| List II | List II |
|---|---|
| A. Osmosis | I. Solvent molecules pass through semi permeable membrane towards solvent side. |
| B. Reverse osmosis | II. Movement of charged colloidal particles under the influence of applied electric potential towards oppositely charged electrodes. |
| C. Electro osmosis | III. Solvent molecules pass through semi permeable membrane towards solution side. |
| D. Electrophoresis | IV. Dispersion medium moves in an electric field. |
Adding surfactants in non polar solvent, the micelles structure will look like

Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: