The layer of atmosphere between 10 km to 50 km above the sea level is called as:

We recall that Earth’s atmosphere is divided into distinct layers on the basis of altitude. The commonly accepted sequence starting from the Earth’s surface is:

$$\text{Troposphere} \; < \text{Stratosphere} \; < \text{Mesosphere} \; < \text{Thermosphere}$$

These layers have approximate vertical extents that are widely memorised for elementary atmospheric science:

Troposphere: $$0\;\text{km} \text{ to } 10\;\text{km}$$

Stratosphere: $$10\;\text{km} \text{ to } 50\;\text{km}$$

Mesosphere: $$50\;\text{km} \text{ to } 80\;\text{km}$$

Thermosphere: $$80\;\text{km} \text{ upward (variable)}$$

The question explicitly describes the layer lying between $$10\;\text{km}$$ and $$50\;\text{km}$$ above mean sea level. Consulting the altitude ranges stated above, we see that $$10\;\text{km} \le h \le 50\;\text{km}$$ corresponds exactly to the stratosphere.

None of the other given options match this altitude band: $$\begin{aligned} \text{Troposphere} &: 0\text{-}10\;\text{km} \quad (\text{too low}),\\ \text{Mesosphere} &: 50\text{-}80\;\text{km} \quad (\text{starts higher}),\\ \text{Thermosphere} &: \gt 80\;\text{km} \quad (\text{much higher}). \end{aligned}$$ So, by direct comparison, the only correct identification is the stratosphere.

Hence, the correct answer is Option A.