question_answer

The area in the first quadrant between \[{{x}^{2}}+{{y}^{2}}={{\pi }^{2}}\] and y = sin x is

A) \[\frac{{{\pi }^{3}}-8}{4}\]

B) \[\frac{{{\pi }^{3}}}{4}\]

C) \[\frac{{{\pi }^{3}}-16}{4}\]                         

D) \[\frac{{{\pi }^{3}}-8}{2}\]

Correct Answer: A

Solution :

\[\begin{align}   & OHO \\  & ||| \\  & C{{H}_{3}}-C=CH-C-O{{C}_{2}}{{H}_{5}} \\  & \left( enol \right) \\ \end{align}\] is a circle of radius \[N{{a}_{2}}S\] and centre at origin.                  Required area =  Area of circle (1st quadrant  ) \[N{{a}_{2}}S+{{\left( C{{H}_{3}}COO \right)}_{2}}Pb\to \] \[\underset{ppt}{\mathop{\underset{Black}{\mathop{PbS}}\,}}\,+2C{{H}_{3}}COONa\] \[=5.6\times normality\]