If $C$ is a point on the line segment joining $A(-3, 4)$ and $B(2, 1)$ such that $AC = 2BC$, then the coordinates of $C$ are

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of set $A$ is $56$ more than the total number of subsets of set $B$. Then the distance of the point $P(m, n)$ from the point $Q(-2, -3)$ is

If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

In what ratio does the $y$-axis divide the line segment joining the points $(-3, -4)$ and $(1, -2)$?

If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

The points which trisect the line segment joining the points $(0, 0)$ and $(9, 12)$ are