The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5 m) is

1. 15 m

2. 16 m

3. 10 m

4. 12 m

The longest pole in a cuboid is equal to the diagonal of cuboid.

Diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$

$= \sqrt{10^2 + 10^2 + 5^2} \\[1em] = \sqrt{100 + 100 + 25} \\[1em] = \sqrt{225} \\[1em] = 15 \text{ m}.$

Hence, Option 1 is the correct option.