Escape velocity:
Escape velocity is defined as the minimum velocity required for an object to escape the gravitational pull of a planet or any other celestial body without any additional propulsion. It is the speed at which an object needs to be projected to overcome the gravitational force and move away indefinitely from the planet.

Factors affecting escape velocity:
The escape velocity of a planet depends on the following factors:

1. The mass of the projected body:
The mass of the projected body affects the escape velocity. The greater the mass of the object, the greater the escape velocity required to overcome the gravitational pull. This is because a larger mass will experience a greater gravitational force and will require more energy to escape.

2. The mass and radius of the planet:
The mass and radius of the planet from which the object is being projected also play a significant role in determining the escape velocity. The escape velocity is directly proportional to the mass and inversely proportional to the radius of the planet. A planet with a larger mass or a smaller radius will have a higher escape velocity. This is because a greater mass or a smaller radius will result in a stronger gravitational pull, requiring a higher velocity to escape.

3. The angle and direction of projection:
The angle and direction of projection do not directly affect the escape velocity. The escape velocity is a scalar quantity and depends only on the mass and radius of the planet. The angle and direction of projection only affect the trajectory of the object after it has overcome the escape velocity.

Conclusion:
In conclusion, the value of escape velocity primarily depends on the mass and radius of the planet from which the object is being projected. The mass of the projected body and the angle and direction of projection do not directly affect the escape velocity. Therefore, the correct answer is option 'B' - the mass and radius of the planet.