The cube ABCDEFGH in the figure has each edge equal to 'a'. The area of the triangle with vertices at A, C and F is?

A circle of radius $5$ units in the XY plane has its centre in the first quadrant, touches the x-axis and has a chord of length $6$ units on the y-axis. The co-ordinates of its centre are?

A long ribbon is wound around a spool up to a radius $\mathrm{R}$. Holding the tip of the ribbon, a boy runs away from the spool with a constant speed maintaining the unwound portion of the ribbon horizontal. In $4$ minutes, the radius of the wound portion becomes $\mathrm{R}/\sqrt{2}$. In what further time, it will become $\mathrm{R}/2$?

If $\mathrm{AB}$ is parallel to $\mathrm{CD}$ and $\mathrm{AO}=2\mathrm{OD}$, then the area of triangle $\mathrm{OAB}$ is bigger than the area of triangle $\mathrm{OCD}$ by a factor of?

Four lines are drawn on a plane where no two are parallel and no three lines are concurrent. Lines are drawn joining the points of intersection of the previous four lines. The number of new lines obtained this way is?

The edges of a cube are $12 \mathrm{cm}$ long. An ant moves on the cube surface from point A to point B along the path shown. The length of the ant's path is?

What is the maximum number of rectangular wooden blocks with dimensions $20 \mathrm{cm}\times 30 \mathrm{cm}\times 40 \mathrm{cm}$ that could fit into a rectangular box with inner dimensions $40 \mathrm{cm}\times 60 \mathrm{cm}\times 80 \mathrm{cm}$?