Suppose that the mean and median of the non-negative numbers $21,8,17, a, 51,103, b, 13,67,(a>b)$, are 40 and 21 , respectively. If the mean deviation about the median is 26 , then $2 a$ is equal to :

Let the line $\mathrm{L}_1: x+3=0$ intersect the lines $\mathrm{L}_2: x-y=0$ and $\mathrm{L}_3: 3 x+y=0$ at the points A and B , respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point $C$. Then $B C^2: A C^2$ is equal to:

Let the vertex A of a triangle ABC be $(1,2)$, and the mid-point of the side AB be $(5,-1)$. If the centroid of this triangle is $(3,4)$ and its circumcenter is $(\alpha, \beta)$, then $21(\alpha+\beta)$ is equal to :

Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3 y=0$ are bisected by the $y$-axis. If the other ends of these chords are R and S , and the mid point of the line segment RS is $(\alpha, \beta)$, then $6(\alpha+\beta)$ is equal to :