
Both P and Q have asymmetric carbon(s).
Both Q and R have asymmetric carbon(s).
Both P and R have asymmetric carbon(s).
P has asymmetric carbon(s), S does not have any asymmetric carbon.
An asymmetric carbon (or chiral center) is a carbon atom that is bonded to four different atoms or groups. If a carbon atom is bonded to four different groups, it is considered a chiral center and leads to chirality, meaning the molecule is non-superimposable on its mirror image.
To determine if product P contains asymmetric carbons, analyze its structure. Look for any carbon atoms that are connected to four different groups. If such a carbon is found, product P will contain an asymmetric carbon.
Similarly, for product Q, inspect the structure to identify any carbon atom that is bonded to four distinct groups. If such a carbon exists, then Q will have an asymmetric carbon.
In product R, analyze the structure to locate any carbon attached to four different groups. If found, R will have an asymmetric carbon.
Study product S and check whether any carbon atom is connected to four different groups. If no such carbon exists, product S will not have an asymmetric carbon.
To verify this option, check both product P and product Q. If both have at least one asymmetric carbon, then this option is correct.
Similarly, evaluate both products Q and R. If both have asymmetric carbons, this option is correct.
Check both P and R. If both have at least one asymmetric carbon, then this option is valid.
Finally, verify if product P contains asymmetric carbon(s), while product S does not. If this is true, then this option is correct.
Based on the structural analysis of the products:
Both P and R have at least one asymmetric carbon, making Option 3 correct.
P has asymmetric carbon(s), while S does not have any asymmetric carbon, making Option 4 valid.
Option 3: Both P and R have asymmetric carbon(s).
Option 4: P has asymmetric carbon(s), and S does not have any asymmetric carbon.
This analysis confirms the correct statements based on the structural analysis of the chemical products P, Q, R, and S.
4o mini

The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:
There are many chemical properties of amines.
The primary and secondary amines, including several amine derivatives, have a direct impact on their properties due to the presence of hydrogen bonding. The compounds containing phosphorus have a lower boiling point and the compounds containing amines and alcohol have a higher boiling point. The structure of alkanols is immensely similar to that of amine except the presence of the hydroxyl group. In such a case, oxygen has a higher electronegativity than that of nitrogen, so alkanol compounds are more acidic in nature in comparison to the amines.
On account of the ability to form hydrogen bonds, the amines have tendencies of high solubility in water. The amine molecules such as Ethyl, diethyl, triethyl, and Methyl are gaseous in nature. Whereas, higher weight amines have a solid structure and alkyl amines have a liquid structure. There is an ammonia smell to gaseous amines and a fishy smell to liquid amines. The solubility of amines entirely depends upon the number of carbon atoms in the molecule.