The correct sequence of the given hydraulic turbines in decreasing order of their specific speeds is option 'B': Propeller turbine, Francis turbine, and Pelton wheel. Let's understand why.

**1. Specific Speed**
Specific speed is a parameter used to characterize the performance of hydraulic turbines. It is defined as the speed at which a turbine would run if it were geometrically similar to a unit turbine delivering one unit of head with one unit of discharge. Turbines with higher specific speeds operate at higher speeds and are typically used for low-head applications, while turbines with lower specific speeds operate at lower speeds and are used for high-head applications.

**2. Types of Hydraulic Turbines**
There are various types of hydraulic turbines, including Pelton wheel, Francis turbine, Kaplan turbine, and propeller turbine. Each turbine type is designed for specific applications based on head and flow.

- **Pelton Wheel**: Pelton wheel turbines are impulse turbines designed for high-head applications. They consist of a series of buckets or cups arranged around the circumference of a wheel. Water is directed onto the buckets, and the resulting impulse causes the wheel to rotate. Pelton wheels have the highest specific speed among hydraulic turbines.

- **Francis Turbine**: Francis turbines are reaction turbines designed for medium-head applications. They have a spiral casing and adjustable guide vanes to control the flow of water. The water enters the turbine and passes through both fixed and moving blades, causing the turbine to rotate. Francis turbines have a moderate specific speed.

- **Kaplan Turbine**: Kaplan turbines are also reaction turbines, but they are designed for low-head applications. They have adjustable propeller-like blades and a spiral casing. Water enters the turbine axially and passes through the blades, causing the turbine to rotate. Kaplan turbines have a lower specific speed compared to Francis turbines.

- **Propeller Turbine**: Propeller turbines are also reaction turbines designed for low-head applications. They have fixed blades and a casing similar to Kaplan turbines. Water enters the turbine axially and passes through the fixed blades, causing the turbine to rotate. Propeller turbines have the lowest specific speed among hydraulic turbines.

**3. Arranging the Turbines in Decreasing Order of Specific Speed**
Based on the above information, we can arrange the hydraulic turbines in decreasing order of their specific speeds as follows:

Propeller turbine < francis="" turbine="" />< pelton="" />

Hence, option 'B' is the correct sequence, where the propeller turbine has the lowest specific speed, followed by the Francis turbine, and finally the Pelton wheel which has the highest specific speed.