Which of the following options shows lengths arranged in ascending order?

We must express all of the specified lengths in a single unit in order to compare them.
The given lengths are: 10 mm, 1 km, 2 ft, and 5 cm

Let's express all the lengths in mm.
1 km = 1000000 mm ($\because$1 km= 1000 m and 1 m= 1000 mm)

5 cm = 50 mm ($\because$1 cm = 10 mm)

2 ft = 609.6 mm ($\because$1 ft= 304.8 mm)

Therefore, the correct increasing order is 10 mm, 5 cm, 2 ft, and 1 km.