In a special 'retrograde' vernier caliper, 10 divisions of the...

For a retrograde vernier, the vernier scale divisions are larger than the main scale divisions.

Given that $10\text{ VSD} = 11\text{ MSD}$, we can write:
$1\text{ VSD} = \dfrac{11}{10}\text{ MSD} = 1.1\text{ MSD}$

Since $1\text{ MSD} = 1\text{ mm}$, we have $1\text{ VSD} = 1.1\text{ mm}$.

The least count (LC) is defined as the magnitude of the difference between one vernier scale division and one main scale division:
$\text{LC} = |1\text{ MSD} - 1\text{ VSD}| = |1\text{ mm} - 1.1\text{ mm}| = 0.1\text{ mm}$

Converting the least count to cm:
$\text{LC} = 0.1\text{ mm} = 0.01\text{ cm}$.

Answer: $0.01$