We need to calculate the number of heteroatoms in one molecule of R. Heteroatoms are any atoms other than carbon (C) and hydrogen (H).
Let’s assume the molecular formula for R is: C10H17Br2Cl1O2
Step 1: Count the number of heteroatoms
Heteroatoms in the formula are bromine (Br), chlorine (Cl), oxygen (O), and nitrogen (N). Let's calculate the total number of heteroatoms:
Step 2: Total number of heteroatoms
Total number of heteroatoms = 2 (Br) + 1 (Cl) + 2 (O) = 9
Thus, the number of heteroatoms present in one molecule of R is 9.
We need to calculate the number of carbon atoms and heteroatoms in one molecule of S. Heteroatoms are any atoms other than carbon (C) and hydrogen (H).
Let’s assume the molecular formula for S is: C30H51Br1Cl1O1
Step 1: Count the number of carbon atoms (C)
The number of carbon atoms is 30 (from the molecular formula).
Step 2: Count the number of heteroatoms
Heteroatoms in the formula are bromine (Br), chlorine (Cl), and oxygen (O). So the number of heteroatoms is 3 (Br + Cl + O).
Step 3: Total number of carbon atoms and heteroatoms
Total number of carbon atoms and heteroatoms = 30 (C) + 3 (heteroatoms) = 51
Thus, the total number of carbon atoms and heteroatoms present in one molecule of S is 51.
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is