0.5 g of an organic compound on combustion gave 1.46 g of $ CO_2 $ and 0.9 g of $ H_2O $. The percentage of carbon in the compound is ______ (Nearest integer) $\text{(Given : Molar mass (in g mol}^{-1}\text{ C : 12, H : 1, O : 16})$
Organic Compound → CO2
Applying POAC on ‘C’
Option (mole) of ‘C’ in compound = $n_{\text{CO}_2} \times 1$
So mass of ‘C’ in compound = $\dfrac{1.46}{44} \times 12$
So, % of ‘C’ in compound =
\[
\dfrac{1.46}{44} \times \dfrac{12}{0.5} \times 100
\]
= 79.63
Among the following, choose the ones with an equal number of atoms.
Choose the correct answer from the options given below:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to: