Match the LIST-I with LIST-II
LIST-I (Expressions) | LIST-II (Values) | ||
---|---|---|---|
A. | \( i^{49} \) | I. | 1 |
B. | \( i^{38} \) | II. | \(-i\) |
C. | \( i^{103} \) | III. | \(i\) |
D. | \( i^{92} \) | IV. | \(-1\) |
Choose the correct answer from the options given below:
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: