Explanation:

Introduction:
When a positively charged particle enters a uniform magnetic field with a uniform velocity, its trajectory can be a straight line, a circle, or a helix. The exact trajectory depends on the initial conditions of the particle, such as its velocity, charge, and angle of entry into the magnetic field.

Effect of Magnetic Field on Charged Particle:
When a charged particle moves through a magnetic field, it experiences a force called the magnetic Lorentz force. This force acts perpendicular to both the velocity of the particle and the magnetic field. The magnitude of the magnetic force can be given by the equation F = qvBsinθ, where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.

Force Acting on a Particle:
The force acting on a positively charged particle in a magnetic field can be determined by the right-hand rule. If the thumb of the right hand points in the direction of the velocity of the particle, and the fingers point in the direction of the magnetic field, then the palm will point in the direction of the force acting on the particle.

Possible Trajectories:
The trajectory of a charged particle in a magnetic field depends on the initial conditions of the particle. The following are the possible trajectories:

1. Straight Line:
If the initial velocity of the particle is parallel or antiparallel to the magnetic field, then the force acting on the particle will be zero. In this case, the particle will continue to move in a straight line without any deflection.

2. Circle:
If the initial velocity of the particle is perpendicular to the magnetic field, the force acting on the particle will be maximum. This force will act as a centripetal force and cause the particle to move in a circular path with a constant radius.

3. Helix:
If the initial velocity of the particle has both a component perpendicular to the magnetic field and a component parallel to the magnetic field, the force acting on the particle will have both a radial and an axial component. This will cause the particle to move in a helical path.

Conclusion:
In conclusion, when a positively charged particle enters a uniform magnetic field with a uniform velocity, its trajectory can be a straight line, a circle, or a helix depending on the initial conditions of the particle. Therefore, the correct answer is option 'D' - any one of (i), (ii), and (iii).