C

Step 1: The problem involves a particle projected on an inclined plane, with an angle \( \theta \) defined as \( \tan^{-1}(n) \).
Step 2: We need to consider the angles of projection and incidence on the inclined plane. Let \( \alpha = \tan^{-1}(k) \) be the angle of projection.
Step 3: The normal and tangential components of velocity before and after impact can be derived using the coefficient of restitution, \( e \). The final velocity component must also sustain motion up the inclined plane.
Step 4: The conditions of motion require that after impact, the tangential velocity remains positive for the particle to continue moving up the incline.
Step 5: Analyzing the energy and momentum exchange along with the inclines gives the inequalities:
\( \text{Final Tangential Velocity} = e \cdot v_{initial} \cdot \cos(\theta) < v_{initial} \cdot \sin(\theta) \). This implies that \( e < \tan(\alpha) \) and must also satisfy the conditions of energy conservation.
Therefore, solving the equations we find the required values leading to conclusion in option C.