

All marked carbon atoms are \( sp^2 \) hybridized.
There are 28 \( sp^2 \) hybridized carbon atoms in the major product \( P \).
Therefore, the total number of \( sp^2 \) hybridized carbon atoms is: \[ \text{Answer} = 28 \]


The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Organic Chemistry is a subset of chemistry dealing with compounds of carbon. Therefore, we can say that Organic chemistry is the chemistry of carbon compounds and is 200-225 years old. Carbon forms bond with itself to form long chains of hydrocarbons, e.g.CH4, methane and CH3-CH3 ethane. Carbon has the ability to form carbon-carbon bonds quite elaborately. Polymers like polyethylene is a linear chain where hundreds of CH2 are linked together.
Read Also: Organic Compounds
Organic chemistry is applicable in a variety of areas including-