The number of shortest paths from point A to D (as show in figure)

A ray of light is to travel from point A to point B in figure in the shortest possible time after reflecting from P. Then OP is ………cm.

A ray of light is to travel from point A to point B in figure in the shortest possible time after reflecting from P. Then OP is ………cm.

The number of ways in which a person can reach from the point A to B along the grid through the shortest path as shown in the figure is -

A B is a line segment. P\ a n d\ Q are points on opposite sides of A B such that each of them is equidistant from the points A\ a n d\ B (in figure). Show that the line P Q is perpendicular bisector of A B .

What is the minumum number of unshaded boxes to be crossed for covering the shortest path from 'A' to 'B' (both exclusive) without retracing the path and without diagonal movements ?

A stone is projected from ground. Its path is a shown in figure. At which point its speed is decreasing at fastest rate?