Explanation:

Introduction:
The most probable velocity of a gas is the velocity at which the majority of the gas molecules are moving. As the temperature of a gas increases, the average kinetic energy of the gas molecules also increases. This increase in kinetic energy leads to an increase in the most probable velocity of the gas.

Explanation of the answer:
The given question asks about the fraction of molecules having velocities within a given range around the most probable velocity. Let's consider a range around the most probable velocity.
- Initially, at a lower temperature, the fraction of molecules within the given range around the most probable velocity is relatively high because the distribution of velocities is narrower.
- However, as the temperature increases, the distribution of velocities becomes broader. This means that the fraction of molecules within the given range around the most probable velocity decreases.

Reasoning:
When the temperature of a gas increases, the kinetic energy of the gas molecules increases, leading to a broader distribution of velocities. This broader distribution means that the fraction of molecules within a given range around the most probable velocity decreases because there are now more molecules with velocities outside of that range.

Example:
For example, let's consider a gas at a low temperature where the distribution of velocities is narrow. If we take a range around the most probable velocity, let's say ±10% of the most probable velocity, we would find a relatively high fraction of molecules within that range. However, if we increase the temperature of the gas, the distribution of velocities becomes broader. Now, if we take the same range around the most probable velocity, the fraction of molecules within that range would decrease because there are now more molecules with velocities outside of that range.

Conclusion:
Therefore, with the increase in temperature of a gas, the fraction of molecules having velocities within a given range around the most probable velocity decreases. The correct answer is B) decrease.

Increases