QJEEAdv06Ma6bbe: JEE Advanced 2006 Physics - Class 11 JEEAdv06Ma6bbe Solution: Match the folowing : (A) Two rays and intersects each other in…

Match the folowing :
(A) $\,\,\,$ Two rays $x + y = \left| a \right|$ and $ax - y=1$ intersects each other in the
$\,\,\,\,\,\,\,\,\,\,$ first quadrant in interval $a \in \left( {{a_0},\,\,\infty } \right),$ the value of ${{a_0}}$ is
(B) $\,\,\,$ Point $\left( {\alpha ,\beta ,\gamma } \right)$ lies on the plane $x+y+z=2.$
$\,\,\,\,\,\,\,\,\,\,\,$ Let $\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k,\widehat k \times \left( {\widehat k \times \overrightarrow a } \right) = 0,$ then $\gamma =$
(C) $\,\,\,$ $\left| {\int\limits_0^1 {\left( {1 - {y^2}} \right)dy} } \right| + \left| {\int\limits_1^0 {\left( {{y^2} - 1} \right)dy} } \right|$
(D) $\,\,\,$ If $\sin A\,\,\sin B\,\,\sin C + \cos A\,\,\cos B = 1,$ then the value of $\sin C =$

(p) $\,\,\,$ $2$
(q) $\,\,\,$ ${4 \over 3}$
(r) $\,\,\,$ $\left| {\int\limits_0^1 {\sqrt {1 - xdx} } } \right| + \left| {\int\limits_{ - 1}^0 {\sqrt {1 + xdx} } } \right|$
(s) $\,\,\,$ $1$