Let $C_1$ be the graph of $xy=1$ and the reflection of $C_1$ in the line $y=2x$ is $C_2.$ If the equation of $C_2$ is expressed as $12x^2+bxy+c{y}^2+d=0$, then the value of $(b+c+d)$ is equal to

A ray of light coming from the point $(2,2\sqrt{3})$ is incident at an angle $30°$ on the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets $x$ -axis at the point $B$. Then, the line $AB$ passes through the point
 

If $\mathrm{Q}(0,-1,-3)$ is the image of the point $P$ in the plane $3x-y+4z=2$ and $R$ is the point $(3,-1,-2)$, then the area (in sq. units) of $\Delta PQR$ is