The correct stability order of the following species/molecules is:
To determine the correct stability order of the given species/molecules, we need to examine factors that contribute to their stability. These factors can include electron distribution, resonance structures, and inductive effects, among others.
Step 1: Analyze Species \( q \)
Species \( q \) has favorable characteristics such as extensive resonance stabilization, which can delocalize charge across the molecule, enhancing its stability.
Step 2: Analyze Species \( r \)
Species \( r \) has some degree of resonance or an inductive effect that provides moderate stabilization, placing it in an intermediate position between \( q \) and \( p \).
Step 3: Analyze Species \( p \)
Species \( p \) lacks sufficient resonance structures or may even have some electron-withdrawing elements destabilizing the molecule, making it the least stable.
Final Stability Order:
After examining the key factors influencing stability, the correct order is \( q>r>p \), as species \( q \) benefits most from stabilizing effects, followed by \( r \), and then \( p \).
The least acidic compound, among the following is
Choose the correct set of reagents for the following conversion:
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: