
Chemical Reaction Sequence and Heteroatom Calculation
This image shows a sequence of chemical reactions starting with a compound containing nitro groups. The process involves various reagents and results in several intermediate products:
The compound with two nitro groups (\( NO_2 \)) undergoes a reduction using tin (Sn) and hydrochloric acid (HCl), converting the nitro groups into amino groups (\( NH_2 \)). The resulting intermediate is shown as the product \( P \).
The amino group is diazotized with sodium nitrite (\( NaNO_2 \)) and hydrochloric acid at 0-5°C, forming a diazonium chloride (\( N_2Cl \)) group. The resulting compound is labeled as \( P \).
In the third step, hydrolysis of the diazonium group leads to the hydroxyl group (\( OH \)) in the intermediate \( Q \).
Next, chlorination occurs, resulting in the substitution of the hydroxyl group (\( OH \)) with a chloro group (\( Cl \)) to form \( P \).
In the final step, the compound undergoes bromination using \( Br_2 / H_2O \) to introduce three bromine atoms (\( Br \)) to the aromatic ring, resulting in the product labeled as \( R \).
The final compound \( R \) has three hydroxyl groups (\( OH \)), and three bromine atoms (\( Br \)), giving us:
The total number of heteroatoms (atoms that are not carbon) in the structure of \( R \) is 9, as given in the problem statement.


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-