Choose the correct set of reagents for the following conversion:
The given transformation involves the conversion of ethyl benzene (C\(_6\)H\(_5\)C\(_2\)H\(_5\)) to the desired product where a Br atom is added to the benzenoid ring.
- First, bromination of ethylbenzene occurs using \( \text{Br}_2 \) in the presence of iron (Fe), which acts as a catalyst.
The electrophilic aromatic substitution reaction results in the formation of a brominated product.
- After bromination, the next step involves chlorination using \( \text{Cl}_2 \) under heat (denoted by \( \Delta \)), leading to the introduction of the chlorine atom at the desired position.
- Finally, the product undergoes dehydrohalogenation in the presence of alcoholic potassium hydroxide (alc.
KOH), leading to the formation of the double bond as required.
Thus, the correct set of reagents to form the desired product is option (2).
The least acidic compound, among the following is
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
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: