Consider the following for the next two (02) items that follow: A hall is of length l, breadth b and height h. The maximum distance between any two points (say P and Q) inside the hall is 14 m, whereas the maximum distance between any two points (say P and R) on the floor is 6 m. If α is the angle between the line joining P and Q, and the line joining P and R, then what is cos α equal to?
- A2√5/7
- B3√5/7
- C1/3
- D2/3
Explanation
The height follows from the two diagonals: h^2 = 14^2 - 6^2 = 160, so h = 4*sqrt(5) m. Take P at a bottom corner, Q at the opposite top corner and R at the opposite floor corner; then cos(alpha) = (PQ.PR)/(|PQ||PR|) = 36/(14*6) = 3/7. Since 3/7 is none of the listed options, the item as printed has no valid answer and appears defective; the stored key (b) is retained as keyed. Key disputed: verify against the official UPSC key.