In a Pelton turbine, the inlet and outlet blade velocities of the vanes are equal. This is because the Pelton turbine is specifically designed to work with high head and low flow rate conditions.

Here is a detailed explanation:

Pelton Turbine:
- The Pelton turbine is a type of impulse turbine that operates with a high head and low flow rate. It is commonly used in hydroelectric power plants for harnessing the energy of high-velocity water streams.
- The turbine consists of a set of buckets or vanes arranged around the circumference of a wheel. These buckets are known as Pelton buckets or Pelton cups.
- The water jet, which is highly pressurized and accelerated, is directed onto the buckets. The jet strikes the buckets at a tangent and imparts a high velocity to the buckets.
- As the water jet strikes the buckets, it gets deflected in the opposite direction, causing the wheel to rotate. The high velocity of the water jet is converted into the rotational kinetic energy of the turbine.
- The vanes of the Pelton turbine are designed in such a way that the inlet and outlet blade velocities are equal.
- This design ensures that the water jet imparts maximum energy to the buckets and minimizes any energy losses due to turbulence or eddies.
- By making the inlet and outlet blade velocities equal, the Pelton turbine achieves maximum efficiency in converting the kinetic energy of the water into mechanical work.

Other Turbines:
- Francis turbine: The Francis turbine is a type of reaction turbine, which means it operates with both pressure and velocity changes. In this turbine, the inlet and outlet blade velocities of the vanes are not equal. The water flows through the turbine, and its pressure and velocity change as it passes through the blades.
- Kaplan turbine: The Kaplan turbine is also a type of reaction turbine and is specifically designed for low head and high flow rate conditions. Similar to the Francis turbine, the inlet and outlet blade velocities of the vanes are not equal in a Kaplan turbine.
- Propeller turbine: The propeller turbine is a type of reaction turbine that is mainly used for low head and high flow rate conditions. Like the Francis and Kaplan turbines, the inlet and outlet blade velocities of the vanes are not equal in a propeller turbine.

Therefore, the correct answer is option 'C' - Pelton turbine, where the inlet and outlet blade velocities of the vanes are equal.