Coordinate Geometry Questions

If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ in the ratio $3:2$, then $k$ equals:

The length of the diameter of the circle which touches the $x$ -axis at the point $(1,0)$ and passes through the point $(2,3)$ is:

A line is drawn through the point $(1,2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $OPQ$, where $O$ is the origin. If the area of the triangle $OPQ$ is least, then the slope of the line $PQ$ is: