QJEEAdv06Ma8c63: JEE Advanced 2006 Mathematics - Class 12 JEEAdv06Ma8c63 Solution: Match the following : Column (A) (B) Area bounded by and (C)…

Column $I$
(A) $\int\limits_0^{\pi /2} {{{\left( {\sin x} \right)}^{\cos x}}\left( {\cos x\cot x - \log {{\left( {\sin x} \right)}^{\sin x}}} \right)dx}$
(B) Area bounded by $- 4{y^2} = x$ and $x - 1 = - 5{y^2}$
(C) Cosine of the angle of intersection of curves $y = {3^{x - 1}}\log x$ and $y = {x^x} - 1$ is
(D) Let ${{dy} \over {dx}} = {6 \over {x + y}}$ where $y(0)=0$ then value of $y$ when $x+y=6$ is

Column $II$
(p) $1$
(q) $0$
(r) $6\ln 2$
(s) ${4 \over 3}$