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
If 0.01 mol of $\mathrm{P_4O_{10}}$ is removed from 0.1 mol, then the remaining molecules of $\mathrm{P_4O_{10}}$ will be:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: