In the (i) absence of electric field, and in the (ii) presence of electric field, the paths of electrons between successive collisions with the positive ions of the metal, are

The correct option is (i) Straight line, (ii) Curved in general.

To understand why this is correct, let us analyze the behavior of electrons moving through a metallic conductor under two different conditions:

(i) In the absence of an electric field:
When there is no external electric field applied across the conductor, the free electrons inside the metal move randomly due to their thermal energy. Since there is no electric force acting on the electrons between collisions, they do not experience any acceleration during their free path. According to Newton's first law of motion, a particle moving with constant velocity (zero acceleration) travels in a straight line. Therefore, the path of electrons between successive collisions with the positive ions of the metal is a straight line.

(ii) In the presence of an electric field:
When an electric field $E$ is applied across the conductor, each electron of charge $e$ experiences a constant electrostatic force given by:
$F=-eE$
This force produces a constant acceleration in the direction opposite to the electric field:
$a=-\frac{eE}{m}$
where $m$ is the mass of the electron.
Since the electrons already possess random thermal velocities in arbitrary directions, this constant acceleration acting in a specific direction (superimposed on their random motion) causes their trajectory to bend. The combination of a constant acceleration in one direction and an initial velocity in another direction results in a parabolic path. Hence, between successive collisions, the paths of the electrons become curved in general.