| List II | List II |
|---|---|
| A. Elastomeric polymer | I. Urea formaldehyde resin |
| B. Fibre Polymer | II. Polystyrene |
| C. Thermosetting Polymer | III. Polyester |
| D. Thermoplastic Polymer | IV. Neoprene |
Polymers used for making toys are?
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:
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