2

=(π-2) \;\text " sq units "\;

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