An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

The magnetic field inside a solenoid is along its axis. An electron moving along the axis has velocity parallel to the magnetic field.

The magnetic force on a charged particle is: $$\vec{F} = q\vec{v} \times \vec{B}$$

Since $$\vec{v}$$ is parallel to $$\vec{B}$$, the cross product $$\vec{v} \times \vec{B} = 0$$.

Therefore, no magnetic force acts on the electron, and it continues to move with uniform velocity along the axis.

The correct answer is Option 1.