Match List-I with List-II
List-I | List-II |
---|---|
(A) \(^{8}P_{3} - ^{10}C_{3}\) | (I) 6 |
(B) \(^{8}P_{5}\) | (II) 21 |
(C) \(^{n}P_{4} = 360,\) then find \(n\). | (III) 216 |
(D) \(^{n}C_{2} = 210,\) find \(n\). | (IV) 6720 |
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: